The van der Waals equation of state is

When the temperature of a given gas is equal to its critical temperature, the gas has a state at which the pressure as a function of V at constant T and n exhibits an inflection point at which dP/dV = 0 and d²P/dV² = 0. This inflection point corresponds to the critical point of the gas. Write P as a function of T, V, and n and write expressions for dP/dV and d²P/dV², treating T and n as constants. Set these two expressions equal to zero and solve the simultaneous equations to find an expression for the pressure at the critical point.

Transcribed Image Text:

n?a P + (V – nb) = nRT. V2