Answer to Question #120758 in Molecular Physics | Thermodynamics for Abhishek

Question

State Kelvin — Planck and Clausius statements of the second law of thermodynamics. Show by deduction that both the statements are equivalent.

Answer 1

The second law of thermodynamics sets limits on the direction of processes that can occur in thermodynamic systems, and excludes the possibility of creating a perpetual motion machine of the second kind. In fact, Sadi Carnot already arrived at this result in his essay "On the driving force of fire and on machines capable of developing this force." However, Carnot relied on the concepts of the caloric theory and did not give a clear formulation of the second law of thermodynamics. This was done in the years 1850-1851 independently by Clausius and Kelvin. There are several different, but at the same time equivalent formulations of this law.

Kelvin's postulate: “A circular process is impossible, the only result of which would be the production of work by cooling the heat reservoir.” Such a circular process is called the Thomson-Planck process, and it is postulated that such a process is impossible.

Clausius postulate: "Heat cannot spontaneously transfer from a body less heated to a body more heated." The process in which no other changes take place other than the transfer of heat from the cold body to the hot one is called the Clausius process. The postulate states that such a process is impossible. Heat can spontaneously transfer only in one direction, from a warmer body to a less heated one.

Taking as a postulate the impossibility of the Thomson-Planck process, we can prove that the Clausius process is impossible, and vice versa, from the impossibility of the Clausius process, it follows that the Thomson-Planck process is also impossible.