Virial Coefficients of Van der Waals Gas

Question:
Find all virial coefficients Bi for Van der Waals gas.

Solution:
Virial expansion of the equation of state of a gas is give by,

where ρ = N/V is the molar density, and Bi are virial coefficients.
Equation of state of N moles Van der Waals gas is given by,

…………………………………………………………………………………………………………………………………………………………………………………………………..

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