The document discusses heat capacity and specific heat. It defines heat capacity as the ratio of the change in heat to the change in temperature. Specific heat is the ratio of the change in heat to the change in temperature for a given mass of material. Examples are provided for the specific heat of common materials. Two word problems are presented to demonstrate calculating equilibrium temperature when objects of different temperatures come into contact.

1. Heat Capacity

2. Work In
Work done  The work - energy principle
on a system applies to all objects.
v1 v2 • If an object speeds up it
gains kinetic energy.
K1 = (1 / 2)mv12 K 2 = (1 / 2)mv2
2
• If an object slows down it
loses kinetic energy.
∆W = ∆K

3. Heat In
Heat into a  Temperature change is due
system to heat (Q).
• If an object’s temperature
increases it gains heat.
T1 ,U1 T2 ,U 2
• If an object’s temperature
decreases it loses heat.
∆Q ∝ ∆T

4. Heat Capacity
 The ratio of the change in heat to the change in
temperature is the heat capacity (C).
• Depends on material
• Depends on the mass
• Measured in J/K
∆Q = C∆ T

5. Specific Heat
 The ratio of the change in Material Specific heat
heat to the change in Mercury 140 J/kg-K
temperature is the heat Copper 390 J/kg-K
capacity (C).
Steel 500 J/kg-K
• Depends on material
• independent of the mass Granite 840 J/kg-K
• Measured in J/kg-K Aluminum 900 J/kg-K
Wood 1400 J/kg-K
Ice 2100 J/kg-K
∆Q = mc∆T Water 4200 J/kg-K

6. Take a Shower
 You are last to use the  Find the heat required.
shower today and the  ∆Q = mc∆T = (150 kg)
temperature in the water (4200 J/kg-K) ( 32 C)
heater has dropped to 18 °C  ∆Q = 2.1 x 107 J
from the normal temperature
of 50 °C. The heater holds  Find the time from the
150 kg and has a 50 kW
power, and set the heat to
heating coil.
the work.
 P = ∆W/∆t
 How long should you wait  t = ∆Q / P
before starting your shower?  (2.1 x 107 J) / (5 x 104 W)
 t = 4000 s = 1.1 hr

7. Equilibrium Temperature
 Two systems in thermal contact will adjust to reach
the same temperature - thermal equilibrium
 If they are thermally insulated, all the heat goes from
the hot system to the cold system.
1 2 m1c1∆T1 + m2 c2 ∆T2 = 0

8. Doing Dishes
 A 1.5 kg aluminum pan is  Setup the equation for an
heated to 180 °C then unknown equilibrium
placed into a sink with 8 kg temperature T.
water at 20 °C. m p c p (T − Tp ) + mwcw (Tw − T ) = 0
 If no water boils, what is the  Solve for T.
equilibrium temperature? m p c pTp + mwcwTw
T=
m p c p + mwcw
 T = 26 °C
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