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Thermodynamics note chapter:5 second law of thermodynamics
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5 Chapter: 5 Second Law of Thermodynamics
5.1 Necessity of Formulation of Second Law
Drawbacks of First Law of Thermodynamics
The first law of thermodynamics states that during any cycle that a system undergoes, the
cyclic integral of the heat is equal to the cyclic integral of the work. ( ∫ ∫= WQ ) The first
law, however, places no restriction on the direction of flow of heat and work.
A cycle in which a given amount of heat is transferred from the system and an equal
amount of work is done on the system satisfies the first law just as well as a cycle in
which the flows of heat and work are reversed. However, we know from the experience
that because a proposed cycle doesn’t violate the first law doesn’t ensure that the cycle
will actually occur. This leads to the formulation of second law of thermodynamics.
Thus, a cycle will occur only if both the first law and second law are satisfied.
The second law tells that processes proceed in a certain direction but not in the opposite
1. A hot cup of coffee cools by virtue of heat transfer to the surroundings, but heat
will not flow from the cooler surroundings to the hotter cup of coffee.
2. Steam is kept in a chamber and other chamber is vacuum. If suddenly the partition
is removed, the steam fills up the vacuum but the reverse doesn’t happen
3. Two blocks at different temperature eventually come to a same temperature but
the process doesn’t occur in reverse direction.
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Thus, the second law needs to describe the direction for processes, and the direction is
described in terms of a system property that characterizes the system’s randomness,
disorder, or uncertainty.
Qualitative differences between heat and work
The first law of thermodynamics states that a certain energy balance will hold when a
system undergoes a change of state or a process but it doesn’t give any information on
whether that change of state or the process is at all feasible or not.
Joule’s experiment demonstrate that energy, when supplied to a system in the form of
work, can be completely converted into heat but the complete conversion of heat into
work in a cycle is not possible. So heat and work are not completely interchangeable
forms of energy.
Work Internal Energy Heat (100% conversion)
Heat can’t be converted completely and continuously into work in a cycle. Some heat has
to be rejected without conversion. The conversion of low grade of energy (heat) into high
grade of energy (work) in a cycle is impossible.
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Heat Work (100% conversion impossible)
Q > W
5.2 Entropy and Second Law of Thermodynamics for an Isolated System
The entropy of a system is a thermodynamic property which is a measure of the degree of
molecular disorder existing in the system. It describes the randomness or uncertainty of
the system. It is a function of a quantity of heat which shows the possibility of conversion
of heat into work. Thus, for maximum entropy, there is minimum availability for
conversion into work and for minimum entropy there is a maximum availability for
conversion into work.
1. It increases when heat is supplied irrespective of the fact whether temperature
changes or not.
2. It decreases when heat is removed whether the temperature changes or not.
3. It remains unchanged in all adiabatic reversible processes.
4. The increase in entropy is small when heat is added at a high temperature and is
greater when heat addition is made at a lower temperature.
Entropy and Second Law of Thermodynamics for an Isolated System
The microscopic disorder of a system is prescribed by a system property is called
“The entropy S, an extensive equilibrium property, must always increase or
remain constant for an isolated system.”
This is expressed mathematically as,
0)( ≥− IsolatedInitialFinal SS …………………………………eq(2)
Entropy, like our other thermodynamic properties, is defined only at equilibrium states or
for quasi-equilibrium processes. Equation (2) shows that the entropy of the final state is
never less than that of the initial state for any process which an isolated system
Entropy is a measure of the molecular disorder of the substance. Larger values of entropy
imply larger disorder or uncertainty and lower values imply more microscopically
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The term entropy production or entropy generation Sgen is considered in eq (1) to
eliminate the inequality sign.
0)( =− isolatedgenSdS δ
0)( =−− IsolatedInitialgenFinal SSS
Here, genSδ is the entropy generated during a change in system state and is always
positive or zero.
5.3 Reversible and Irreversible Process
A reversible process for a system is defined as a process that once having taken place can
be reversed so that the system and surroundings can be restored to their initial state.
An irreversible process is a process which once having taken place can’t be restored to its
The reversible process is an idealization, and all the actual processes are normally
5.3.1 Types of irreversibility
1. Mechanical and Thermal Irreversibility
2. Internal and External Irreversibility
Mechanical irreversibility is associated with the fluid friction among the molecules and
the mechanical friction between surfaces. Thermal irreversibility is associated with heat
transfer with finite temperature difference between the parts of system or between a
system and surroundings.
Internal irreversibility is associated with fluid friction and temperature variation within
the fluid. Combustion and diffusion also cause internal irreversibility. External
irreversibility is associated with friction between the atmosphere and rotating members.
All these absorb some work developed by the system. External irreversibility occurs
outside the boundary of the system.
5.3.2 Factors that makes process irreversible
2. Unrestricted Expansion
3. Heat transfer through a finite temperature difference
4. Mixing of two different fluids
Reversible Processes Irreversible Processes
1. Frictionless adiabatic expansion or
2. Friction less isothermal expansion
3. Condensation or boiling of liquid
1. Free Unrestricted Expansion
2. Combustion, diffusion
3. Electric current flow through
4. Mixing of two fluids
5. Heat transfer from high temperature
to low temperature
4. Process involving friction
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5.3.4 For a process to be reversible, it should obey following conditions.
1. The process should not involve friction of any kind.
2. Heat transfer should not take place with finite temperature difference.
3. There should be no mixing.
4. There should be no free or unrestricted expansion.
The process must proceed in a series of equilibrium states. It should move at an infinitely
5.4 Heat Engine and Refrigeration Cycles
Processes that return to their initial state are called cyclic processes.
A thermal energy reservoir (TER) is defined as a large body of infinite heat capacity,
which is capable of absorbing or rejecting an unlimited quantity of heat without suffering
appreciable changes in its thermodynamic properties. For example: River, Sea,
A heat engine cycle is a thermodynamic cycle in which there is a net heat transfer to the
system and a net work transfer from the system. The device which executes a heat engine
cycle is called a heat engine. This device takes heat as input and converts into work as
The cycles have a common feature – they operate between two limiting temperatures.
The high temperature results from the combustion process in the steam generator or
within the cylinder. The low temperature results from the cooling process. The
characteristics of these two temperature cycles are shown from a general viewpoint as a
high temperature heat transfer reservoir or source (hot reservoir) at TH and a low
temperature heat transfer reservoir or sink (cold reservoir) at TL. The cycle operating
between these two temperatures is arbitrary. The general power cycle or engine is shown
schematically in figure below.
The first law for an arbitrary cycle states; ∫∫ = WQ ……………….eq(1)
which is valid for an arbitrary collection of processes and for both reversible and
irreversible cycles. For the heat engine cycle shown in above figure;
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LH QQW −= ………………..eq(2)
Second law for all heat engine cycles is:
0)( ≤∫ T
For reversible heat transfer with the two heat transfer reservoirs, the equation(3) becomes
The efficiency of a cycle η is defined as;
A power cycle or engine as shown in above figure has a work output W and an input
from the high-temperature reservoir QH. Thus, this efficiency is;
From equation (2) , the eq(5) becomes as;
= 1η …………..eq(6)
The ratio of heat in eq(6) can be eliminated with eq(4) as;
Where, equality applies to reversible cycle and inequality applies to irreversible cycle.
Therefore, it can be written as;
−=< 1Reηη ……………………….eq(8)
This shows that the maximum efficiency of a heat engine operating between two heat
transfer reservoirs occurs for a reversible cycle.
Refrigerator and Heat Pump
A refrigerator is a device operating in a cycle which maintains a body, at a temperature
lower than the temperature of the surroundings.
The performance for a refrigerator is termed as the coefficient of performance (COP) and
is given as
First law; HL QQW −=− ………………….eq(2)
Second law; for cyclic process ∫ ≤ 0
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From eq(1) and eq(3),
revRIrrevR COPCOP ,, ≤
The equality applies to the reversible refrigerator and the inequality to the irreversible
A Heat pump is a device operating in a cycle which maintains a body, at a temperature
higher than the temperature of the surroundings.
Coefficient of Performance of Heat Pump
5.5 Carnot Cycle
Carnot cycle is a heat engine cycle which operates between the given high-temperature
and low-temperature reservoirs such that every process is reversible. If every process is
reversible, the cycle is also reversible and if the cycle is reversed, the heat engine cycle
becomes refrigerator or heat pump. This cycle was proposed by a French engineer Sadi
Carnot (1796-1832). The working substance for Carnot cycle is air, an ideal gas.
Assumptions for Carnot cycle
1. No friction is involved.
2. The transfer of heat doesn’t affect the temperature of source or sink.
3. Working medium air is perfect gas.
4. Compression and expansion are reversible.
5. Perfectly reversible adiabatic conditions are achieved.
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It is a reversible isothermal process in which heat is transferred from the high-
temperature reservoir at constant temperature (T1). The source at a high temperature is
brought in contact with the bottom of the cylinder so that air expands isothermally from
V1 to V2.
It is a reversible adiabatic process in which the temperature of the fluid decreases from
T1 to T2. The source is removed and the bottom of the cylinder is insulated so that the air
is allowed to expand adiabatically so that the volume increases from V2 to V3.
It is a reversible isothermal process in which heat is rejected to the low temperature
reservoir at T2. The bottom of the cylinder is brought in contact with the sink at
temperature T2 so that air is compressed isothermally from V3 to V4.
It is a reversible adiabatic process in which temperature of working fluid is increased
from T1 to T2 by compressing it reversibly and adiabatically. The sink is removed and the
bottom of the cylinder is insulated so that the air is allowed to compress adiabatically so
that the volume decreases from V4 to V1.
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And, the efficiency of a Carnot cycle is:
It is impossible to construct an engine operating between only two heat reservoirs
which will have a higher efficiency that a reversible engine operating between the same
In other words, for the same source and sink, a reversible engine has the higher
efficiency. This is also known as Carnot’s Theorem.
All reversible engines (Carnot Engines) operating between the same two reservoirs
have the same efficiency.
5.6 Classical Statements of Second Law of Thermodynamics
5.6.1 Kelvin-Planck Statement
It is impossible to construct a device that will operate in a cycle and produce no effect
other than the extraction of heat from a single reservoir and the performance of
equivalent amount of work.
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5.6.2 Clausius Statement
It is impossible to construct a device that operates in a cycle and produces no effect other
than the transfer of heat from a body at low temperature to a body at high temperature
without work input.
5.6.3 Equivalence of Kelvin-Planck and Clausius Statement
It can be proved that these statements are equivalent by proving the violation of one
statement leads to the violation of other statement.
1. Violation of Kelvin-Planck statement leads to the violation of Clausius Statement:
Let us assume a cyclic Heat Pump (HP) extracting heat Q2 from a low temperature
reservoir at T2 and discharging heat to high temperature reservoir at T1 with the
expenditure of work (W). Let’s assume a cyclic Heat Engine (HE) extracting heat Q1
from a high temperature reservoir and produces net work (W = Q1) without rejecting any
heat thus violating Kelvin-Planck statement. These two constitute a device extracting heat
Q2 from low temperature reservoir and rejecting to high temperature reservoir without
any work input. Thus Clausius statement is violated. So, a violation of Kelvin-Planck
statement leads to the violation of Clausius statement.
2. Violation of Clausius statement leads to the violation of Kelvin-Planck Statement:
Let us consider a Heat Pump (HP) that requires no work and thus violates the Clausius
statement. Let an amount of heat Q2 be transferred from the low temperature reservoir to
the HP, and let same amount of heat Q2 be transferred to the high-temperature reservoir.
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Let us consider a Heat Engine (HE) where an amount of heat Q1 be transferred from the
high-temperature reservoir and let the engine reject the amount of heat Q2 and does net
work (W = Q1-Q2). Because there is no net heat transfer to the low-temperature reservoir,
the low-temperature reservoir along with the HE and HP can be considered together as a
device that operates in a cycle and produces no effect other than the exchange of heat
with a single reservoir and performance of equal amount of work. Thus Kelvin-Planck
Statement is also violated. So a violation of Clausius Statement leads to the violation of