Second Law of Thermodynamics Statement by Kelvin-Planck

Kelvin-Planck’s statement is based on the fact that the efficiency of the heat engine cycle is never 100%. This means that in the heat engine cycle some heat is always rejected to the low temperature reservoir. The heat engine cycle always operates between two heat reservoirs and produces work.

The statement made by Kelvin-Planck for third law of thermodynamics says, “It is impossible for a heat engine to produce net work in a complete cycle if it exchanges heat only with bodies at a single fixed temperature.” Thus to produce the work the cycle should exchange heat with two reservoirs which are a different temperatures. The high temperature reservoir is called as source and low temperature reservoir is called as sink.

W = Q_H – Q_C

As per the above statement the net work will be produced in the cycle as long as there is difference in temperature between the source and sink. In due course of time if source loses too much heat and sink gains too much heat and their temperatures become equal, the net work produced in the cycle will be zero.

The Kelvin-Planck statement tells the condition for producing work within the cycle, the Carnot’s statement tells maximum work or efficiency that can be obtained within the cycle.

The ratio of the maximum mechanical work obtain to the total heat supplied to the engine is known as maximum thermal efficiency (η_max) of the engine. Mathematically

η_max = Maximum work obtain / Total heat supplied

= Q_H – Q_C/Q_H = 1 – Q_C/Q_H = 1 – T_C/T_H

For a reversible engine, Q_H/T_H = Q_C/T_C