THERMO SAMPLE PROBLEMS 2

1. MECHANICAL ENGINEERING REVIEW
Problem Set no. 1
MULTIPLE CHOICE
1. A cubic meter of water at room temperature has weight of 9.8 KN at a location where g = 9.8 m/sec2. What is its specific weight at a
location where g = 9.77 m/sec2.
KN77.9
1000
)77.9(1000
W
kg1000m
1000
mg
W
m/sec9.8=g;KN9.8=W;m1=V 23



2. The acceleration of gravity is given as function of elevation above sea level by the relation g = 9.81- 3.32 x 10-6h m/sec2, with h measured
in meters. What is the weight of an airplane at 10 km elevation when its weight at sea level is 40 KN.
Given:
g = 9.81-3.32 x 10-6h
h = 10,000 m
at sea level W = 40 KN
KN40
1000
)81.9(m
W 
m = 4077.47 kg
at h = 10,000 m
g = 9.7768 m/sec2
KN86.39
1000
)7768.9(47.4077
W 
3. (a) What is the total or absolute pressure on the back of a scuba diver in a lake at a depth 8 m?
(b) What is the force on the divers back due to the water alone, taking the surface of the back to be a rectangle 60 cm x 50 cm.
A) h = 8 m
P = 101.325 + 9.81(8)
P = 179.805 KPa
B) F =PA
P = 9.81(8) = 78.48 KPa
F = 78.48(0.6)(0.5) = 23.544 KN
4. A mercury barometer at the ground floor of a commercial building reads 735 mm Hg. At the same time another barometer at the top
of the tower reads 590 mmHg. Assuming the air to be constant at 1.21 kg/m3, what is the approximate height of the tower using g = 9.7
m/sec2.
meters1647.8=h
)7.9(21.1
)PP(1000
h
KPa78.66=Hgmm590=P
KPa98=Hgmm735=P
21
2
1


5. A tank contains a mixture of 20 kg of nitrogen and 20 kg of carbon monoxide. The total tank volume is 20 m3. Determine the density,
specific volume and specific weight of the mixture if local g = 9,81 m/sec2.
m1 = 20 kg ; m2 = 20 kg ; V = 20 m3
m = 40 kg
 = 2 kg/m3
 = 0.5 m3/kg
 = 0.01962 KN/m3
W = 392.4 Newton = 0.3924 KN
6. A block of aluminum 10 cm on a side is cooled from 100C to 20C. If the energy removed from the aluminum block were added to a
copper block of similar dimensions at 20C , what would be the final temperature of the copper block be?
(al= 2700 kg/m3; copper = 8900 kg/m3)
V = (0.10)3 = 0.001 m3
ta1 = 100C ; ta2 = 20C
mal = 2700(0.001) = 2.7 kg
mcu = 0.001(8900) = 8.9 kg
2.7(0.896)(100 – 20) = 8.9(0.383)(t – 20)
t = 76.8C

2. 8. How many kilograms of aluminum will experience the same temperature rise as 3 kg of copper when the same amount of heat is added
to each? ?(Cal = 0.896 KJ/kg-K; Ccopper = 0.383 KJ/kg-K)
mal(0.896)(t) = 3(0.383) (t)
mal = 1.282 kg
9. A certain fluid is flowing in a 0.5 m x 0.3 m channel at the rate of 3 m3/sec and has a specific volume of 0.0012 m3/kg. Determine the mass
flow rate of water flowing in kg/sec.
m = 39/0.0012 = 2,500 kg
10. Steam expands in a nozzle fro an initial conditions of 2.8 MPa and 240C (h = 2834.48 KJ/kg; = 0.0746 m3/kg) to a pressure of 140
KPa (h = 2320 KJ/kg;  = 1.045 m3kg). For a mass flow rate of 2 kg/sec and neglecting the velocity at inlet determine the velocity and
the diameter at exit.
W = Q - h - KE - PE
W = 0 ; Q = 0; PE = 0
KE = -h
cm51051.0D
v
m4
D
4
vDAv
m
m/sec9.1013v
)hh)(1000(2v
0v
)hh)(1000(2vv
2
2
212
1
21
2
1
2
2







π
υ
υ
π
υ
11. Steam flows steadily through a turbine with a mass flow rate of 2.5 kg/sec. The inlet steam conditions are, P = 7000 KPa; t = 500C; h =
3410.3 KJ/kg and at exit P = 20 KPa; t = 60.6C; h = 2239.45 KJ/kg.The inlet is 3 m higher than its outlet. Assuming no heat losses
determine the actual work developedby the turbine if mechanical losses amounts to 10%.
m = 2.5 kg/sec
h1 = 3410.3 KJ/kg ; h2 = 2239.45 KJ/kg
Z = - 3 m
Q = 0
W = - h - PE
h = -1170.85 KJ/kg
PE = - 0.0294 KJ/kg
W = 2927.2 KW
Wa = 2634.5 KW
12. A piston cylinder arrangement contains 0.02 m3/sec of air at 50 C and 400 Kpa. Heat is added in the amount of 50 KJ and work is done
by a paddle wheel until the temperature reaches 700 C. If the pressure is held constant, how much paddle wheel work must be added
to the air. (R = 0.287 KJ/kg-K ; k = 1.4)
Given: V1 = 0.02 m3/sec ; T1 = 323K; T2 = 973K; P1 = 400 KPa; Q = 50 KJ;
Q = U + W - Wp
KW6.14Wp 




KW04.16)T-mR(TW
system)(closedCPAt
kg/sec086.0
RT
VP
m
KW1.40)TT(mCvU
12
1
11
12Δ
13. Calculate the change of entropy per kg of air when heated from 300K to 600K while the pressure drops from 400 Kpa to 300 KPa.
1
2
1
2
υ
υ
Rln
T
T
CvlnΔS 
1
2
1
2
P
P
Rln
T
T
CplnΔS 

3. Kkg
KJ
779.0SΔ
400
300
ln287.0
300
600
ln0045.1SΔ




14.An air compressor receives 20 m3/min of air at 101.325 KPa and 20C and compresses it to 10 000 KPa in an isentropic process.
Calculate the power of the compressor.
KW3211
P
P
60)k1(
VkP
W
k
1k
1
211




















15. A gas turbine expands 50 kg/sec of helium (M = 4; k = 1.666) polytropically, PV1.8 = C, from 1000K and 500 KPa to 350K. Determine;
a. The final pressure in KPa
b. The power produced in KW
c. The heat loss in KW
d. The entropy change in KW/K
Given:
m = 50 kg/sec; T1 = 1000K; T2 = 350K
M = 4 ; k =1.666
R = 2.0785 KJ/kg-K
Cv = 3.121 KJ/kg-K
Cp = 5.1995 KW
1n
n
1
2
12
n
1n
1
2
1
2
T
T
PP
P
P
T
T
















P2 = 47.11 KPa
KW990,151W
1
T
T
n1
nmRT
W
1
21

















)TT(
n1
nk
mCvQ 12 








Q = -16,990 KW
1
2
T
T
ln
n1
nk
mCvSΔ 








S = -22.44 KW/K

4. 16. A fuel mixture of 50% (by volume) of C7H16 and 50% (by volume) of C8H18 is burned with 20% excess air. Determine
a. the air – fuel ratio in kg/kg
b. the volumetric analysis of the products
c. the molecular weight of the products
d. the gas constant of the products
e. the combustion equation
Combustion with 100% theoretical air
175,1a
850)750(2a2
850c
c2)50(18)50(16
750b
b)8(50)50(7
N)76.3(aOcHbCON)76.3(aaOHC50HC50 22222188167







Combustion with 20% excess air
235d
d
2
850
750a20.1
N)76.3(a)20.1(dOOcHbCON)76.3(a)20.1(aO)20.1(HC50HC50 222222188167



Combustion Equation
222222188167 N6.301,5O235OH850CO750N6.301,5O410,1HC50HC50 
a = 1,175
b = 750
c = 850
d = 235
Gas n M m yi
C7H16 50 100 5,000
C8H18 50 114 5,700
O2 1,410 32 45,120
N2 5,301.6 28 148,444.8
CO2 750 44 33,000 10.5%
H2O 850 18 15,300 11.9%
O2 235 32 7,520 3.3%
N2 5,301.6 28 148,444.8 74.3%
Np = 7,131.6 Moles of Flue gas
A/F = 18.09 kg/kg
Mp = 28.622 kg/kgm
Rp = 0.2905 KJ/kg-K

5. 17. Helium (M = 4 kg/kgmol ; k = 1.666) expands polytropically through a turbine according to the process PV1.5 = C. The inlet temperature is
1000 K, the inlet pressure is 1000 KPa, and the exit pressure is 150 KPa. The turbine produces 100,000 KW of work. Determine
a. The exit temperature
b. The heat transferred in KW
c. The mass flow rate in kg/sec
KW16,616.6Q
sec
kg
2.34m
K-kg
KJ
079.2
4
3143.8
R
1
P
P
n1
nmRT
dPVhΔQ
PEΔKEΔhΔQW
n1
nk
CC
)TT(mCQ
P
P
T
T
n
1n
1
21
vn
12n
n
1n
1
2
1
2










































18. A mass of 0.05 kg of air is heated at constant pressure of 200 KPa until the volume occupied is 0.0658 m3. Calculate the heat supplied,
the work and the change in entropy for the process if the initial temperature is 130ºC. (Q = 25.83 KJ; W = 7.38 KJ)
K403T
K917.1T
m0.0289V
mRTPV
KW7.4)V-P(VW
KW25.82)TT(mCQ
1
2
3
1
12
12p






19. A 1 kg of nitrogen is compressed reversibly and isothermally from 101 KPa, 20ºC to 420 KPa. Calculate the nonflow work and the heat
flow during the process assuming nitrogen to be a perfect gas.
kg
KJ
-124
420
101
ln)27320)(287.0(1
P
P
nlmRTWQ
gas)ideal,isothermal(For0UΔ
WUΔQ
2
1
1 


20. Air at 102 KPa, 22ºC, initially occupying a cylinder volume of 0.015 m3 is compressed isentropically by a piston to a pressure of 680 KPa.
Calculate the final temperature, the final volume, the work done on the mass of air in the cylinder. (234.3 ºC; .00387 m3; 2.76 KJ)
21. A cubic meter of water at room temperature has weight of 9.8 KN at a location where g = 9.8 m/sec2. What is its specific weight at a
location where g = 9.77 m/sec2. (9.77 KN/m3)
22. The acceleration of gravity is given as function of elevation above sea level by the relation g = 9.81- 3.32 x 10-6h m/sec2, with h measured
in meters. What is the weight of an airplane at 10 km elevation when its weight at sea level is 40 KN. (39.9 KN)
23. A 1500 kg vehicle traveling at 60 km/hr collides head on with a 1000 kg vehicle traveling at 90 km/hr. If they come to rest immediately
after impact, determine the increase in internal energy, taking both vehicles as the system. (521 KJ)
24. Energy is added to a piston cylinder arrangement, and the piston is withdrawn in such a way that the quantity PV = C. The initial pressure
and volume are 200KPa and 2 m3, respectively. If the final pressure is 100 KPa, calculate the work done by the gas on the piston.
( 277 KJ)
25. The drive shaft in an automobile delivers 100 N-m of torque as it rotates at 3000 RPM. Calculate the horsepower delivered. (42.1 HP)
26. Air is compressed in a cylinder such that the volume changes from 0.2 to 0.02 m3. The pressure at the beginning of the process is 200
KPa. Calculate the work if the temperature is constant at 50C. (-92.1 KJ)
27. Estimate the work necessary to compress the air in an air compressor cylinder from a pressure of 100 KPa to 2000 KPa. The initial
volume is 1000 cm3. An isothermal process is to be assumed. (-0.300 KJ)
28. A 5 kg block of copper at 300C is submerged in 20 liters of water at 0C contained in an insulated tank. Estimate the final equilibrium
temperature. Cp of copper = 0.39 KJ/kg-C and Cp of water = 4.187 KJ/kg-C. (6.84C)

6. 29. 1 kg of air is compressed from 110 KPa, 27 ºC in a polytropic process where n = 1.3 until the final pressure is 660 KPa. Calculate:
a) ∫PdV
b) - ∫VdP
c) S
30. There are 1.36 kg of air at 138 KPa stirred with internal paddles in an insulated rigid container, whose volume is 0.142 m3 until the
pressure becomes 689.5 KPa. Determine the work input and PV. ( 196.2 KJ; 78.3 KJ)
31. During an isentropic process of 1.36 kg/sec of air, the temperature increases from 4.44ºC to 115.6 ºC. for a non-flow process and for a
steady flow process (KE = 0 and PE = 0) Find:
a) U in KW
b) H in KW
c) W in KW
d) S in KW/ºK
e) Q in KW
32. A certain perfect gas is compressed reversibly from 100 KPa, 17 ºC to a pressure of 500 KPa in a perfectly thermally insulated cylinder,
the final temperature being 77 ºC. The work done on the gas during the compression is 45 KJ/kg. Calculate, k , Cv, R and M of the gas.
( 1.132; 0.75 KJ/kg-ºK; 0.099 KJ/kg-ºK; 84)
33. 1 kg of air at 102 KPa, 20 ºC is compressed reversibly according to a law PV1.3 = C to a pressure of 550 KPa. Calculate the work done
on the air and the heat supplied during the compression. (133.46 KJ/kg; -33.3 KJ/kg)
34. Oxygen (M = 32) is compressed polytropically in a cylinder from 105 KPa, 15ºC to 420 KPa in such a way that one third of the work input
is rejected as heat to the cylinder walls. Calculate the final temperature of the oxygen. Assume oxygen to be perfect gas and take Cv =
0.649 KJ/kg-K. (113 ºC)
35. Air at 690 KPa, 260ºC is throttled to 550 KPa before expanding through the nozzle to a pressure of 110 KPa. Assuming that the air flows
reversibly in steady flow through the nozzle and that no heat is rejected, calculate the velocity of the air at exit from the nozzle when
the inlet velocity is 100 m/sec. ( 636 m/sec)
28. Air at 40ºC enters a mixing chamber at a rate of 225 kg/sec where it mixes with air at 15ºC entering at a rate of 540 kg/sec. Calculate
The temperature of the air leaving the chamber, assuming steady flow conditions. Assume that the heat loss is negligible. (22.4ºC)
29. A heat engine has a thermal efficiency of 45%. How much power does the engine produce when heat is transferred into it at a rate of 109
kJ/Hr?
a. 50 MW
b. 75 MW
c. 100 MW
d. 125 MW
28. A refrigerator has a coefficient of performance of 1.6. How much work must be supplied to this refrigerator for it to reject 1000 kJ of
heat?
a. 385 kJ
b. 627 kJ
c. 836 kJ
d. 1000 kJ
29. The thermodynamic efficiency of a heat engine that rejects heat at a rate of 20 MW when heat is supplied to it at a rate of 60 MW is:
a. 33.3%
b. 50%
c. 66.7%
d. 75%
30. A Carnot engine operates using a 527 °C energy reservoir and a 27 °C energy reservoir. The thermodynamic efficiency of this engine
is:
a. 50%
b. 62.5%
c. 73.6%
d. 103%

7. 31. A Carnot heat pump uses thermal reservoirs at -27 °C and 57 °C. How much power does this pump consume to produce a 100 kW
heating effect?
a. 9.1 kW
b. 10.1 kW
c. 15.3 kW
d. 20.7 kW
32. Saturated water vapor at 150 kPa is condensed to saturated liquid in a steady-flow, isobaric heat exchanger. The released heat is
transferred to the surrounding air whose temperature is 20 °C. The increase of the entropy associated with this process is:
a. -4.731 kJ/kg-K
b. -2.366 kJ/kg-K
c. 2.366 kJ/kg-K
d. 4.731 kJ/kg-K
33. Steam at 2 MPa, 300 °C is expanded in a steady-flow, adiabatic turbine to 30 kPa. What is the lowest possible temperature at the outlet
of this turbine?
a. 69.1 °C
b. 101.1 °C
c. 150.7 °C
d. 203.2 °C
Steam at 2 MPa, 300 °C is expanded through a steady-flow, adiabatic turbine to 30 kPa. How much work does this turbine produce?
478.7 kJ/kg
523.2 kJ/kg
639.2 kJ/kg
741.6 kJ/kg
Air at 5 MPa, 967 °C is expanded through a steady-flow device to 100 kPa, 27 °C. What is the change in the specific entropy of the air?
-1.372 kJ/kg-K
-0.269 kJ/kg-K
1.742 kJ/kg-K
2.638 kJ/kg-K
A 0.5-kg steel (C = 0.5 kJ/kg-k) rivet cools from 800 K to 300 K upon being installed in a riveted building structure. The entropy change of this rivet
is:
-0.631 kJ/K
-0.245 kJ/K
0.245kJ/K
0.631 kJ/K
Oxygen at 100 kPa, 27 °C is compressed to 1 MPa in an adiabatic compressor whose isentropic efficiency is 0.80. The oxygen temperature at
the compressor outlet is:
376 K
421 K
566 K
649 K
Water undergoes the reversible process illustrated here as it passes through a steady-flow device that has one outlet and one outlet. How much
work does this device produce?
0 kJ/kg
P (v2 - v1) kJ/kg
R (T2 - T1) kJ/kg
cv (T2 - T1) kJ/kg
Air is expanded in a closed system from 1 MPa, 327 °C to 100 kPa in an isentropic process. The system surroundings are at 100 kPa, 27 °C.
How much useful work did this system produce during this process?
A) 91 kJ/kg
B) 103 kJ/kg
C) 135 kJ/kg
D) 210 kJ/kg

8. A 1 m3 vessel contains air at 1 MPa, 327 °C. Assuming standard conditions for the surroundings, what is the maximum amount of work that can
be done by the air in this vessel?
A) 790 kJ
B) 826 kJ
C) 1012 kJ
D) 1290 kJ
Steam enters a turbine at 3 MPa, 350 °C with a velocity of 15 m/s. What is the specific exergy of this steam assuming the surroundings are at
standard conditions?
A) 678 kJ/kg
B) 827 kJ/kg
C) 968 kJ/kg
D) 1116 kJ/kg
Steam at 3 MPa, 350 °C is expanded through an adiabatic, steady-flow turbine to a saturated vapor at 100 kPa. The second law efficiency of this
turbine is:
A) 48.2%
B) 63.7%
C) 70.7%
D) 82.1%
A heat exchanger maintains the air temperature in a room at 25 °C by condensing saturated water vapor at 125 kPa to saturated liquid water. The
specific exergy destruction associated with this heat exchanger is:
A) 932 kJ/kg
B) 958 kJ/kg
C) 1241 kJ/kg
D) 1378 kJ/kg
Air is compressed from 100 kPa, 27 °C to 900 kPa, 327 °C in an adiabatic piston-cylinder device. What is the irreversibility of this process?
A) 19.66 kJ/kg
B) 22.31 kJ/kg
C) 28.73 kJ/kg
D) 32.17 kJ/kg
An adiabatic, steady-flow heat exchanger condenses 10,000 kg/hr of saturated steam vapor at 200 kPa to a saturated liquid also at 200 kPa. The
condensing steam heats 220,000 kg/hr of air at 100 kPa, 25 °C to 100 kPa, 125 °C. What is the rate at which exergy is destroy ed by this heat
exchanger?
A) 0 MJ/hr
B) 270 MJ/hr
C) 1327 MJ/hr
D) 2295 MJ/hr
A Carnot vapor power cycle operates its boiler at 3.0 MPa and its condenser at 50 kPa. What is the thermal efficiency of this cycle?
A) 20%
B) 30%
C) 40%
D) 50%
A simple Rankine cycle operates the boiler at 3 MPa with an outlet temperature of 350 °C and the condenser at 50 kPa. Assuming ideal operation
and processes, what is the thermal efficiency of this cycle?
A) 7.7%
B) 17.7%
C) 27.7%
D) 37.7%
A simple Rankine cycle operates its boiler at 3 MPa with an outlet temperature of 350 °C and its condenser at 50 kPa. The turbine has an isentropic
efficiency of 0.9 while all other operating conditions and process are ideal. What is the thermal efficiency of this cycle?
A) 25.0%
B) 30.9%
C) 35.9%

9. D) 40.9%
A simple, ideal Rankine cycle operates the boiler at 3 MPa and the condenser at 50 kPa. The temperature at the boiler outlet is 400 °C. What is
the rate at which heat must be supplied to the water in the boiler for a power production of 100 MW?
A) 157 MW
B) 218 MW
C) 273 MW
D) 352 MW
An ideal Rankine cycle with reheat operates the boiler at 3 MPa, the reheater at 1 MPa, and the condenser at 50 kPa. The temperature at the
boiler and reheater outlets is 350 °C. What is the thermal efficiency of this cycle?
A) 24.5%
B) 26.5%
C) 28.5%
D) 30.5%
An ideal Rankine cycle with reheat operates the boiler at 3 MPa, the reheater at 1 MPa, and the condenser at 50 kPa. The temperature at the
boiler and reheater outlets is 350 °C. The boiler and reheater are fired with a fuel that releases 9,000 kJ/kg of heat as it is burned. What is the
mass flow rate of the fuel for such a cycle when sized to produce 50 MW of net work?
A) 40 Mg/hr
B) 50 Mg/hr
C) 60 Mg/hr
D) 70 Mg/hr
An ideal Rankine cycle with an open-feedwater-heater regenerator operates the boiler at 3 MPa, the regenerator at 125 kPa, and the condenser
at 50 kPa. At the boiler outlet, the temperature is 350 °C. What percentage of the mass flow rate passing through the boiler is bled from the turbine
for the regenerator?
A) 4.85%
B) 7.31%
C) 10.6%
D) 13.2%
An ideal Rankine cycle with an open-feedwater-heater regenerator operates the boiler at 3 MPa, the regenerator at 125 kPa, and the condenser
at 50 kPa. At the boiler outlet, the temperature is 350 °C. What is the thermal efficiency of this cycle?
A) 24.6%
B) 28.6%
C) 32.6%
D) 36.6%
A simple Rankine cycle operates the boiler at 3 MPa and the condenser at 50 kPa. The temperature at the boiler outlet is 350 °C. The energy
source is at 400 °C and the energy sink is at 27 °C. What is the irreversibility of this cycle per unit of mass passing through the boiler?
A) 561.2 kJ/kg
B) 613.4 kJ/kg
C) 694.2 kJ/kg
D) 767.8 kJ/kg
A simple Rankine cycle produces 40 MW of power, 50 MW of process heat and rejects 60 MW of heat to the surroundings. What is the utilization
factor of this cogeneration cycle neglecting the pump work?
A) 50%
B) 60%
C) 70%
D) 80%
A basic R-134a, ideal vapor-compression refrigerator operates its evaporator at -16 °C and its evaporator at 1.4 MPa. How much power will the
compressor require to service a 10 kW cooling load?
A) 4.03 kW
B) 5.97 kW
C) 7.32 kW

10. D) 10.0 kW
A basic R-134a, ideal vapor-compression refrigerator operates its evaporator at 157 kPa and its evaporator at 1.4 MPa. What is the rate at which
the condenser rejects heat when this refrigerator services a 100 kW load?
A) 80 kW
B) 103 kW
C) 120 kW
D) 141 kW
An ideal R-134a vapor-compression heat pump operates its evaporator at 1.4 MPa and its condenser at -16 °C. The coefficient of performance
of this heat pump is:
A) 2.48
B) 2.79
C) 3.43
D) 3.79
A R-134a vapor-compression refrigerator operates its evaporator at 1.4 MPa and its condenser at 157 kPa. All the cycle states and processes are
ideal except for the compressor, which has an isentropic efficiency of 79%. How much power must be supplied to the compressor when this
refrigerator serves a100 kW cooling load?
A) 27.3 kW
B) 34.2 kW
C) 52.0 kW
D) 100 kW
A simple R-134a vapor-compression refrigerator system operates its evaporator at 157 kPa and the exit of the compressor at 1.4 MPa. The
working fluid enters the throttle valve as a saturated liquid at 1.2 MPa as a result of pressure losses in the condenser and connection lines. What
is the coefficient of performance of this device?
A) 2.64
B) 2.93
C) 3.26
D) 3.69
An ideal R-134a, dual compressor vapor-compression refrigerator system uses a flash chamber to separate the vapor in the evaporator feed line.
This system operates the evaporator at 133 kPa, the flash chamber at 400 kPa, and the condenser at 1.4 MPa. What fraction of the mass flow
rate passing through the evaporator passes through the condenser?
A) 0.80
B) 1.00
C) 1.20
D) 1.50
An ideal R-134a, dual compressor vapor-compression refrigerator system uses a flash chamber to separate the vapor in the evaporator feed line.
This system operates the evaporator at 133 kPa, the flash chamber at 400 kPa, and the condenser at 1.4 MPa. What is the coefficient of
performance of this device?
A) 1.87
B) 2.63
C) 2.95
D) 3.17
A simple, ideal reversible Brayton cycle uses air as the working fluid and has a pressure ratio of 6. What is the refrigerator COP of this cycle when
the temperature at the compressor entrance is -13 °C and that at the turbine entrance is 37 °C?
A) 0.33
B) 0.72
C) 1.48
D) 1.97
The composition of a mixture of nitrogen and carbon dioxide gases is 30% -N2 and 70%-CO2 by mole fraction. What is the mass fraction of the
nitrogen constituent?
A) 15.2%
B) 21.4%

11. C) 30.2%
D) 63.7%
A mixture of helium and nitrogen is 50%-He and 50%-N2 by mass analysis. What is the mole fraction of the helium in this mixture?
A) 39.7%
B) 43.2%
C) 67.2%
D) 87.5%
The composition of a gas mixture is 40%-O2, 40%-N2, and 20%-He by mass analysis. What is the apparent molecular weight of this mixture?
A) 6.71 kg/kg-mol
B) 13.02 kg/kg-mol
C) 15.70 kg/kg-mol
D) 18.60 kg/kg-mol
The composition of a mixture of gases is 50%-CO2, 40%-O2, and 10%-He by volume analysis. What is the apparent molecular weight of this
mixture?
A) 19.3 kg/kg-mol
B) 24.6 kg/kg-mol
C) 28.7 kg/kg-mol
D) 35.2 kg/kg-mol
A 1 m3 container contains a mixture of gases composed of 0.02 kg-mol of O2 and 0.04 kg-mol of He at a pressure of 200 kPa. What is the
temperature of this ideal gas mixture?
A) 300 K
B) 350 K
C) 400 K
D) 450 K
A 200 liter container holds 0.5 kg of air and 0.2 kg of helium at a temperature of 350 K. What is the pressure of this ideal gas mixture?
A) 1.4 MPa
B) 1.6 MPa
C) 1.8 MPa
D) 2.0 MPa
A mixture composed of 70%-CO2 and 30%-He by volume analysis is contained at 1 MPa. What is the partial pressure of the He in this mixture?
A) 300 kPa
B) 450 kPa
C) 600 kPa
D) 700 kPa
A mixture of 30%-Ar and 70%-CO2 by volume analysis. This mixture is contained in a rigid vessel at 200 kPa, 27 °C. The vessel is now heated
until the mixture temperature is 127 °C. Assuming that the specific heats do not change, how much heat was required?
A) 1.10 MJ/kg-mol
B) 2.40 MJ/kg-mol
C) 1.10 MJ/kg
D) 2.40 MJ/kg
A mixture consists of 30%-Ar and 70%-CO2 by volume analysis. This mixture is contained in a rigid vessel at 200 kPa, 27 oC. The vessel is now
heated until the mixture temperature is 127 oC. Assuming constant specific heats, what is the change in the entropy of the mixture?
A) 4.780 kJ/kg-mol-K
B) 6.900 kJ/kg-mol-K
C) 4.780 kJ/kg-mol-K
D) 6.900 kJ/kg-mol-K
A mixture of 20%-CO2 and 80%-N2 by volume is expanded from 1 MPa, 227 °C to 200 kPa as it passes through an adiabatic, steady-flow turbine.
Assuming this process is reversible and the specific heats are constant, how much work is produced by this expansion?
A) 137.9 kJ/kg

12. B) 164.5 kJ/kg
C) 174.3 kJ/kg
D) 194.2 kJ/kg
What is the specific humidity of air at 150 kPa whose dry bulb temperature is 20 °C and relative humidity is 70%?
A) 0.000981 kg-wv/kg-da
B) 0.00382 kg-wv/kg-da
C) 0.00514 kg-wv/kg-da
D) 0.00686 kg-wv/kg-da
Using saturated liquid water and 0 °C as the reference state, what is the specific enthalpy of humid air at 120 kPa, 20 °C, and 50% relative
humidity?
A) 32.71 kJ/kg-da
B) 35.63 kJ/kg-da
C) 38.93 kJ/kg-da
D) 41.72 kJ/kg-da
What is the dew-point temperature of humid air at 200 kPa, 30 °C, and 55% relative humidity?
A) 10 °C
B) 15 °C
C) 20 °C
D) 25 °C
Humid air at 150 kPa, 30 °C, and 80% relative humidity undergoes an isobaric cooling process until its temperature is 25 °C. Will any liquid
condensate form during this process?
A) Yes
B) No
C) Not applicable
D) Not applicable
Humid air is cooled, dehumidified and reheated during an isobaric process. Which one of the psychometric charts below correctly depicts these
processes?
A) a
B) b
C) c
D) d
One-hundred cubic meters per minute of humid air at 101 kPa, 35 °C, 40% relative humidity is cooled to 25 °C in a constant pressure process.
The cooling rate for this process is:
A) 9.3 kW
B) 17.8 kW
C) 20.2 kW
D) 22.3 kW
Saturated humid air at 101 kPa, 20 °C is heated to 35 °C during an isobaric process. What is the final relative humidity of this air?
A) 42%
B) 53%
C) 68%
D) 75%
Humid air at 101 kPa, 35 °C, 80% relative humidity is conditioned to 101 kPa, 25 °C, 50% relative humidity. How much condensate is formed
during this process?
A) 0.0087 kg/kg-da
B) 0.0168 kg/kg-da
C) 0.0193 kg/kg-da
D) 0.0231 kg/kg-da
Humid air at 101 kPa, 35 °C, 80% relative humidity is conditioned to 101 kPa, 25 °C, 50% relative humidity. How much heat must be removed to
accomplish this when the condensate leaves the system at 25 °C?
A) 41.7 kJ/kg-da
B) 46.7 kJ/kg-da

13. C) 52.3 kJ/kg-da
D) 57.5 kJ/kg-da
A standard atmospheric pressure cooling tower uses humid air at 30 °C, 60% relative humidity to cool liquid water from 55 °C to 40 °C. Saturated
humid air leaves this tower at 35 °C. How much make-up water must be supplied to this tower?
A) 0.0206 kg/kg-da
B) 0.0313 kg/kg-da
C) 0.0347 kg/kg-da
D) 0.0404 kg/kg-da
Five kilogram-mol of octane are burned with a stiochiometric amount of air. How much water is formed in the products if the combustion is
complete?
A) 15 kg-mol
B) 25 kg-mol
C) 35 kg-mol
D) 45 kg-mol
Methyl alcohol is burned with 30% excess air. How much unburned oxygen will there be in the products if the combustion is complete?
A) 0.35 kg-mol-o2/kg-mol-fuel
B) 0.45 kg-mol-o2/kg-mol-fuel
C) 0.55 kg-mol-o2/kg-mol-fuel
D) 0.65 kg-mol-o2/kg-mol-fuel
Gaseous methane fuel is burned with 100% excess air. This combustion is incomplete with 10% of the carbon in the fuel forming CO. The products
of combustion are at 100 kPa. What is the partial pressure of the CO in the products?
A) 0.51 kPa
B) 1.36 kPa
C) 2.78 kPa
D) 10.5 kPa
Gaseous methane fuel is burned with 50% excess air. When the temperature of the products is 30 °C and the pressure is 100 kPa, what fraction
of the water in the products is liquid?
A) 31%
B) 48%
C) 62%
D) 74%
Dodecane is burned at constant pressure with 150% excess air. What is the air-fuel ratio for this process?
A) 37.5
B) 42.3
C) 48.7
D) 51.3
Liquid octane fuel is burned in an isobaric, steady-flow burner with 80% excess air. The air and fuel enter the burner at 25 °C and the combustion
products leave at 427 °C. How much heat is released by this burner when the combustion is complete?
A) 18,530 kJ/kg-fuel
B) 31,800 kJ/kg-fuel
C) 38,460 kJ/kg-fuel
D) 42,610 kJ/kg-fuel
One gallon of gasoline (octane) has a mass of 2.66 kg. What is the maximum amount of heat that can be produced when one gallon of gasoline
is burned with air?
A) 17,320 kJ/gal
B) 111,270 kJ/gal
C) 116,320 kJ/gal
D) 127,650 kJ/gal
In a metallurgical process, methane is burned at constant pressure, with a stiochiometric amount of air both of which are at 25 °C. What is the
maximum temperature of the products?
A) 1930 K
B) 2320 K

14. C) 2890 K
D) 3170 K
How irreversible is the combustion of methane at standard atmospheric pressure with 20% excess air when all reactants and products are at 25
°C and the water in the products is all liquid?
A) 630,000 kJ/kg-mol-CH4
B) 780,200 kJ/kg-mol-CH4
C) 884,700 kJ/kg-mol-CH4
D) 1,110,000 kJ/kg-mol-CH4
What is the reversible work for CH4 burned with stiochiometric air when all products and reactants are at the standard referance state?
A) 673,500 kJ/kg-mol-fuel
B) 718,300 kJ/kg-mol-fuel
C) 793,000 kJ/kg-mol-fuel
D) 817,900 kJ/kg-mol-fuel
At what temperature will 20% of carbon dioxide disassociate to carbon monoxide when the pressure is 0.1 atm?
A) 2240 K
B) 2420 K
C) 2690 K
D) 3120 K
Excess air is used in combustion reactions to control flame temperatures. Excess air will also _________________ when Dn is positive.
A) Produce more incomplete combustion
B) Produce more complete combustion
C) Produce undesirable combustion
D) Have no effect
A mixture of 1 kg-mol of CO and 1 kg-mol of O2 is heated to 3000 K at a pressure of 1 atm. What fraction of the original CO becomes CO2?
A) 27.8%
B) 37.6%
C) 69.2%
D) 90.1%
Increasing the temperature of an ideal gas increases ________________.
A) The number of reactants in the products
B) The number of inert gases in the product
C) The number of disassociation products
D) None of these
A mixture consists of 1 kg-mol of CO, 1 kg-mol of O2, and 2 kg-mol of N2. Treating the nitrogen as an inert gas, how much CO2 is formed when
the temperature and pressure of this mixture is 2600 K and 1 atm?
A) 0.371 kg-mol
B) 0.615 kg-mol
C) 0.832
D) 0.957 kg-mol
A mixture of 1 kg-mol of CO2, 1 kg-mol of O2, and 2 kg-mol of N2 is heated to 4000 K at a pressure of 1 atm. Assuming that the final mixture
consists of CO2, CO, O2, O, and N2, how much atomic oxygen is present in the final mixture?
A) 0.33
B) 0.50
C) 0.67
D) 0.90
What is the approximate heat of reaction at 3400 K for the disassociation of CO2 to CO?
A) 5961 kJ/kg-mol
B) 7482 kJ/kg-mol
C) 8785 kJ/kg-mol
D) 9213 kJ/kg-mol

15. A system is composed of gasoline liquid and vapor, and air. According to Gibbs phase rule how many independent properties are required for
phase equilibrium?
A) 0
B) 1
C) 2
D) 3
When the water temperature of the Great Salt Lake is 20 °C, what is the mass fraction of the salt dissolved in the water?
A) 26.5%
B) 32.1%
C) 36.7%
D) 40.3%
The contents of a can of soft drink consists of CO2 dissolved in water and a vapor space filled with CO2 and H2O vapor. At 17 oC and 2 atm,
what is the mole fraction of the CO2 in the liquid mixture?
A) 0.00156
B) 0.00735
C) 0.0107
D) 0.0312
At one location in a nozzle, the air temperature is 400 K and the air velocity is 400 m/s. What is the stagnation enthalpy (based on temperature
dependent specific heats) of the air at this location?
A) 300 kJ/kg
B) 357 kJ/kg
C) 470 kJ/kg
D) 481 kJ/kg
At one location in a nozzle, the air temperature is 400 K and the air velocity is 450 m/s. What is the Mach number at this location?
A) 0.97
B) 1.12
C) 1.37
D) 2.02
Air at 20 kPa flows with a Mach number of 1.5. What is the stagnation pressure of this air?
A) 22.2 kPa
B) 41.7 kPa
C) 56.2 kPa
D) 73.4 kPa
Air in a large tank at 350 K and 200 kPa is supplied to an isentropic converging-diverging nozzle. What is the temperature at a point in this nozzle
where the Mach number is 1.2?
A) 198 K
B) 271 K
C) 360 K
D) 395 K
An isentropic, converging-diverging nozzle operates with stagnation conditions 400 kPa, 500 K. This nozzle has a throat area of 0.01 m2 and is
chocked. What is the mass flow rate through this nozzle?
A) 5.01 kg/s
B) 7.23 kg/s
C) 8.32 kg/s
D) 9.81 kg/s
The exit of the diverging section of an isentropic nozzle has twice the area of the nozzle throat. What is the Mach number at the exit when the exit
flow is supersonic?
A) 1.80
B) 2.00
C) 2.20
D) 2.40

16. The exit of the diverging section of an isentropic nozzle has twice the area of the nozzle throat. If the stagnation pressure at the throat is 200 kPa,
what is the pressure at the nozzle exit when the exit flow is supersonic?
A) 18.7 kPa
B) 32.2 kPa
C) 87.3 kPa
D) 137.2 kPa
An aircraft flies through 80 kPa, 270 K still air with a Mach number of 1.30. A normal shock wave will form directly in front of this aircraft. What is
the stagnation pressure acting on this aircraft?
A) 61 kPa
B) 73 kPa
C) 101 kPa
D) 193 kPa
A normal shock wave forms in the diverging portion of a nozzle at a point where Mx = 1.5. The area at the exit of this nozzle is 50% larger then
that where the shock wave forms. What is the Mach number at the nozzle exit?
A) 1.2
B) 1.12
C) 0.38
D) 0.24
Steam at 3.0 MPa, 500 °C, and negligible velocity is expanded to 0.8 MPa through an isentropic nozzle. What is the velocity of the steam at the
nozzle exit?
A) 268 m/s
B) 522 m/s
C) 738 m/s
D) 894 m/s
A gaseous mixture has the following volumetric analysis O2, 30%; CO2, 40% N2, 30%. Determine
a) the analysis on a mass basis
b) the partial pressure of each component if the total pressure is 100 KPa and the temperature is 32C
c) the molecular weight and gas constant of the mixture
Gas yi M k Cp Cv R xi Pi Mixture
O2 0.30 32 1.395 0.918 0.658 0.260 0.27 30 M 35.6
CO2 0.40 44 1.288 0.845 0.656 189 0.494 40 R .234
N2 0.30 28 1.399 1.041 0.744 0.297 0.236 30 P 100

17. Assume 28 m3 of a gaseous mixture whose gravimetric analysis is 20% CO2, 15% O2, 65% N2, are at 103.4
KPa and 150C. Find
a) the volumetric analysis
b) the respective partial pressures
c) R and M
d) the moles of mixture and of each constituent
e) the heat transferred with no change in pressure to reduce the
temperature to 75C
f) the volume the mixture occupies after the cooling
K-kg
KJ
2698.0R
82.30yiMiM
KPa931.73P
KPa993.14P
KPa476.14P
%5.71y
%5.14y
%14y
03245.0
28
65.0
32
15.0
44
20.0
Mi
xi
Mi
xi
Mi
xi
yi
2
2
2
2
2
2
N
O
CO
N
O
CO













kg365.25)823.0(82.30Mnm
moles58845.0)823.0(715.0n
moles11934.0)823.0(145.0n
moles1152.0)823.0(14.0n
moles823.0
)423(3143.8
)28(4.103
TR
PV
n
2
2
2
N
O
CO





kCO2 = 1.228; kO2 = 1.395; kN2 = 1.399
K-kg
KJ
7136.0Cv
RCvCp
K-kg
KJ
9834.0)0814.001655.002033.0(3143.8Cp
)399.0(28
)399.1(65.0
)395.0(32
)395.1(15.0
)288.0(44
)288.1(20.0
3143.8
)1k(M
kx
RCp
CxCp
i
ii
pi i















Q = mCp(t2 – t1) = 25.365(0.9834)(75 – 150) = -1870.8 KJ
Q = 1870.8 KJ (heat is rejected)
At constant pressure
3
2
2
1
1
m035.282V
T
V
T
V


69. Consider 2 kg of CO and 1 kg of CH4 at 32C that are in a 0.6 m3 rigid drum. Find:
a) the mixture pressure P in KPa
b) the volumetric analysis

18. c) the partial pressures in KPa
d) the heat to cause a temperature rise of 50C.
70. A gaseous mixture has the following volumetric analysis O2, 30%; CO2, 40% N2, 30%. Determine
a) the analysis on a mass basis
b) the partial pressure of each component if the total pressure is 100 KPa and the temperature is 32C
c) the molecular weight and gas constant of the mixture
71. A gaseous mixture has the following analysis on a mass basis, CO2, 30%; SO2, 30%; He, 20% and N2, 20%.
For a total pressure and temperature of 101 KPa and 300 K, Determine
a) the volumetric or molal analysis
b) the component partial pressure
c) the mixture gas constant
d) the mixture specific heats
P = 101 KPa ; T = 300 K
KPa2.10)101(104.P
KPa53.730.728(101)P
KPa87.60.068(101)P
KPa1.10)101(10.P
%4.10y
%8.72y
%8.6y
10%y
06865.0
28
20.0
4
20.0
64
30.0
44
30.0
Mi
xi
Mi
xi
Mi
xi
yi
2
2
2
2
2
N
He
SO
CO
N
He
SO
CO2












M = .10(44) + 0.068(64) + 0.728(4) + 0.104(28) = 14.576
R = 0.5704 KJ/kg-K
Cp = 0.30(0.844) + .30(0.6225) + 0.20(5.1954) + 0.20(1.0399) = 1.68701 KJ/kg-K
Cv = Cp – R = 1.1166 KJ/kg-K
72. A cubical tank 1 m on a side, contains a mixture of 1.8 kg of nitrogen and 2.8 kg of an unknown gas. The
mixture pressure and temperature are 290 KPa and 340 K. Determine
a) Molecular weight and gas constant of the unknown gas
b) the volumetric analysis
73. A mixture of ideal gases at 30C and 200 KPa is composed of 0.20 kg CO2, 0.75 kg N2, and 0.05 kg He.
Determine the mixture volume.
In determining the specific heat of a new metal alloy,0.15 kg of the substance is heated to 400C and then
placed in a 0.2 kg aluminum calorimeter cup containing 0.4 kg of water at 10C. If the final temperature of the mixture is 30.5C, what is the
specific heat of the alloy.( ignore the calorimeter stirrer and thermometer)
CpAl = 0.92 KJ/kg-C; Cpw = 4.186 KJkg-C
An air compressor handles 8.5 m3/min of air with  = 1.26 kg/m3 and P = 101.325 KPa and it discharges at P = 445 KPag with  = 4.86 kg/m3.
The U = 82 KJ/kg and the heat loss by cooling is 24 KJ/kg. Neglecting KE and PE, find W in KJ/min.
A 0.1 kg of aluminum (Cp=0.92 KJ/kg-C) at 90C is immersed in 1 kg of water from 20C . Assuming no heat is lost to the surroundings or
container , what is the temperature of the metal and water when they reached thermal equilibrium?
Water is flowing in a pipe with varying cross section area, and at all points the water completely fills the pipe. At point 1 the cross section area of
the pipe is 0.070 m2 and the velocity is 3.50 m/sec.

19. What is the fluid speed at points in the pipe where the cross section area is 0.105 m2 and 0.047 m2.
Calculate the volume of water discharged from the open end of the pipe in 1 hour.
A sealed tank containing sea water to a height of 11 m also contains air above the water at a gage pressure of 3 atmosphere.
Water flows out from the bottom through a small hole. Calculate the efflux speed of the water.
A copper pot with a mass of 0.500 kg contains 0.170 kg of water at a temperature of 20C. A 0.250 kg block of iron at 85C is dropped into the
pot. Find the final temperature, assuming no heat loss to the surroundings. Ccopper = 0.390 KJ/kg-C; Cwater = 4.19 KJ/kg-C and Ciron = 0.470
KJ/kg-C.
At one point in a pipeline the water speed is 3 m/sec and the gage pressure is 50 KPa. Find the gage pressure at a second point in the line, 11 m
lower than the first , if the pipe diameter at the second point is one half the first.
A closed system containing a gas expands slowly in a piston cylinder in accordance to PV2 = C. If the initial pressure is 500 KPa, initial volume is
50 L and the final pressure is 200 KPa, find the work done by the system.
A steam turbine receives superheated steam at 1.4 MPa and 400C (h = 3121 KJ/kg). The steam leaves the turbine at 0.101 MPa and 100C (h
= 2676 KJ/kg).The steam enters the turbine at 15 m/sec and exits at 60 m/sec. The elevation difference between entry and exit ports is negligible.
The heat loss through the turbine walls is 2 KW. Calculate the power output if the mass flow through the turbine is 0.5 kg/sec.
A small circular hole 6 mm in diameter is cut in the side of a large water tank 14 m below the water level in the tank. The top of the tank is open
to the atmosphere. Find the velocity of water exiting the hole and the volume discharged per unit time.
Oxygen (M = 32) is compressed polytropically in a cylinder from 105 KPa, 15ºC to 420 KPa. The decrease in internal energy of 1.36 kg of an ideal
gas is –342.9 KJ when the pressure decreases from 689.3 KPa to 137.86 KPa and the volume increases from 0.0425 m3 0.127 m3. Cv = 1.047
KJ/kg-K. Determine the value of k.
The working fluid of a gas turbine passes through the machine at a steady rate of 10 kg/sec. It enters with a velocity of 100 m/sec and specific
enthalpy of 2000 KJ/kg and leaves at 50 m/sec with a specific enthalpy of 1500 KJ/kg. If the heat lost to surroundings as the fluid passes through
the turbine is 40 KJ/kg, calculate the power developed.
0.07 m3 of gas at 4.14 MPa is expanded in an engine cylinder and the pressure at the end of expansion is 310 KPa. If the expansion is polytropic
with PV1.35 = C, find the final volume.
Helium gas ( R=2.077 KJ/kg-K; k= 1.667) enters a steady state – steady flow expander at 800 KPa, 300C and exits at 120 KPa. The mass flow
rate is 0.2 kg/sec and the expansion process is PV1.3 = C. Calculate W of the expander in KW.
A pressure gage at elevation 8 m on a side of a tank containing a liquid reads 57.4 KPa. Another gage at elevation 5 m reads 80 KPa. Determine
the density of the liquid.
Gas at a pressure of 95 KPa, volume 0.2 cu.m. and temperature 17C, is compressed until the pressure is 275 KPa and the volume is 0.085
cu.m.. Calculate the final temperature.
A liquid of density 800 kg/cu.m., specific heat of 2.5 KJ/kg-K and temperature of 27C is mixed with another liquid of density 820 kg/cu.m., specific
heat 1.9 KJ/kg-K and temperature of 55C in the ratio of one of the first liquid to three of the second by volume. Find the resulting temperature.
A rigid container contains 1 mole of nitrogen gas that slowly receives 3 KCal of heat. What is the change in internal energy of the gas in KJ.For
N2: M = 28; K = 1.399
A certain perfect gas of mass 0.01 kg occupies a volume of 0.003 m3 at a pressure of 700 KPa and a temperature of 131ºC. The gas is allowed
to expand until the pressure is 100 KPa and the final volume is 0.02 m3. Calculate:
a) the molecular weight of the gas
b) the final temperature
A cubical tank 1 m on a side, contains a mixture of 1.8 kg of nitrogen (M = 28; k = 1.399) and 2.8 kg of an unknown gas. The mixture pressure
and temperature are 290 KPa and 340 K. Determine
a) Molecular weight and gas constant of the unknown gas

20. b) the volumetric analysis
A volume of gas having initial entropy of 5317.2 KJ/K is heated at constant temperature of 540C until the entropy is 8165.7 KJ/K. How much heat
is added and how much work is done during the process.
A 283 L drum contains a gaseous mixture at 690 KPa and 38C whose volumetric composition is 30% O2 and 70% CH4. How many kg of mixture
must be bled and what mass of O2 added in order to produce at the original pressure and temperature a mixture whose new volumetric composition
is 70% O2 and 30% CH4.
For O2: M = 32 ; k = 1.395For CH4; M = 16 ; k = 1.321
100. A certain perfect gas of mass 0.01 kg occupies a volume of 0.003 m3 at a pressure of 700 KPa and a temperature
of 131ºC. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.02 m3. Calculate:
a) the molecular weight of the gas
b) the final temperature
101. When a certain perfect gas is heated at constant pressure from 15ºC to 95ºC, the heat required is 1136 KJ/kg.
When the same gas is heated at constant volume between the same temperatures the heat required is 808 KJ/kg.
Calculate Cp, Cv, k, and M of the gas.
102. A closed vessel of 0.7 m3 internal volume contains a gas at 58 Kpa and 18C and with R = 0.27 KJ/kg-K.If now 0
0.35 kg of another gas at 18C and R = 0.29 KJ/kg-K is also admitted into the vessel. Calculate the final pressure
of the mixture.
103. A closed system consisting of 2 kg of a gas undergoes a process during which the relationship between
pressure and specific volume is PV1.3 = C. The process begins with P1 = 1 bar, 1 = 0.5 m3/kg and ends with P2 =
0.25 bar. Determine the final volume, in m3, and plot the process on a graph of pressure versus specific volume.
104. Four kilograms of a certain gas is contained within a piston–cylinder assembly. The gas undergoes a process for
which the pressure - volume relationship is PV1.5 = C. The initial pressure is 3 bar, the initial volume is 0.1 m3, and
the final volume is 0.2 m3. The change in specific internal energy of the gas in the process is U = - 4.6 kJ/kg.
There are no significant changes in kinetic or potential energy. Determine the net heat transfer for the process, in
kJ. (Q = -0.8 KJ)
105. Calculate the change of entropy per kg of air (R = 0.287 KJ/kg-K; k = 1.4) when heated from 300K to 600K while
the pressure drops from 400 KPa to 300 KPa. (S = 0.78 KJ/kg-K)
106. A 5 kg quantity of oxygen (M = 32; k = 1.395) is heated from 250 K to 400 K at constant pressure. Determine
a. h
b. U
c. S
d. W =  P dV

21. 107. A 5 m3 tank contains chlorine (R = 0.1172 KJ/kg-K) at 300 KPa and 300K after 3 kg of chlorine has been used.
Determine the original mass and pressure if the original temperature was 315 K. (45.66 kg ; 337.15 KPa)
108. A gaseous mixture has the following volumetric analysis: O2 = 30%; CO2 = 40% ; N2 = 30%. Determine the
gravimetric analysis the partial pressure of each component if the total pressure is 100 KPa and the temperature
is 32C the molecular weight and gas constant of the mixture
For
O2: M = 32 ; k = 1.395
CO2: M = 44 ; k = 1.288
N2: M = 28 ; k = 1.399
109. How many kilograms of N2 must be mixed with 3.6 kg of CO2 in order to produce a gaseous mixture that is 50%
by volume of ach constituents.
110. For the resulting mixture, determine M and R, and the partial pressure of the N2 if that of the CO2 is 138 KPa.
111. The exhaust from a diesel engine using a high grade hydrocarbon fuel has an Orsat Analysis of, 10.2% CO2 ;
7.9% O2 and 81.9% N2.Determine
a. the value of n and m from CnHm
b. the ratio of H to C in the fuel by mass
c. the actual air fuel ratio
d. the theoretical air – fuel ratio
d the percent excess air
Given:
Orsat Analysis
CO2 = 10.2 %
O2 = 7.9 %
N2 = 81.9 %
Combustion Equation (Basis 100 moles of dry flue gas)
222222mn N9.81O9.7OyHCO2.10N)76.3(xxOHC 
By carbon, hydrogen, nitrogen and oxygen balance
n = 10.2 ; m = 14.73; x = 21.78 ; y = 7.36
1203.0
n12
m
Cofkg
Hofkg

fuelofkg
airofkg
80.21
73.14)2.10(12
)28)(76.3)(78.21()32(78.21
F
A
actual









22222mn N)76.3(aOcHbCON)76.3(aaOHC 
a = 13.9; b = 10.2 ; c = 7.37
fuelofkg
airofkg
9.13
73.14)2.10(12
)28)(76.3(9.13)32(9.13
F
A
ltheoretica









%5757.0e
1
F
A
F
A
e
ltheoretica
actual















112. A furnace burns natural gas that has the following volumetric analysis: CH4 = 90% ; C2H6 = 7% and C3H8 = 3%.
The gas fuel flow rate is 0.02 m3/sec and 25% excess air is required for complete combustion. The natural gas and
air enter at 25C and 101 KPa. The exhaust gas (products) has a temperature of 1000C and 101 KPa. Determine
the following
The combustion equation
The volumetric analysis of the products
The molecular weight M and gas constant R of the products
The density of the products in kg/m3
The orsat analysis of the products
The flue gas velocity exiting the smokestack if the stack diameter is 1 m

22. 22222283624
22222283624
2222283624
N32.10O55.0OH13.2CO13.1N32.10O74.2HC03.0HC07.0CH9.0
55.0d
N)76.3(a)25.1(dOOcHbCON)76.3(a)25.1(aO)25.1(HC03.0HC07.0CH9.0
0.25eairexcesswithcombustion
13.2c
13.1b
2.2a
N)76.3(aOcHbCON)76.3(aaOHC03.0HC07.0CH9.0








Volumetric analysis
CO2 = 8%
H2O = 15.08%
O2 =3.88%
N2 = 73.04%
M = 27.93 kg/kgm
R = 0.298 KJ/kg-K
Orsat analysis
CO2 = 9.42%
O2 = 4.57%
N2 = 86%
113. A gas fired thermal power plant uses two types of hydrocarbon fuel with the following molal (volumetric analysis)
CH4 = 68% ; C2H6 = 32%. Fuel and air is supplied to the boiler at 101 KPa and 25C with 30% excess air
requirement for complete combustion. Product temperature and pressure are 1000C and 101 KPa, respectively.
Determine the following:
the combustion equation
the theoretical and actual air fuel ratio
the Orsat analysis of the products
the molecular weight and gas constant of the products
the kg of CO2 formed per kg of fuel burned
the partial pressure of H2O in the products
Combustion with 100% theoretical air
0.68CH4 + 0.32C2H6 + 2.48O2 + 9.32N2 → 1.32 CO2 + 2.32 H2O + 9.32 N2
a = 2.48 ; b = 1.32 ; c = 2.32
Combustion with excess air e = 0.30
d = 0.74
0.68CH4 + 0.32C2H6 + 3.22O2 + 12.12N2 → 1.32 CO2 + 2.32 H2O + 0.74O2 + 12.12 N2
61.21
62.16












a
T
F
A
F
A
Orsat Analysis
CO2 = 9.3%
O2 = 5.24%
N2 = 85.45%
Molecular Weight and Gas Constant
M = 28.05
R = 0.296
Kg of CO2/kg of fuel =58.08/20.48 = 2.84 kg/kg
PH2O = 14.24 KPa

23. P T
1
2
T = C
3
12
P = C
114. Air is contained in a cylinder fitted with a frictionless piston. Initially the cylinder contains 500 L of air at 150 KPa and 20 C. The air is then
compressed in a polytropic process ( PVn = C) until the final pressure is 600 KPa, at which point the temperature is 120 C. Determine the work
W and the heat transfer Q. (R = 0.287 KJ/kg-K ; k = 1.4)
Given:
V1 = 0.50 m3 ; P1 = 150 KPa ; T1 = 293 K
P2 = 600 KPa ; T2 = 393 K ;
Process: PVn = C
KJ951
T
T
n1
VP
W
WUQ
27.1n
P
P
ln
T
T
ln
n
1n
P
P
T
T
1
211
1
2
1
2
n
1n
1
2
1
2


























115. A steam turbine of a coal fired thermal power plant receives steam at 7 MPa and 500C (h1 = 3410.3 KJ/kg ; S1 =
6.7975 KJ/kg-K) with a velocity of 30 m/sec and expands isentropically to the condenser at a pressure of 20 KPa
with a velocity of 90 m/sec. Calculate the ideal power developed by the turbine for a steam flow rate of 37.8 kg/sec
assuming PE in the turbine to be negligible.
At 20 KPa
Sf = 0.8320 KJ/kg-K ; Sg = 7.9085 KJ/kg-K ; Sfg = 7.0765 KJ/kg-K
hf = 251.4 KJ/kg ; hg = 2609.7 KJ/kg ; hfg = 2358.3 KJ/kg
SOLUTION:
6.7975 = O.8320 + x2(7.0765)
x2 = 0.839
h2 = 251.4 + (0.839)(2358.3) = 2230.014 KJ/kg
 
KW73.478,44W
)1000(2
)30()90(
)3.3410014.2230(8.37KEhmW
KE-h-W
0PEand0Q
WPEKEhQ
22






 




116. Air which is initially at 120 KPa and 320K occupies 0.11 m3. It is compressed isothermally until the volume is
halved and then compressed it at constant pressure until the volume decreases to ¼ of the initial volume. Sketch
the process on the PV and TS diagrams. Then determine the pressure, the volume and temperature in each state.
(For air: R = 0.287 KJ/kg-K ; k = 1.4)
Given:
P1 = 120 KPa ; T1 = 320K; V1 = 0.11 m3; T2 = 320K; V2 = ½V1; V3 = ¼V1
For air: R = 0.287 KJ/kg-K; k = 1.4
Processes:
1 to 2: T = C
2 to 3: P = C
KJ31Q
1-k
R
C
KJ64)T-(TmCU
kg892.0
RT
VP
m
v
12v
1
11





24. Solution:
At 1 to 2: T = C
P1V1 = P2V2
T1 = T2 = 320K
V2 = ½V1 = ½(0.11) = 0.055 m3
KPa240)2(120
V
V
PP
2
1
12 






At 2 to 3: P = C
P3 = P2 = 240 KPa
V3 = ¼V1 = ¼(0.11) = 0.0275 m3
K160
055.0
0275.0
320T
V
V
T
T
3
2
3
2
3









From
3
3
3
2
2
2
1
1
1
P
RT
P
RT
P
RT
P
RT




1 = 0.765 m3/kg
2 = 0.383 m3/kg
3 = 0.191 m3/kg
117. A cylinder fitted with a frictionless piston contains 5 kg of superheated water vapor at 1,000 KPa & 250C (h1 =
2942.6 KJ/kg ; U1 = 2709.9 KJ/kg ; S1 = 6.9247 KJ/kg-K). This system is now cooled at constant pressure until the
water reaches a quality x2 of 50%. Calculate the heat transferred and the work done during this process, and draw
the process on the PV & TS plane.
At 1000 KPa at saturation
hf = 762.81 KJ/kg; hg = 2778.1 KJ/kg; hfg = 2015.29 KJ/kg
Uf = 761.68 KJ/kg; Ug = 2583.6 KJ/kg ; Ufg = 1281.92 KJ/kg
Sf = 2.1387 KJ/kg-K; Sg = 6.5865 KJ/kg-K; Sfg = 4.4478 KJ/kg-K
KJ5.6756536.3-5860.8U-QW
KJ3.65362709.9)-5(1402.64)U-m(UU
KJ8.58602942.6)-5(1770.44)h-m(hQ
CPAt
KJ/kg1402.64)92.1281(50.068.761U
KJ/kg44.1770)26.2015)(50.0(81.762h
12
12
2
2






P T
12
1
2

25. KJ1808.1645.75Q
KJW
1.3)-400(2.6)V-P(VW
KJQ
600)-12003(1.0045)()T-(TmCQ
K
m
V
V
CPAt
KJ300)-6003(0.7175)(Q
K
P
P
VV
CV
23
p
23pp
3
2
3
v
1
2
21
85.2453
520
1.1808
1200T
600
T
3.1
6.2
6.2V2V
T
T
75.645
600T
T
T
At
3
3
13
2
3
2
1
2















118. A small circular hole 6 mm in diameter is bored in the side of a large water tank 14 m below the water level in the
tank. The top of the tank is open to the atmosphere and the velocity on the water surface is negligible. Find the
velocity of water exiting the hole and the volume discharged in L/sec. (water = 1000 kg/m3)
L/sec47.0/secm10x7.4
4
)57.16()006.0(
m
m/sec57.16)2(9.81)(14v
0Z;0v
v)ZZ(g2v
1000
)ZZ(g
2000
vv
PEKE
0Q
0W
0P
0U
WPEKEPUQ
34-
2
2
11
2
1212
12
2
1
2
2















119. A piston cylinder device, whose piston is resting on a set stops, initially contains 3 kg of air at 200 KPa and 27C.
The mass of the piston is such that a pressure of 400 KPa is required to move it. Heat is now transferred to the air
until its volume doubles. Determine the work done by the air and the total heat transferred to the air during this
process. Also, show the process on a P-V diagram. (For air: R = 0.287 KJ/kg-K ; k = 1.4)
 1
 2
14 m
Q
P
V
T
S
1
2 3
3
1
2
V =
C
P = C

26. 121. A closed system consisting of 2 kg of a gas undergoes a process during which the relationship between
pressure and specific volume is PV1.3 = constant. The process begins with P1 = 1 bar, 1 = 0.5 m3/kg and ends
with P2 = 0.25 bar. Determine the final volume, in m3, and plot the process on a graph of pressure versus
specific volume. (Note: 100 KPa = 1 Bar)
m = 2 kg
P1 = 1 Bar = 100 KPa ; P2 = 0.25 Bar = 25 KPa
1 = 0.5 m3/kg
Process: PV1.3 = C
3
22
3
3.1
1
2
3.1
1
2
1
1
2
3.1
22
3.1
11
m9.2)45.1(2mV
kg
m
45.1
25
100
5.0
P
P
PP


















122. Suppose that 42,200 KJ of heat energy are supplied in a small boiler to 25 kg of water at 90C. What part of the
water in kg will be vaporized, if the initial enthalpy of water is 376.78 KJ/kg and latent heat of vaporization (hfg)of
water is 2257 KJ/kg. Neglect changes in kinetic and potential energies.
vaportovaporizedwaterofmasskg23.18m
m
m
x
793.0x
(2257)x100(4.187)h
KJ/kg78.206478.376
25
200,42
h
)hh(mQ
v
v
2
2
22
2
12






123. Calculate the heat required to be given to 2 kg of ice at -15C to change into steam at atmospheric pressure, taking
the values
Freezing point temperature = 0C
Specific heat of ice = 2.04 KJ/kg-K
Latent heat of fusion = 335 KJ/kg
Specific heat of water = 4.2 KJ/kg-K
Latent heat of evaporation = 2256.7 KJ/kg
 
KJ6.6084Q
7.2256)0100(2.4335)150(04.2mQ


124. A liquid of density 800 kg/m3 specific heat of 2.5 KJ/kg-K and temperature of 27C is mixed with another liquid of
density 820 kg/m3, specific heat 1.9 KJ/kg-K and temperature of 55C in the ratio of one of the first liquid to three
of the second by volume. Find the resulting temperature.
Qh = Qc
mh(Cph)(55 - t) = mc(Cpc)(t – 27)

27. C6.46
)428.1
55.1155
t
55.11t428.0t55
)27t(428.0)t55(
)27t)(5.2)(800(V)t55)(9.1)(820(V3
Vm
Vm
Vm
m
V
V
m
3VV;
3
1
V
V
cc
hhh
ccc
ch
h
c













A 3 m diameter by 4.5 m height vertical tank is receiving water ( = 978 kg/m3) at the rate of 1.13 m3/min and is discharging through a 150 mm
 with a constant velocity of 1.5 m/sec. At a given instant, the tank is half full. Find the water level and the mass change in the tank 15 minutes
later.
Two gaseous streams containing the same fluid enter a mixing chamber and leave as a single stream. For the first gas the entrance condition are:
A1 = 500 cm2 ; v1 = 730 m/sec ; 1 =1.60 kg/m3. For the second gas the entrance condition are A2 = 400 cm2; m2 = 8.84 kg/sec ; 2 = .502 m3/kg.
The exit stream conditions is: v3 = 130 m/sec and 3 = 0.437 m3/kg.
Determine
(a) the total mass flow leaving the chamber
(b) the velocity of gas 2.
In determining the specific heat of a new metal alloy,0.15 kg of the substance is heated to 400C and then placed in a 0.2 kg aluminum calorimeter
cup containing 0.4 kg of water at 10C. If the final temperature of the mixture is 30.5C , what is the specific heat of the alloy. (ignore the
calorimeter stirrer and thermometer)
Cpal = 0.92 KJ/kg-C; Cpw = 4.187 KJkg-C
It is required to lift five people on an elevator a distance of 100 m. The work is found to be 341.2 KJ and g = 9.75 m/sec2. Determine the average
mass per person.
Twenty kilograms of ice at -8C is placed in a 120 kgs of water at 40C. Assuming no heat lost to or absorbed from the surroundings, what will be
the resulting equilibrium temperature of the mixture.
Specific heat of ice = 2.22 KJ/kg-C
Specific heat of water = 4.19 KJ/kg-C
Freezing point temperature of water = 0C

28. hF of ice = 334.9 KJ/kg
A cup of coffee of volume 0.3 L is heated from a temperature of 25oC to 60oC at a pressure of 100 kPa. Determine the change in the (a) internal
energy, (b) enthalpy and (c) entropy. Assume the density and specific heat of coffee to be 1100 kg/m3 and 4.1 kJ/kg.K respectively. Employ the
SL model. (d) What-if scenario: How would the answers change if the heating was done inside a chamber pressurized at 1 MPa? [Manual Solution]
[TEST Solution]
Answers: (a) 47.36 kJ (b) 47.36 kJ (c) 0.15 kJ/kg.K (d) No changes
A block of solid with a mass of 10 kg is heated from 25oC to 200oC. If the change in the specific internal energy is found to be 67.55 kJ/kg, identify
the material. [Manual Solution] [TEST Solution]
Answers: Copper
A block of aluminum with a mass of 10 kg is heated from 25oC to 200oC. Determine (a) the total change in internal energy and (b) entropy of the
block. (c) What-if-Scenario: How would the answer in (b) change if the block was made of copper instead? [Manual Solution] [TEST Solution]
Answers: (a) 1578.5 kJ/kg (b) 4.17 kJ/K (c) 1.783 kJ/K
A 2 kg block of aluminum at 600oC is dropped into a cooling tank. If the final temperature at equilibrium is 25oC, determine (a) Change in internal
energy, and (b) change in entropy of the block as the system. Use the SL model for aluminum (c_v = 0.902 kJ/kg.K). [Manual Solution*] [TEST
Solution*]
Answers: (a) -1037.3 kJ (b) -1.939 kJ/K
10 A copper block of mass 5 kg, initially at equilibrium with the surroundings at 30oC and 100 kPa is placed in a pressurized chamber with a
pressure of 20 MPa and a temperature of 200oC. Determine (a) the change in the internal energy (b) enthalpy and (c) entropy of the block after it
comes to a new equilibrium. (d) What-if-Scenario: How would the answer in (a) change if the block was made of silver? [Manual Solution] [TEST
Solution]
Answers: (a) 65.62 kJ/kg (b) 67.85 kJ/kg (c) 0.17 kJ/kg.K (d) 39.94 kJ/kg
A 2 kg block of aluminum at 60oC is dropped into a tank containing 5 kg of water at 25oC. If the final temperature after equilibrium is 27.77oC.
Determine (a) DU and (b) DS for the combined system of aluminum and water before and after the process. [Manual Solution] [TEST Solution]
Answers: (a) -52.35 kJ (b) -0.1643 kJ/K
] A cup of coffee cools down by transferring heat to the surroundings at a rate of 0.1 kW. If the mass of coffee is 0.2 kg and coffee can be modeled
as water, determine the rate of change of temperature of coffee. [Manual Solution][TEST Solution]
Answers: (a) 1.2 K/s Anim. 3-2-14 (click)
A pump raises the pressure of liquid water from 50 kPa to 5000 kPa in an isentropic manner. Determine (a) the change in temperature and (b)
specific enthalpy between the inlet and exit. [Manual Solution] [TEST Solution]
Answers: (a) 0 (b) 4.965 kJ/kg
Oil (cv=1.8 kJ/kg.K) flows steadily through a long insulated constant-diameter pipe at a volume flow rate of 10 m3/min. The conditions at the inlet
are p = 3000 kPa, T = 20oC, V=20 m/s and z=100 m. The conditions at the exit are p = 2000 kPa, T = 21oC and z=0 m. (a) Use the mass equation
to evaluate the velocity at the exit. (b) Use the energy equation to show that j remains unchanged between the inlet and the exit. (c) Determine
the exit temperature. [Manual Solution] [TEST Solution]
Answers: (a) 20 m/s (b) 21.16oC
Water flows steadily through a device at a flow rate of 20 kg/s. At the inlet the conditions are 200 kPa and 10oC. At the exit the conditions are
2000 kPa and 50oC. (a) Determine the difference between the entropy transported by the flow at the exit and at the inlet. (b) What are the possible
reasons behind the increase in entropy transport? [Manual Solution] [TEST Solution]
Answers: (a) 11.06 kW/K (b) heat addition and irreversibilities
19 In an isentropic nozzle, operating at steady state, the specific flow energy 'j' and specific entropy 's' remain constant along the flow. The
following properties are known at the inlet and exit ports of an isentropic nozzle discharging water at a steady rate of 2 kg/s. Inlet: p=300 kPa, A=4
cm2; Exit: p=100 kPa. Determine (a) the exit velocity and (b) the exit area. Use the SL model for liquid water. (c) What-if scenario: How would the
exit velocity change if the inlet kinetic energy was neglected? [Manual Solution] [TEST Solution]
Answers: (a) 20.65 m/s (b) 97.2 mm2 (c) 20.03 m/s Anim. 3-2-19 (click)
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85022346488366982355
40194120019493348022220
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29. A pipe carries saturated liquid water at a pressure of 500 kPa. Some water squirts out from the pipe through a small leak. As the water is expelled,
it quickly achieves mechanical equilibrium with the atmosphere at 100 kPa. (a) Estimate the temperature of water inside and outside the pipe.
What if scenario: How would the answers change if the fluid was (b) R-134a or (c) R-12 instead? [Manual Solution] [TEST Solution]
Answers: (a) 151.8oC, 99.6oC (b) 15.6oC, -26.6oC (c) 15.6oC, -30.1oC
A vertical piston-cylinder assembly contains water. The piston has a mass of 2 kg and a diameter of 10 cm. Determine the vertical force necessary
on the piston to ensure that water inside the cylinder boils at (a) 120oC or (b) 80oC. Assume atmospheric pressure to be 101 kPa. (c) What-if
scenario: How would the answer in part (a) change if the piston mass was neglected? [Manual Solution] [TEST Solution]
Answers: (a) 0.746 kN (b) -0.441 kN (c) 0.766 kN Anim. 3-3-8 (click)
A vertical piston-cylinder assembly contains a saturated mixture of water at 120oC and a gage pressure of 108.5 kPa. The piston has a mass of
5 kg and a diameter of 12 cm. Determine (a) the atmospheric pressure outside and (b) the external force exerted on the piston to maintain a
constant pressure. [Manual Solution]
Answers: (a) 90 kPa (b) 1.178 kN downward
A cooking pan with an inner diameter of 20 cm is filled with water and covered with a lid of mass 5 kg. If the atmospheric pressure is 100 kPa.
Determine (a) the boiling temperature of water. (b) What-if-Scenario: How would the answer change if a 5 kg block is placed on top of the lid?
[Manual Solution] [TEST Solution]
Answers: (a) 100.04 oC (b) 100.45 oC. Anim. 3-3-10 (click)
11 A heat engine cycle is executed with ammonia in the saturation dome. The pressure of ammonia is 1.5 MPa during heat addition and 0.6 MPa
during heat rejection. What is the highest possible thermal efficiency? Based on the temperatures of heat addition and rejection, could you
comment on possible application of such a low-efficiency cycle? [Manual Solution] [TEST Solution]
Answers: 9.44% Anim. 3-3-11 (click)
16 A 10 L rigid tank contains 0.01 kg of steam. Determine the (a) pressure (b) stored energy E and (c) entropy S of steam if the quality is 50%.
Neglect kinetic and potential energy. (d) What-if scenario: How would the answers change if the quality was 100%? [Manual Solution] [TEST
Solution]
Answers: (a) 83.7 kPa (b) 14.48 kJ (c) 0.043 kJ/K (d) 175.4 kPa, 25.25 kJ, 0.072 kJ/K Anim. 3-3-16 (click)
A tank contains 20 kg of water at 85oC. If half of it (by mass) is in the liquid phase and the rest in vapor phase, determine (a) the volumetric quality,
and the stored energy in the (b) liquid and (c) vapor phases. [Manual Solution] [TEST Solution]
Answers:(a) 99.96% (b) 99.96% (c) 3558.4 kJ (d) 24,883.5 kJ
A vessel having a volume of 0.5 m3 contains 2 kg saturated liquid and saturated vapor mixture of H2O at 500 kPa. Calculate the (a) mass and (b)
volume of each phase. [Manual Solution] [TEST Solution]
Answers: (a) 1.32 kg, 0.67 kg, (b) 0.001 m3, 0.25 m3
A rigid tank of volume 83 m3 contains 100 kg of H2O at 100oC. The tank is heated until the temperature inside reaches 120oC. Determine the
pressure inside the tank at the (a) beginning and (b) end of the heating process. What-if-scenario: How would the final pressure change if the tank
temperature increased to 125oC? [Manual Solution] [TEST Solution]
Answers: (a) 101 kPa (b) 198.5 kPa (c) 216.2 kPa
A rigid tank (v = constant) contains 8 kg of liquid and 2 kg of vapor of H2O at 200oC. To what temperature should the tank be heated until all the
liquid in the tank vaporize? [Manual Solution] [TEST Solution]
Answers: 288oC
A piston cylinder device of volume 1 m3 contains 3 kg of water. The piston, which has an area of 100 cm2, exerts a force of 1.7 kN on the pin that
keeps it from moving. Determine the (a) temperature and (b) quality of H2O inside the cylinder. The water is now heated. (c) Determine the force
on the pin when all the liquid in the tank vaporize. Assume the atmospheric pressure to be 100 kPa and neglect the piston mass. [Manual Solution]
[TEST Solution]
Answers: (a) 130 oC (b) 0.497 (c) 4.64 kN Anim. 3-3-29 (click)
30 A rigid tank with a volume of 3.5 m3 contains 5 kg of saturated liquid-vapor mixture of H2O at 80oC. The tank is slowly heated until all the liquid
in the tank are completely vaporized. Determine the temperature at which this happens. Also show the process on T-v diagram with respect to
saturation lines. [Manual Solution] [TEST Solution]
Answers: 128.33 oC

30. A 50 L rigid tank contains R-134a at a temperature of 50oC with a quality of 2.5%. Heat is added until the all the vapor condense (due to increased
pressure) and the tank is filled completely with saturated liquid. (a) With the aid of a T-v diagram, show that this is quite possible. Also determine
(b) the pressure and (c) temperature in the tank at saturation. [Manual Solution] [TEST Solution]
Answers: (b) 3469 kPa (c) 93.25oC
32 A 1000 L rigid tank contains saturated liquid water at 40oC. (a) Determine the pressure inside. (b) The tank is now heated to 90oC. Use the
compressed liquid table to determine the pressure in the tank. [Manual Solution] [TEST Solution] Table B-4: Compressed
Liquid Table of Water
Answers: (a) 7.39 kPa (b) 43.23 MPaoC
A lid with negligible weight is suddenly placed on a pan of boiling water and the heating is turned off. After about an hour, thermal equilibrium is
reached between the water and the atmosphere, which is at 30oC and 101 kPa. If the inner diameter of the pan is 20 cm. Determine the force
necessary to open the lid. (b) What-if-Scenario: How would the answer change if the lid weight of 1 kg was to be considered? [Manual Solution]
[TEST Solution]
Answers: (a) 3.04 kN (b) 3.05 kN Anim. 3-3-33 (click)
Superheated water vapor at 1.5 MPa and 280oC is allowed to cool at constant volume until the temperature drops to 130oC. At the final state
determine (a) the pressure (b) the quality and (c) the enthalpy. Show the process on a T-s diagram. [Manual Solution] [TEST Solution]
Answers: (a) 270.1 kPa (b) 24.2% (c) 1072 kJ/kg
36 A rigid tank with a volume of 1 m3 contains superheated steam at 500 kPa and 500oC. Determine (a) the mass and (b) the total internal energy
of the steam. The tank is now cooled until the total internal energy decreases to 2076.2 kJ. Determine (c) the pressure and (d) temperature in the
final state. [Manual Solution] [TEST Solution]
Answers: (a) 1.407 kg (b) 4400.4 kJ (c) 120.7 kPa (d) 105.0oC
38 A large industrial tank of volume 200 m3 is filled with steam at 450oC and 150 kPa. Determine (a) the pressure and (b) quality of steam when
the temperature drops to 25oC due to heat loss. (c) If the heat transfer for this constant volume process is given by Q=DU, determine the heat
transfer. [Manual Solution] [TEST Solution]
Answers: (a) 3.17 kPa (b) 5.4% (c) -255.57 MJ
A piston-cylinder device contains 3 kg of saturated mixture of water with a quality of 0.8 at 180oC. Heat is added until all the liquid vaporize.
Determine (a) the pressure (b) the initial volume (c) the final volume and (d) the work performed by the vapor during the expansion process. (e)
Show the process on a p-v diagram. [Manual Solution] [TEST Solution]
Answers: (a) 1 MPa (b) 0.466 m3 (c) 0.582 m3 (d) 116 kJ Anim. 3-3-43 (click)
45 A piston-cylinder device contains 0.6 kg of steam at 350oC and 1.5 MPa. Steam is now cooled at constant pressure until half of the mass
condenses. Determine (a) the final temperature and (b) the boundary work transfer. (c) Show the process on a T-s diagram. [Manual Solution]
[TEST Solution]
Answers: (a) 198.3oC (b) -108 kJ
Water vapor (1 kg) at 0.2 kPa and 30oC is cooled at a constant pressure process until condensation begins. Determine (a) the boundary work
transfer and (b) change of enthalpy, DH, treating water as the system. (c) What-if-Scenario: How would the answers change, if all the vapor
condensed? [Manual Solution] [TEST Solution]
Answers: (a) -18.9 kJ (b) -78.57 kJ (c) -139.9, -2,916.1 kJ
A piston cylinder device contains 10 L of liquid water at 100 kPa and 30oC. Heat is transferred at constant pressure until the temperature increases
to 200oC. Determine the change in the (a) total volume and (b) total internal energy of steam. Show the process on a T-s and P-v diagram.
[Manual Solution] [TEST Solution]
Answers: (a) 21.6 m3 (b) 25221 kJ
A piston-cylinder device contains a saturated mixture of water with a quality of 84.3% at 10 kPa. If the pressure is raised in an isentropic (constant
entropy) manner to 5000 kPa, (a) determine the final temperature. (b) What-if scenario: How would the answer change if water was at saturated
vapor state to start with? [Manual Solution] [TEST Solution]
Answers: (a) 499oC (b) 994oC Anim. 3-3-48 (click)
Water at a pressure of 50 MPa is heated in a constant pressure electrical heater from 50oC to 1000oC. Spot the states on a T-s diagram and
determine (a) the change of enthalpy and (b) entropy. Use compressed liquid model for liquid water. [Manual Solution*] [TEST Solution]

31. Answers: (a) 4241 kJ/kg (b) 6.31 kJ/kg.K, Anim. 3-3-52 (click)
Determine (a) the mass flow rate and (b) the volume flow rate of steam flowing through a pipe of diameter 0.1 m at a pressure of 1000 kPa and a
temperature of 300oC with a velocity of 50 m/s. (c) Also determine the rate of transport of energy by the steam. (d) What-if-Scenario: How would
the answer in (d) change if the temperature was 400oC? [Manual Solution] [TEST Solution]
Answers: (a) 1.52 kg/s (b) 0.392 m3/s (c) 4647 kW (d) 4182 kW Figure 3-3-53
Refrigerant-134 flows through a pipe of diameter 5 cm with a mass flow rate of 0.13 kg/s at 100 kPa, 10 m/s. Determine (a) the temperature and
(b) quality of the refrigerant in the pipe. Also determine the rate of transport of (c) energy and (d) entropy by the flow. [Manual Solution] [TEST
Solution]
Answers: (a) -26.6oC (b) 78.3% (c) 24.19 kW(d) 0.0983 kW/K
Steam at a pressure of 2 MPa and 400oC flows through a pipe of diameter 10 cm with a velocity of 50 m/s. Determine the flow rates of (a) mass
(b) energy and (c) entropy. [Manual Solution] [TEST Solution]
Answers: (a) 2.6 kg/s (b) 8446.8 kW (c) 18.51 kW.K
Liquid water at 100 kPa, 30oC enters a boiler through a 2 cm-diameter pipe with a flow rate of 1 kg/s. It leaves the boiler as a saturated vapor
through a 20 cm-diameter pipe without any significant pressure loss. Determine (a) the exit velocity, and the rate of transport of energy at the (b)
inlet and (c) exit. Neglect potential energy, but not kinetic energy. (d) What-if-Scenario: How would the answers change if kinetic energy was
neglected? [Manual Solution] [TEST Solution]
Answers: (a) 53.92 m/s (b) 125.8 kW (c) 2,676.95 kW (d) 125.79 kW, 2,675.5 kW
Water is pumped in an isentropic (constant entropy) manner from 100 kPa and 25oC to 40 MPa. Determine the change in enthalpy, Dh, using the
(a) compressed liquid table (b) compressed liquid model and (c) solid/liquid model. [Manual Solution] [TEST Solution]
Answers: (a) 40.94 kJ/kg (b) 39.99 kJ/kg.K (c) 40.02 kJ/kg
In an isentropic nozzle the specific flow energy j and entropy s remain constant along the flow. Superheated steam flows steadily through an
isentropic nozzle for which the following properties are known at the inlet and exit ports. Inlet: p=100 kPa, T=400oC, A=100 cm2, Vel=5 m/s; Exit:
p=200 kPa. Determine (a) the exit velocity (b) the exit temperature and (c) the exit area. [Manual Solution] [TEST Solution]
Answers: (a) 630 m/s (b) 302oC(b) 1.36 cm2 Anim. 3-3-61 (click)
1 Determine (a) the mass of air at 100 kPa, 25oC in a room with dimensions 5m x 5m x 5m. (b) How much air must leave the room if the pressure
drops to 95 kPa at constant temperature? (c) How much air must leave the room if the temperature increased to 40oC at constant pressure?
[Manual Solution] [TEST Solution]
Answers: (a) 146 kg (b) 7.3 kg (c) 7.0 kg Figure 3-4-1
A cylinder of volume 2 m3 contains 1 kg of hydrogen at 20oC. Determine the change in (a) pressure (b) stored energy and (c) entropy of the gas
as the chamber is heated to 200oC. Use the PG model for hydrogen. (d) What-if-Scenario: How would the answer change if the chamber contained
carbon-dioxide instead? [Manual Solution] [TEST Solution]
Answers: (a) 371.2 kPa (b) 1,833 kJ (c) 4.88 kJ/kg.K (d) 17 kPa, 118.3 kJ, 0.315 kJ/K Anim. 3-4-2 (click)
The gage pressure in an automobile tire is measured as 250 kPa when the outside pressure is 100 kPa and temperature 25oC. If the volume of
the tire is 0.025 m3, (a) determine the amount of air in kg that must be bled in order to reduce the pressure to the recommended value of 220 kPa
gage. Use the PG model for air. (b) What-if-scenario: How would the answer in change if the IG model was used instead? [Manual Solution] [TEST
Solution]
Answers: (a) 8.77 g (b) No change
A 1 L piston-cylinder device contains air at 500 kPa and 300 K. An electrical resistance heater is used to raise the temperature of the gas to 500
K at constant pressure. Determine (a) the boundary work transfer, and the change in (b) stored energy and (c) entropy of the gas. (d) What-if
scenario: Which part of the answers would not change if the IG model was used? [Manual Solution] [TEST Solution]
Answers: (a) 0.333 kJ (b) 0.834 kJ (c) 0.00298 kJ/K (d) part a Anim. 3-4-10 (click)
11 A piston-cylinder device contains 0.01 kg of nitrogen at 100 kPa and 300oC. Using (a) the PG model and (b) IG model, determine the boundary
work transfer as nitrogen cools down to 30oC. Show the process on a T-s and a p-v diagram. [Manual Solution] [TEST Solution]
Answers: (a) -0.8 kJ (b) -0.8 kJ
Oxygen at 100 kPa and 200oC is compressed to half its initial volume. Determine the final state in terms of pressure and temperature if the
compression is carried out in an (a) isobaric (b) isothermal and (c) isentropic manner. Use the PG model for oxygen. [Manual Solution] [TEST
Solution]

32. Answers: (a) -36.5oC (b) 200 kPa (c) 263 kPa, 348oC Anim. 3-4-12 (click)
Air at 15oC and 100 kPa enters the diffuser of a jet engine steadily with a velocity of 100 m/s. The inlet area is 0.2 m2. Determine (a) the mass
flow rate of the air, (b) What-if-scenario: How would the conclusion change if the entrance velocity was 150 m/s? [Manual Solution] [TEST Solution]
Answers: (a) 24.2 kg/s (b) 36.3 kg/s
Air flows through a nozzle in an isentropic manner from p = 400 kPa, T = 25oC at the inlet to p = 100 KPa at the exit. Determine the temperature
at the exit, modeling air as a perfect gas. [Manual Solution] [TEST Solution]
Answers: -72.5 oC Anim. 3-4-20 (click)
A tank of volume 10 m3 contains nitrogen at a pressure of 0.5 MPa and a temperature of 200 K. Determine the mass of nitrogen in the tank using
the (a) ideal gas and (b) real gas model. (c) What-if-Scenario: How would the answer in part (a) change if the pressure and temperature in the
tank were 3 MPa and 125 K respectively? [Manual Solution] [TEST Solution]
Answers: (a) 84.23 kg (b) 85.98 kg (c) 806.5 kg
A closed rigid tank contains carbon-dioxide at 10 MPa and 100oC. It is cooled until its temperature reaches 0oC. Determine the pressure at the
final state. Use (a) the RG model with the Lee Kesler chart (b) the RG model with the Nelson Obert chart and (b) the PC model. [Manual Solution*]
[TEST Solution]
Answers: (a)3.87 MPa (b) Out of Range (c) 3.48 MPa
A 15 L tank contains 1 kg of R-12 refrigerant at 100oC. It is heated until the temperature of the refrigerant reaches 150oC. Determine the change
in the (a) internal energy DU and (b) entropy DS. Use the RG model with Lee Kesler charts. [Manual Solution*] [TEST Solution]
Answers: (a) 28.02 kJ/kg (b) 0.07 kJ/kg.K
A piston cylinder device contains 10 L of nitrogen at 10 MPa and 200 K. It is heated at a constant pressure to a temperature of 400 K. Determine
(a) DH and (b) DS. Use the RG model with Lee Kesler charts. (c) What-if-scenario: How would the answers change if the PC model was used? If
the PC model is always more accurate, then why should one use the RG model at all? [Manual Solution] [TEST Solution]
Answers: (a) 490.5 kJ (b) 1.8 kJ/K (c) 495.9 kJ, 1.77 kJ/K Anim. 3-5-13 (click)
Consider an ideal gas at 400 K and 100 kPa. As a result of some disturbance, the conditions of the gas change to 404 K and 98 kPa. Estimate
the change in the specific volume of the gas using the ideal-gas relation at each state. [Manual Solution*]
Determine the enthalpy change and the entropy change of carbon di-oxide per unit mass as it undergoes a change of state from 250 K and 7 MPa
to 280 K and 12 MPa, (a) by assuming ideal-gas behaviour, and (b) by accounting for the deviation from ideal-gas bahaviour.
Methane is compressed adiabatically by a steady-state flow compressor from 2 MPa and -10oC to 10 MPa and 110oC at a rate of 0.8 kg/s. Using
the generalized charts, determine the required power input to the compressor.
A cylindrical tank contains 4.0 kg of carbon monoxide at -45 oC has an inner diameter of 0.2 m and a length of 1 m. Using the RG model (L-K
charts), determine (a) the pressure exerted by the gas. (b) (c) What-if-scenario: How would the answer in (a) change if the IG model is used
instead? [Manual Solution] [TEST Solution]
Methane is adiabatically compressed by a piston-cylinder device from 1 MPa and 100oC to 4 MPa. Calculate (a) the work done per unit mass.
Assume the adiabatic efficiency to be 90%. Use the real gas model. (b) What-if-scenario: How would the answer in (a) change if the gas
compressed were ethane instead? [Manual Solution*]
Answers: (a) -277 kJ/kg, (b) -149 kJ/kg
________________________________________
BP2-91. In a Rankine cycle, saturated liquid water at 1 bar is compressed isentropically to 150 bar. First by reheating in a boiler and then by
superheating at constant pressure of 150 bar, the water substance is brought to 750K. After adiabatic reversible expansion in a turbine to 1 bar,
it is then cooled in a condenser to a saturated liquid. How much work is generated in the turbine? (Steam properties h, kJ/kg, s, kJ/kg-K: @ 150
bar&750 K, h = 3240.5, s1 = 6.2549; @ 1 bar, hf=417.46, hfg=2258, sf=1.3026, sfg=6.0568)
769.9 b. 796.9 c .967.9 d.976.9
BP1-91. A reheat steam has 13850 kPa throttle pressure at the turbine inlet and 2800 kPa reheat pressure. The throttle and reheat temperature
of the steam is 540oC, condenser pressure is 3.4 kPa, engine efficiency of high pressure and low pressure is 75%. Find the cycle thermal efficiency.
34.46% b. 35.56 c. 36.66 d. 37.76

33. BP2-99 In a Rankine cycle, steam enters the turbine at 2.5 MPa and condenser of 50 kPa. What is the thermal efficiency of the cy cle in percent?
(Steam properties h, kJ/kg, s, kJ/kg-K: @ 2.5 MPa; hg = 2803.1 sg = 6.2575; @ 50 kPa, hf= 340.49, hfg= 2305.4, sf= 1.091, sfg= 6.5029, vf=0.001.3
m3/kg)
25.55 b. 28.87 c. 30.12 d. 31.79
BP2-95. A supercritical steam Rankine cycle has turbine inlet conditions of 17.5 MPa and 530oC expands in a turbine to 7 kPa. The turbine and
pump polytropic efficiencies are 0.9 and 0.7, respectively. Pressure losses between pump and turbine inlet are 1.5 MPa. What should be the pump
work in kJ/kg.
27.13 b. 29.87 c. 32.47 d. 33.25
Sol. Wp = vf(P4-P3)/n; vf = 1000 m3/kg
BP2-97 Steam enters the superheater of a boiler at a pressure of 25 bar and dryness of 0.98 and leaves at the same pressure at a temperature
of 370oC. Calculate the heat energy supplied per kg of steam supplied in the superheater.
(Steam properties: @ 25 bar &370oC, h = 3171.8 kJ/kg; @ 25 bar, hf = 962.11, hfg = 1841.0 kJ/kg)
405.51 b. 504.15 c. 154.15 d. 245.25.
A BP2-94. A back pressure steam turbine of 100 MW capacity serves as a prime mover in a cogeneration system. The boiler admits the return
water at a temperature of 66oC and produces the steam at 6.5 MPa and 455oC. Steam then enters a back pressure turbine and expands to the
pressure of the process, which is 0.52 MPa. Assuming a boiler efficiency of 80% and neglecting the effect of pumping and the pressure drops at
various location, what is the incremental heat rate for electric? The following enthalpies have been found: at turbine entrance = 3306.8 kJ/kg, exit
= 2700.8 kJ/kg; boiler entrance = 276.23 kJ/kg, exit = 3306.8 kJ/kg)
22,504.23 kJ/kW-hr b. 52,244.32 kJ/kW-hr
c. 12,435.72kJ/kW-hr d. 32,234.82 kJ/kW-hr
BP2-98. In an open feedwater for a steam power plant, saturated steam at 7 bar is mixed with sub-cooled liquid at 7 bar and 25oC. Just enough
steam is supplied to ensure that the mixed steam leaving the heater will be saturated liquid at 7 bar when heater efficiency is 90%. Calculate the
mass flow rate of sub cooled liquid if steam flow rate is 0.865 kg/s. (Steam properties h, kJ/kg, @ 7 bar, hg = 2763.5, hf = 697.22; @ 7 bar & 25oC,
hf= 105.5)
2.725 b. 2.286 c. 3.356 d. 3.948
BP2-95. A steam plant operates with an initial pressure of 1.7 MPa and 370oC temperature and exhaust to a heating system at 0.17 MPa. The
condensate from the heating system is returned to the boiler at 65.5oC and the heating system utilizes from its intended purpose 90% of the
energy transferred from the steam it receives. The turbine efficiency is 70%. If the boiler efficiency is 80%, what is the cogeneration efficiency of
the system in percent? Neglect pump work. (Steam properties h, kJ/kg, s, kJ/kg-K: @ 1.7 MPa & 370oC; h = 3787.1, s = 7.1081; @ 1.7 MPa, hf=
483.20, hfg= 2216.0, sf= 1.4752, sfg= 5.7062; @ 65oC, hf=274.14)
69 b. 78 c. 91.24 d. 102.10
BP1-96. In a cogeneration plant, steam enters the turbine at 4 MPa and 400oC. One fourth of the steam is extracted from the turbine at 600kPa
pressure for process heating. The remaining steam continues to expand to 10 kPa. The extracted steam is then condensed and mixed with
feedwater at constant pressure and the mixture is pumped to the boiler pressure of 4 MPa. The mass flow rate of the steam through the boiler is
30 kg/s. Disregarding any pressure drops and heat losses in the piping, and assuming the turbine and pump to be isentropic, how much process
heat is required in kW? (Steam properties h, kJ/kg, s, kJ/kg-K: @ 4 MPa & 400oC, h = 3213.6 s = 6.7690; @ 600 kPa, hf= 670.56, hfg= 2086.3,
sf= 1.9312, sfg= 4.8288)
1,026.90 b. 2,468.2 c. 3,578.5 d. 15,646.8
BP1-96. A 23.5 kg/s at 5 MPa and 400oC is produced by a steam generator. The feedwater enters economizer at 145oC and leaves at 205oC. The
steam leaves the boiler drum with a quality of 98%. The unit consumes 2.75 kg of coal per second as received having an heating value of 25,102
kJ/kg. What would be the overall efficiency of the unit in percent? (Steam properties h, kJ/kg, s, kJ/kg-K: @ 5 MPa & 400oC, h=3195.7; @ 0 MPa,
hf= 1154.23, hfg= 1640.1; @ 205oC , hf= 610.63)
65 b. 78 c. 88 d. 95
BP2-94. A coal-fired power plant has a turbine-generator rated at 1000 MW gross. The plant required about 9% of this power for its internal
operations. It uses 9800 tons of coal per day. The coal has a heating value of 6,388.9 kCal/kg, and the steam generator efficiency is 86%. What
is the net station efficiency of the plant in percent?
30.12 b. 33.07 c. 36.74 d. 40.01
BP2-97. Steam enters the turbine of a cogeneration plant at 7 MPa and 500oC. Steam at a flow rate of 7.6 kg/s is extracted from the turbine at
600 kPa pressure for process heating. The remaining steam continues to expand to 10 kPa. The recovered condensates are pumped back to the
boiler. The mass flow rate of steam that enters the turbine is 30 kg/s. Calculate the cogeneration efficiency in percent. (Steam properties h, kJ/kg,
s, kJ/kg-K: @ 7 MPa & 500oC, h = 3410.3 s = 6.7975; @ 600 kPa, hf= 670.56, hfg= 2086.3, sf= 1.9312, sfg= 4.8228; @ 10 kPa, hf= 191.83, hfg=
2392.8, sf= 0.6493, sfg= 7.5009)
50 b. 55 c. 60 d. 65
BP2-96. A 60 MW turbine generator running at 3600 rpm receives steam at 4.0 MPa and 450oC with back pressure of 10 kPa. Engine efficiency
is 78% and the combined mechanical and electrical efficiency is 95%. What would be the exhaust enthalpy of the steam in kJ/kg.
2,400.12 kJ/kg b. 20,432.10 kJ/kg

34. c. 28,124.20 kJ/kg d. 30,101.15 kJ/kg
BP2-95. Steam enters a throttling calorimeter at a pressure of 1.03 MPa. The calorimeter downstream pressure and temperature are respectively
0.100 MPa and 125oC. What is the percentage moisture of the supply steam? (Steam properties h, kJ/kg, s, kJ/kg-K: @1.03 MPa, hfg = 2010.7,
hg = 2779.25; @ 0.1 MPa & 125oC, h=2726.6)
1.98 b. 2.62 c.3.15 d. 5.21
BP2-97. Steam expands adiabatically in a turbine from 2 MPa, 400oC to 400 kPa, 250oC. What is the effectiveness of the process in percent
assuming an atmospheric temperature of 15oC. Neglect changes in kinetic and potential energy. (Steam properties h, kJ/kg, s, kJ/kg-K: @ 2.0
MPa and 400oC; h = 3247.6 s = 7.1271; @ 400 kPa & 250oC, h= 2964.2, s= 7.3789)
79.62 b. 84.52 c. 82.45 d. 74.57
BP2-93. A drum containing steam with 2.5 m in diameter is 7.5 m long. Of the total volume, 1/3 contains saturated steam at 800 kPa and the other
2/3 contains saturated water. If this tank should explode, how much water would evaporate? Consider the process to be of constant enthalpy.
(Steam properties h, kJ/kg, v, m3/kg @0.8 MPa, hf = 721.11, hg = 2769.1, vf= 0.0011148, vg=0.2404; @ 0.101325 MPa & 100oC, hf=419.04,
hg=2676.1, vf=0.0010435, vg=2769.1)
2,123.76 kg b. 2,424.62 kg
c. 2,651.24 kg d. 2,948.11 kg
BP2-92. A Batangas base industrial company operates a steam power plant with reheat and regeneration. The steam enters a turbine at 300 bar
and 900 K and expands to 1 bar. Steam leaves the first stage at 30 bar and part of it entering a closed heater while the rest reheated to 800K.
Both section of the turbine have adiabatic efficiency of 93%. A condensate pump exists between the main condenser and the heater. Another
pump lies between the heater and condensate outlet line from the heater (condensed extracted steam). Compute for the extracted fraction of the
total mass flow to the heater.
0.234 b. 0.543 c. 0.765 d. 0.485
Methane is isothermally compressed by a piston-cylinder device from 1 MPa and 100oC to 4 MPa. For 1 kg of Methane Calculate (a) the entropy
change (b) the work and c) the heat transfer (For Methane: M = 16 ; k = 1.321)
One kgmol of argon (M = 39.95 ; k = 1.666) at 320 K is initially confined to one side of a rigid, insulated container divided into equal volumes of
0.2 m3 by a partition. The other side is initially evacuated. The partition is removed and the argon expands to fill the entire container. Determine
(a) the final temperature of argon.
K640
)1(3143.8
)4.0(88.302,13
T
VolumeFinalm4.00.2(2)V
PP
KPa13302.88P
TRnPV
3
A
A






35. Kkg
KJ
223.0
28
2
32
8
12
3143.8
R
m934.1
180
93)4(0.297)(2
V
m552.6
100
5)8(0.26)(31
V
kg1248m
mixturetheFor
kkg
KJ
297.0
28
8.3143
R
KPa180P
K29327320T
kg4m
)nitrogen(2Component
kkg
KJ
26.0
32
8.3143
R
KPa100P
K31527342T
kg8m
(oxygen)1Component
3
2
3
1
2
2
2
2
1
1
1
1



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228.0
486.8
934.1
y
772.0
486.8
552.6
y
m8.486934.1552.6V
2
1
3



An insulated rigid tank is divided into two compartments by a partition. One compartment contains 8 kg of oxygen gas at 42oC and 100 kPa, and
the other compartment contains 4 kg of nitrogen gas at 20oC and 180 kPa. Now the partition is removed and the two gases are allowed to mix.
Determine (a) the mixture temperature, and (b) the mixture pressure after equilibrium has been reached. (For O2: M = 32 ; k = 1.395 For N2: M =
28 ; k = 1.399)
Air in a piston cylinder occupies 0.12 m3 at 552 KPa. the air expands in reversible adiabatic process in which PV1.4 = C, doing work on the piston
until the volume is 0.24 m3. Determine
a) the wok done by/on the system
b) the net work if the atmospheric pressure is 101 KPa.
CPV
m30.24V
KPa552P
m312.0V
1.4
2
1
1




An insulated rigid tank is divided into two compartments by a partition. One compartment contains 4 kgmol of O2, and the other compartment
contains 5 kgmol of C02. Both gases are initially at 25oC and 150 kPa. Now the partition is removed and the two gases are allowed to mix. Determine
the new pressure of the mixture.(For O2: M = 32 ; k = 1.395 : For CO2: M = 44 ; k = 1.288)
KPa150P
TRnPV
m148.66.8266V
kg9n
m6.82V
150
)298)(3143.8(5
V
kg5n
m66V
150
)27325)(3143.8(4
P
TRn
V
kg4n
3
mol
3
2
2
mol2
3
1
1
11
1
mol1











Helium (M = 4 ; k = 1.666) at 200 kPa and 20oC is heated by mixing it with argon (M = 39.95 ;k=1.666) at 200 kPa, 500oC in an adiabatic chamber.
Helium enters the chamber at 2 kg/s and argon at 0.5 kg/s. If the mixture leaves at 200 kPa, determine the temperature at the exit.
  KJ98.270.12)-101(0.24-40.10Wnetb.
KJ10.40W
1
V
V
k1
VP
W.a
1k
2
111
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36. KJ2.95
n1
)T-mR(T
W
WUQ
KJ2.31Q
K-kg
KJ
-0.3494
n-1
n-k
CC
)T-(TmCQ
kg892.0m
mRTVP
12
vn
12n
111

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

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
K-kg
KJ
52.0Cp
K-kg
KJ
208.0
39.95
8.3143
R
:Arfor
K-kg
KJ
2.5
1k
Rk
Cp
K-kg
KJ
2.079
4
8.3143
R
:HeFor
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C71.31t
t)264.4(5.2500)52.0(5.020)2.5(2
K-kg
KJ
4.264
5.2
)52.0(5.02(5.2)
C
Cpth
hmhmhm
2.5m
m35.02
mmm
chambermixingtheinbalanceenergymassandBy
3
3
p3
332211
3
321

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
A rigid tank contains 3 m3 of argon (M = 39.95 ;k=1.666) at - 100oC and 1 MPa. Heat is transferred until the temperature rises to 0oC. Determine
(a) the mass of argon, (b) the final pressure and (c) heat transferred.
KJ2605.3)T-(TmCQ
KPa1578P
T
P
T
P
CVAt
K2732730T
kg37.83m
mRTPV
K-kg
KJ
3125.0
1-k
R
Cv
KPa1000P
K173273100T
K-kg
KJ
208.0
95.39
3143.8
R
m3V
12v
2
2
2
1
1
2
1
1
3
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Air (R = 0.287 KJ/kg-K ; k = 1.4)is contained in a cylinder fitted with a frictionless piston. Initially the cylinder contains 500 L of air at 150 KPa and
20C. The air is then compressed in a polytropic process PVn = C until the final pressure is 600 KPa, at which point the temperature is 120C.
Determine the work W and the heat transfer Q.
Calculate the change of entropy per kg of air when heated from 300K to 600K while the pressure drops from 400 Kpa to 300 KPa. (S = 0.78
KJ/kg-K)
K-kg
KJ
0.7175
1-k
R
Cv
K-kg
KJ
1.0045
1k
Rk
Cp
269.1n
P
P
ln
T
T
ln
n
1n
P
P
T
T
K393273120T;K29327320T
JPa600P:KPa150P
V;m500.0V
Given
1
2
1
2
n
1n
1
2
1
2
21
21
2
3
1
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37. KPa670P
K9.271T
K-kg
KJ
0.297R
kg10m
m10.4V
K9.271273-1.1T
KPa1379P
K-kg
KJ
4.16
2
3143.8
R
kg5m
2
2
2
2
3
1
1
1
1
1






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
KPa7.1219P
m3.52.110.4V
mRTPV
kg
kg
25.5
585.1
3143.8
M
K-kg
KJ
585.1
15
10(0.297)5(4.16)
R
3
mol



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

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Kkg
KJ
78.0
400
300
ln287.0
300
600
ln0045.1S
P
P
lnR
T
T
lnCS
nintegratioBy
P
dP
R
T
dT
CdS
Tbyequatontheofsidesbothdividing
dP
P
RT
dTCTdS
dP
P
RT
TdSdTC
P
RT
RTP
dPdQdh
1
2
1
2
p
p
p
p

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



One kg of oxygen (M = 32 ; k = 1.395) are compressed polytropically from a pressure of 96.5 KPa and 21C to 675.5 KPa. The compression
process follows PV1.3= C. Determine (a) the work (b) the heat transfer and (c)the change of entropy change in KJ/K
KJ/K-0.103S
KJ-34.73)T-(TmCQ
KJ-144.4
n-1
)T-mR(T
W
K6.460
P
P
TT
Kkg
KJ
208.0
3.11
3.1395.1
66.0C
Kkg
KJ
66.0
1395.1
26.0
C
Kkg
KJ
26.0
32
3143.8
R
K294273)21(T;kg1m
12n
12
n
1n
1
2
12
n
v
1
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
Air (R = 0.287 KJ/kg-K ; k = 1.4) drawn into a compressor is at 16C and 101.325 KPa. Flash point of the lubricating oil used is 180C. If the
compression is a reversible adiabatic, what pressure could be attain in the compressor if the maximum allowable temperature is 28C below the
flash point of the oil.
KPa359.54P
P
P
T
T
K415T
27314238-180T
KPa101.325P
K28927316T
1.4k
K-KJ/kg0.7175C
K-KJ/kg1.0045C
K-KJ/kg0.287R
:airFor
2
n
1n
1
2
1
2
2
2
1
1
v
p
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
A perfectly insulated vessel is divided into two compartments, one holding 0.5 kg of H2 (M = 2; k = 1.4)at 1379 KPa and –1.1C and the other
holding 10 kg of N2 (M = 28 ;k = 1.399) at 670 KPa and –1.1C. If the partition is removed, find (a) the molecular weight M and Gas constant R of
the mixture (c) the final pressure in KPa.

38. Helium gas (R=2.077 KJ/kg-K; k= 1.667) enters a steady state–steady flow expander at 800 KPa, 300C and exits at 120 KPa. The mass flow
rate is 0.2 kg/sec and the expansion process is PV1.3=C. Calculate W and Q of the expander in KW.
KW154.78Q
K-kg
KJ
-3.809Cn
K-kg
KJ
3.1139
1k
R
C
n-1
n-k
CC
)T-mCn(TQ
KW4.316W
1
P
P
n-1
nmRT
W
T
CPV:Process
kg/sec20.0m
KPa120P
K573T;KPa800P
v
vn
12
n
1n
1
21
2
1.3
2
11

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
When a certain gas is heated at constant pressure from 15C to 95C, the heat required is 1136 KJ/kg. When the same gas is heated at constant
volume between the same temperature the heat required is 808 KJ/kg. Calculate Cp, Cv, k and M of the gas.
mol
vp
v
p
p
p
kg
kg
03.2
1.4
3143.8
M
Kkg
KJ
1.41.102.14R
RCC
Kkg
KJ
1.10
)1595(
808
C
Kkg
KJ
2.14
)1595(
1136
C
406.1k
k
Cv
Cp
808
1136
2Eq.divide1.Eq
2)1595(Cv808
)1595(CvQ
1)1595(C1136
)1595(CQ
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