JEE Advanced 2020 · Paper 1 · Chemistry Q7

ChemistryMultiple correct+4 / -2Question 25 of 54

In thermodynamics, the $P-V$ work done is given by

$w = -\int dV\,P_{\text{ext}}.$

For a system undergoing a particular process, the work done is,

$w = -\int dV\left(\frac{RT}{V-b} - \frac{a}{V^2}\right).$

This equation is applicable to a

system that satisfies the van der Waals equation of state.

process that is reversible and isothermal.

process that is reversible and adiabatic.

process that is irreversible and at constant pressure.

Answer and worked solution

Official answer: A, B, C

The integrand $\dfrac{RT}{V-b}-\dfrac a{V^2}$ is the van der Waals pressure of the gas.

Writing $w=-\int P_{ext}\,dV$ with $P_{ext}$ equal to the gas pressure needs two things:

Any reversible path qualifies, isothermal (B) or adiabatic (C), since $T$ can change along the path inside the integral.

An irreversible constant-pressure process has a constant $P_{ext}$ , not this function of $V$ . So (D) is false.

(A), (B), (C)

JEE Advanced 2020 · Paper 1, Chemistry question 7