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

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Homework Help Overview

The discussion revolves around the Gibbs free energy expression for a specific system, focusing on deriving expressions for entropy, the equation of state relating volume, pressure, number of particles, and temperature, as well as internal energy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between Gibbs free energy and its derivatives to derive entropy and volume. There is an attempt to connect the equation of state to known equations like PV = NKT. Questions arise regarding the correct application of derivatives and the implications of the equations of state.

Discussion Status

Some participants have provided values for volume derived from the expression V = (dG/dP), and there appears to be agreement on the value obtained. However, the overall discussion includes exploration of different aspects of the problem without reaching a final consensus on all parts.

Contextual Notes

The original poster expresses uncertainty due to the lack of guidance in provided texts and the nature of the university exam question, indicating a need for clarity on the derivations involved.

cake-jake1
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Homework Statement


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

Homework 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

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 I am 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 realize 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.
 
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Well, what is the value of V you get from V = \frac{dG}{dP}?
 
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I ended up getting a Value of V = kTN/P
 
cake-jake1 said:
I ended up getting a Value of V = kTN/P

And that's exactly right.
 

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