(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For the van der Waals equation of state, confirm the following property:

(∂P/∂T)_{V}(∂T/∂V)_{P}(∂V/∂P)_{T}= -1

2. Relevant equations

The van der Waals equation of state is:

P = nRT/(v-nb) - an^{2}/V^{2}

*R, n, a, b are const.

3. The attempt at a solution

I have come up with some partial derivatives, however, I cannot seem to figure out the algebra to make their product equal to -1. Perhaps my derivatives are incorrect?

(∂P/∂T)_{V}= nR/(v-nb)^{-1}

(∂T/∂V)_{P}= P - an^{2}/V^{2}+ 2abn^{3}/V^{3}

(∂V/∂P)_{T}= 1/ (2an^{2}/V^{3}- nRT/(v-nb)^{2})

Any hints or ideas?

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# Chain relation/ triple partial derivative rule

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