# Reversible, Isothermal Compression from P1 to P2. How much heat?

1. Feb 9, 2013

### FatPhysicsBoy

1. The problem statement, all variables and given/known data

Compress a body reversibly and isothermally from P1 to P2. How much heat goes in or out?

2. Relevant equations

Maxwells four relations, differential forms of the four thermodynamic potentials (Central, Enthalpy, Gibbs, Helmholtz)

3. The attempt at a solution

My problem is that I've been told that the way this is done is saying that S=S(T,P) therefore dS=(dS/dT)P dT + (dS/dP)T dP Isothermal hence dS= second term and using the fourth maxwell relation you can rewrite it as:

dS = - (dV/dT)P dP and since it is reversible we have dQ=TdS so dQ = -T(dV/dT)P dP [The derivatives inside the brackets are partial derivatives]

Integrating gives: Q = T ∫ dQ between P1 and P2.

The first part of this solution seems fishy where we say that S=S(T,P) I understand that this is still a function of state, however when deriving the Maxwell relations we used either the central equation and the other differential forms of the thermodynamic potentials to give us an idea of what something was a function of e.g. U=U(S,V) since dU=TdS-PdV

2. Feb 10, 2013

Anyone?