- #1

tjlaxs

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## Homework Statement

For temperatures [tex]T >> T_C[/tex] (critical temperature) derive the heat capacity at constant pressure [tex]C_P[/tex] from van der Waals equation.

## Homework Equations

Critical temperature:

[tex]T_C = \frac{2N(V - Nb)^2}{kV^2}[/tex]

[tex]T_C[/tex] is derived from the fact that it exist at the point in which

[tex](\frac{\mathrm{d}P}{\mathrm{d}V})_T = 0[/tex] but I'm pretty certain that this is not needed in this derivation.

Van der Waals equation:

[tex](P + aN^2/V^2)(V - Nb) = NkT[/tex]

Heat capacity:

[tex]C_P = (\frac{\mathrm{d}U}{\mathrm{d}T})_P + P(\frac{\mathrm{d}V}{\mathrm{d}T})_P[/tex]

## The Attempt at a Solution

I've tried to get the point in this. The first term in the equation of [tex]C_P[/tex] is easy, but the problem is the second term.

If I try to solve for the [tex]V[/tex] in the van der Waals equation I get a long equation set to derive. And I don't think this is what is the point of the exercise.

Is there another approach or something to simplify the van der Waals equation before the derivation?