# Form p = f(V)

1. May 11, 2010

### mahdert

1. The problem statement, all variables and given/known data
Show that the internal energy of a material whose equation of state has the form p = f(V), T is independent of the volume and the pressure. That is

$$\left(\frac{\partial U}{\partial V}\right)_{T} = 0$$

$$\left(\frac{\partial U}{\partial p}\right)_{T} = 0$$

2. Relevant equations
TdS = dU + pdV

3. The attempt at a solution
I know the answer intiutively, i just dont know how one would go about showing it.
I assume that U = f(p,v) and then take the partial derivatives, but I do not see where T comes into play

Last edited: May 11, 2010
2. May 11, 2010

### RTW69

Re: Thermodynamics

Hmmm, Divide through by dv to get T ds/dv= dU/dv + p I am guessing you need to use a maxwell relation to get ds/dv to dp/dT I don't see how you get the partials to equal 0 though.

3. May 11, 2010

### mahdert

Re: Thermodynamics

I am trying to use the fundamental relation: Tds = dU + pdV and equate it with the partial expansion of U = U(V,p), however, I keep getting stuck because I do not know how to get the relationship of the change in U with either a change in V or p for a given temperature.

4. May 11, 2010

### RTW69

Re: Thermodynamics

not sure this helps but If U=U(V,p) you can use the chain rule to get to dU= (partial U/ partial V) dU + (partial U/partial p) dp

5. May 11, 2010

### mahdert

Simple Thermodynamics Problem

Is this a single variable problem?