Tds Equation and Entropy

Studiot

The material you require to answer all three of your questions was presented by Caratheodory in 1909.

You will find good discussions of this in books by

Wilson (1951) Thermodynamics and Statistical Mechanics (Cambridge University Press)

Pippard (1964) Classical Themodynamics (Oxford University Press)

Carrington (1994) Basic Thermodynamics (Oxford University Press)


All three follow and further develop Caratheodory's highly mathematical method and discuss the conditions under which dw and dq may be integrated and prove mathematically that entropy is a state function.

All three are highly readable, but different, and contain penetrating insights into classical thermodynamics.

I'm sorry but there are no short form solutions to this. Each proof is many pages long.