(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Critical Pressure and Temperature of a van der Waals Gas

**Physics Forums | Science Articles, Homework Help, Discussion**