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

From the van der Waals equation of state, show that the critical temperature and pressure are given by

[tex]T_{cr} = \frac{8a}{27bR}[/tex]

[tex]P_{cr} = \frac{a}{27b^2}[/tex]

Hint: Use the fact that the [itex]P[/itex] versus [itex]V[/itex] curve has an inflection point at the critical point so that the first and second derivatives are zero.

2. Relevant equations

[tex]P = \frac{RT}{V/n - b} - \frac{a}{(V/n)^2}[/tex]

3. The attempt at a solution

The first and second derivative have powers of [itex]V[/itex] greater than 2. Unfortunately I don't have the skills to solve for [itex]dp/dt = 0[/itex] or [itex]d^2p/dt^2 = 0[/itex]. Perhaps there's a simpler way?

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# Critical Pressure and Temperature of a van der Waals Gas

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