Chapter 4 : Second Law of Thermodynamics

Section 4 : Mathematical Statement of the 2nd Law
 

Since the above conclusion is not premised on any specific internal nature of the system, the above result may be generalized: all irreversible processes are accompanied by a positive change of entropy of the universe. This leads to a mathematical statement of the second law:

(4.24)

At this point we can revert to the question that was stated at the beginning of this chapter: what change in a system is thermodynamically feasible? The second law provides answer to this, i.e., a process can only proceed in a direction that results in a positive change in the total entropy of the universe, the limiting value of zero being attained only by a fully reversible process. The corollary to this is: no process is possible for which the total entropy of the universe decreases.

Example 4.2
A rigid vessel of 0.06 m3 volume contains an ideal gas, CV = (5/2)R, at 500 K and 1 bar. (a) If 15 kJ of heat is transferred to the gas, determine its entropy change. (b) If the vessel is fitted with a stirrer that is rotated by a shaft so that work in the amount of 15 kJ is done on the gas, what is the entropy change of the gas if the process is adiabatic? What is ΔStotal ?
(Click for solution)
Example 4.3

An ideal gas, Cp = (7/2)R, is heated in a steady-flow heat exchanger from 70°C to 190°C by another stream of the same ideal gas which enters at 320°C. The flow rates of the two streams are the same, and heat losses from the exchanger are negligible. Calculate the molar entropy changes of the two gas streams for both parallel and countercurrent flow in the exchanger. What is ΔStotal in each case?
Click for solution