Answer to Question #95816 in Molecular Physics | Thermodynamics for Angshuman thakuria

Question

Obtain van der wall's equation of state of real gases. What is the limitations of this equation.?

Answer 1

The equation of state for a mole of an ideal gas PV = RT,

Part of the volume is occupied by the molecules themselves, i.e. free volume less; pressure on the wall due to the interaction of molecules is less than that of an ideal gas by an amount proportional to the square of the concentration of molecules. Based on the foregoing, the original equation must be adjusted to $(p + \frac{a}{V^2})(V-b) = RT.$

The van der Waals equation is capable of conveying the observed phenomenon of gas condensation and indicates the existence of critical gas parameters, establishing a relationship between them. However, it only approximately describes processes with real gases; to increase accuracy, it is necessary to consider the constants a and b to be temperature-dependent, but this approach does not eliminate all the problems and contradictions.