Critical Parameters

Consider a system described by the Dietrici equation of state

where A, B, R are constants and P, V, τ, and n are the pressure, volume, temperature, and number of moles. Calculate the critical parameters, i.e., the values of P, V, and τ at the critical point.

SOLUTION

At the critical point we have the conditions

(1)

(2)

Substituting the Dietrici equation into (1) gives

(3)

so

(4)

Using the second criterion (2) gives

(5)

(6)

where

by (3), so

(7)

by (6). (7) then yields

which combined with (4) gives

(8)

(9)

Substituting this result in the RHS of (4) finally yields

(10)

(11)

Rearranging the original equation of state gives

(12)