5
Second Law of Thermodynamics and Entropy
5.1. Limitations of first law of thermodynamics and introduction to second law. 5.2. Performance
of heat engines and reversed heat engines. 5.3. Reversible processes. 5.4. Statements of second
law of thermodynamics—Clausius statement—Kelvin-planck statement—Equivalence of clausius
statement to the kelvin—Planck statement. 5.5. Perpetual motion machine of the second kind.
5.6. Thermodynamic temperature. 5.7. Clausius inequality. 5.8. Carnot cycle. 5.9. Carnot’s
theorem. 5.10. Corollary of Carnot’s theorem. 5.11. Efficiency of the reversible heat engine.
5.12. Entropy—Introduction—Entropy—A property of a system—Change of entropy in a reversible
process. 5.13. Entropy and irreversibility. 5.14. Change in entropy of the universe.
5.15. Temperature—Entropy diagram. 5.16. Characteristics of entropy. 5.17. Entropy changes
for a closed system—General case for change of entropy of a gas—Heating a gas at constant
volume—Heating a gas at constant pressure—Isothermal process—Adiabatic process—Polytropic
process—Approximation for heat absorbed. 5.18. Entropy changes for an open system. 5.19. The
third law of thermodynamics—Highlights—Objective Type Questions—Theoretical Questions—
Unsolved Examples.5.1. LIMITATIONS OF FIRST LAW OF THERMODYNAMICS AND INTRODUCTION
TO SECOND LAW
It has been observed that energy can flow from a system in the form of heat or work. The
first law of thermodynamics sets no limit to the amount of the total energy of a system which can
be caused to flow out as work. A limit is imposed, however, as a result of the principle enunciated
in the second law of thermodynamics which states that heat will flow naturally from one energy
reservoir to another at a lower temperature, but not in opposite direction without assistance. This
is very important because a heat engine operates between two energy reservoirs at different tem-
peratures.
Further the first law of thermodynamics establishes equivalence between the quantity of
heat used and the mechanical work but does not specify the conditions under which conversion of
heat into work is possible, neither the direction in which heat transfer can take place. This gap
has been bridged by the second law of thermodynamics.5.2. Performance of Heat Engines and Reversed Heat Engines
Refer Fig. 5.1 (a). A heat engine is used to produce the maximum work transfer from a
given positive heat transfer. The measure of success is called the thermal efficiency of the engine
and is defined by the ratio :Thermal efficiency, ηth =
W
Q 1 ...(5.1)
where, W = Net work transfer from the engine, and
Q 1 = Heat transfer to engine.
For a reversed heat engine [Fig. 5.1 (b)] acting as a refrigerator when the purpose is to
achieve the maximum heat transfer from the cold reservoir, the measure of success is called the
co-efficient of performance (C.O.P.). It is defined by the ratio :
227