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e(ho0n3
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Homework Statement
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.
Homework Equations
[tex]P = \frac{RT}{V/n - b} - \frac{a}{(V/n)^2}[/tex]
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?