254 ENGINEERING THERMODYNAMICSdharm
/M-therm/th5-3.pm5Hence equation (5.18) may be written asdS =δQ
T RF
HGI
KJ ...(5.19)
where dS is an exact differential.
Thus, from equation (5.19), we find that the change of entropy in a reversible process is
equal to δQ
T
. This is the mathematical formulation of the second law of thermodynamics.
Equation (5.19) indicates that when an inexact differential δQ is divided by an integrating
factor T during a reversible process, it becomes an exact differential.
The third law of thermodynamics states “When a system is at zero absolute tempera-
ture, the entropy of system is zero”.
It is clear from the above law that the absolute value of entropy corresponding to a given
state of the system could be determined by integrating δQ
T RF
HGI
KJ between the state at absolute zero
and the given state. Zero entropy, however, means the absence of all molecular, atomic, elec-
tronic and nuclear disorders.
As it is not practicable to get data at zero absolute temperature, the change in entropy is
calculated either between two known states or by selecting some convenient point at which the
entropy is given an arbitrary value of zero. For steam, the reference point at which the entropy is
given an arbitrary value of zero is 0°C and for refrigerants like ammonia, Freon-12, carbon dioxide
etc. the reference point is – 40°C, at which the entropy it taken as zero.
Thus, in practice we can determine the change in entropy and not the absolute value of
entropy.
5.13. Entropy and Irreversibility
We know that change in entropy in a reversible process is equal to
δQ
T RF
HGI
KJ (eqn. 5.19). Let
us now find the change in entropy in an irreversible process.
p 2 L M 1 VFig. 5.22. Entropy change for an irreversible process.
Consider a closed system undergoing a change from state 1 to state 2 by a reversible process
1-L-2 and returns from state 2 to the initial state 1 by an irreversible process 2-M-1 as shown in
Fig. 5.22 on the thermodynamic coordinates, pressure and volume.