Is there a clear analogy here between volume and entropy? Looking at: (dQ)/T=dS, (dW)/P=dV

Bernard Boyer

Bernard Boyer

Answered question

2022-07-20

Is there a clear analogy here between volume and entropy? Looking at: d Q T = d S , d W P = d V

Answer & Explanation

minotaurafe

minotaurafe

Beginner2022-07-21Added 22 answers

The general expression for the first law (using the OP sign convention) is: d E = δ q + δ w. When the process is reversible it is possible to write: d E = T d S + P d V. This expression is the diferential of a function E(S,V):
d E = E S d S + E V d V
The similarity between V and S in the expression is that both are independent functions of the internal energy, while temperature and pressure are partial derivatives:
T = E S
P = E V

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