GROUP (3)
1
CHAPTER THREE
THE SECOND LAW OF
THERMODYNAMICS
2
3.1 Introduction
 The First Law of Thermodynamics, when applied to
a change of state of a thermodynamic system,
defines two extreme cases in which either, dw=0
( isochoric process ) or q = 0 (adiabatic process ); in
these cases , q = ∆u and w =∆u , respectively .
 But if q ≠ 0 and w ≠ 0 , is there a definite maximum
amount of work which the system can do during its
change of state ? the answer to this question requires
an examination of the nature of process .
 The examination which will be made in this chapter
results in the identifications of two classes of
processes : reversible and irreversible processes , and
in the introduction of a state function called the
ENTROPY ( S ).
 The concept of the entropy will be introduced from two
different starting points : in the first , the entropy will be
introduced and discussed as result of a need for
quantification of the degree of irreversibility of a
processes ; and in the second , the entropy is
introduced as a result of the examination of the
properties of reversibly operated cyclic heat engine .
 This examination leads to a statement known as the
Second Law of Thermodynamics which together with
the First Law of Thermodynamics lays the foundation
for the development of the thermodynamic methods of
describing the behavior of matter.
3
3.2 Spontaneous ( Natural Process )
 A system left to itself will do one of two things : either
it will remain in the state in which it happen to be (in
this case, this state will be called an equilibrium state);
or it will move of its own to some other state (the
initial state in this case will be named nonequilibrium
state )
 A process which involves the spontaneous movement
of a system from a nonequilibrium state to an
equilibrium state is called a spontaneous or natural
process.
 Examples of natural processes are:
1. The mixing of two gases ,
2. The equalization of temperature ,
3. The spontaneous occurrence of chemical reaction:
A+B=C+D
in either direction , depending on the initial mixture
of A,B reaching the equilibrium A, B, C, and D until
state the system is equilibrated.
 The natural processes can not be reversed without the
application of an external effects, thus a natural
process would leave a permanent change in the
external environment . such a process is said to be
irreversible, therefore the terms spontaneous , natural,
and irreversible are synonymous in this context .
 If a closed system undergoes a spontaneous process
involving the performance of work and the production
of heat, then as the process continuous, the capacity
4
of the system for further spontaneous change
decreases.
 Finally, once equilibrium is reached, the capacity of
the system for doing further work is exhausted.
 This means that in the initial nonequilibrium state of an
isolated system , some of the energy of the system
which is available as useful work in the system get
degraded by converting it to thermal energy (or heat)
which is a form of energy that is no longer available for
external purpose.
3.3 Quantification of Irreversibility and
Entropy
 Since the capacity of the system for spontaneous
change decreases with the occurrence of the natural
process, there should be a quantitative measure for
the degree of irreversibility ( or the degree of
degradation ) of the spontaneous process ( the natural
process ).
 The existence of processes which exhibit differing
degrees of irreversibility can be illustrated by the
weight –pulley- paddle wheels heat reservoir system
shown in figure (3.1).
5
Figure (3.1) : the weight-pully-paddle wheels-heat
reservoir system.
6
 Lewis and Randall considered the following three
processes :
1. The weight is allowed to fall, performing work w,
and the heat produced ,q , enters the heat reservoir
at T2.
2. The heat reservoir at the temperature T2 is placed
in contact with the heat reservoir at temperatureT1,
which is lower than T2 , and the same heat q is
allowed to flow from the heat reservoir at T2 to the
heat reservoir at T1.
3. The weight is allowed to fall, performing work w,
and the heat produced ,q , enters directly the heat
reservoir at T1.
 Since process (3) is equivalent to processes (1) and
(2) , the degree of irreversibility of process (3) is
higher than the degree of irreversibility of process (1) ,
and as T2 is higher than T1 then, (q / T2 ) will be lower
than (q / T1 ).
 Thus , when a system undergoes a spontaneous
process which involves absorption of heat q at the
constant temperature T, then the entropy change ,ΔS,
which can be used as the capacity of spontaneous
change or the degree of irreversibility, can be
expressed as: ΔS = ( q / T ).
 The entropy increases as a result of the process is
thus a measure of the degree of irreversibility of the
process.
7
3.4 Reversible Processes
 Since the capacity of a system for spontaneous
change decreases with the occurrence of the natural
process (a change from nonequilibrium state to
equilibrium state ) until equilibrium is attained at which
the capacity of the system for spontaneous change
will be exhausted ; thus, if the process proceeds under
infinitesimally small driving force such that during the
process, the system is never more than infinitesimal
distance .
 Thus , for equilibrium the degree of irreversibility will
approach zero value and the process becomes a
reversible process .
 Therefore , a reversible process is a process
during which the system is never away from
equilibrium states ; or , the reversible process is
the process which takes a system from state A to
state B along a path of continuum equilibrium
states .
3.5 An Illustration of Irreversible and
Reversible Processes
 Example: Water evaporation (or condensation) in a
system of water and water vapor at uniform
temperature T contained in a cylinder fitted with a
8





frictionless piston placed in thermal contact with a heat
reservoir at constant temperature T as shown in figure
(3.2) .
Let the system to be initially at the state: Pvap
(saturated water vapor pressure at temperature T) ,
Pvap = PH2O(T) = Pext , Tsystem = Theat reservoir = T ; so
the system is mechanically and thermally is in
equilibrium state.
If we consider the evaporation process, i.e. if the
external pressure is suddenly decreased by ΔP, a
nonequilibrium state is induced, so the piston will
move outward causing a pressure drop inside the
cylinder, thus the liquid water evaporate in a process
of establishment mechanical equilibrium by
equalization of the external and internal pressure.
The evaporation process leads to a temperature drop
between the temperature of reservoir and the
temperature of the system (vapor + water) which is
lowered because of the endothermic nature of the
evaporation process.
This temperature gradient forces a heat transfer from
the reservoir to the content of the cylinder to
reestablish thermal equilibrium by equalizing the
temperature of the whole system at temperature T.
The mechanical equilibrium at Psystem= Pext = Pvap will
be reestablished again by increasing the external
pressure back to Pext = PH2O(T) which causes
instantaneous compression of the water vapor raising
the system content temperature to T2>T which leads
to heat flow from the system to the heat reservoir
9
causing the temperature of the system to drop to a
value of T.
 Thus: the work done on the system during this cycle is
given by : Pext ΔV – (Pext – ΔP) ΔV = ΔV ΔP
where ΔV is the volume change during the process.
Thus, the permanent change in the external energy of
the heat reservoir as a result of the cycle process is
ΔVΔ P ( see figure 3.3 ) .
 Now if we consider the condensation process, i.e. if
the cyclic process started by increasing the external
pressure, which equals PH2O(T), by ΔP, it is possible
to show that, for the condensation cycle (see also
figure 3.3 ), a permanent change in the external
energy of the heat reservoir is ΔV ΔP.
 Thus, as ΔP approaches infinitesimal value, ΔP→δP,
reversibility is approached, i.e. when evaporation or
condensation processes are carried out in such
manner that Pext is never more than infinitesimally
different from PH2O(T) , the degree of irreversibility
approaches the zero value.
 It can also be seen that, as true reversibility is
approached the process becomes infinitely slow.
10
Figure (3.2) : piston and cylinder containing liquid water
and water vapor.
11
Figure (3.3) : the evaporation and condensation cycles
12