# Gibbs Free Energy -- Connection between V, P, N & T

1. Apr 20, 2017

### cake-jake1

1. The problem statement, all variables and given/known data
For a Particular system the following expression for Gibbs free energy is known:

G = -kTN ln (a T^(5/2) / P)

where a is a constant (whose dimensions make the argument of the logarithm dimensionless). Obtain expressions for

a) The entropy, S
b) The connection between V, P, N and T (Called the equation of state)
c) The Internal energy U

2. Relevant equations
a) For entropy it is known that S = - (dG/dT)p where p denotes constant pressure, I understand that this gives a derivative and I believe I have this section correct.

b) Main confusion comes from where to begin but would assume it is is PV=NKT equation.

c) calculating internal energy. It is known that G = U -TS + PV

3. The attempt at a solution
Nothing besides the problem statement was provided in the question and my main issue is with calculating part b.
As far as im aware there are many equations of state, but have read here that V= (dG/dP) due to the relationship dG = -SdT + VdP.
Does this differential for V supply me with the correct answer?

I realise it seems that I may have answered my own question, however I just wish to be certain as its a university exam question with little guidance in our supplied texts.

2. Apr 20, 2017

### stevendaryl

Staff Emeritus
Well, what is the value of $V$ you get from $V = \frac{dG}{dP}$?

3. Apr 21, 2017

### cake-jake1

I ended up getting a Value of V = kTN/P

4. Apr 22, 2017

### stevendaryl

Staff Emeritus
And that's exactly right.