Blundell Thermal Physics · Problem 27.3

Cooling real gases

Physics — Statistical Mechanics · dieterici-gas-inversion-curve

Problem

For a gas obeying Dieterici's equation of state

p(V - b) = RT e^{-a/RTV},

for 1 mole, prove that the equation of the inversion curve is

p = \left(\frac{2a}{b^2} - \frac{RT}{b}\right)\exp\left(\frac{1}{2} - \frac{a}{RTb}\right),

and hence find the maximum inversion temperature

T_{\max}