WBJEE 2026 Physics and Chemistry Paper

Concept:The standard van der Waals equation for $n$ moles of a real gas is compared with the given form to determine the value of $n$.Explanation:For $n$ moles of a real gas, the van der Waals equation is:$$\left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT$$The given equation is:$$\left(P+\frac{a}{4V^2}\right)\left(V-\frac{b}{2}\right)=\frac{RT}{2}$$Comparing the coefficient of $\frac{a}{V^2}$ gives:$$n^2 = \frac{1}{4} \Rightarrow n = \frac{1}{2}$$Comparing the volume correction term gives:$$nb = \frac{b}{2} \Rightarrow n = \frac{1}{2}$$Comparing the right-hand side gives:$$nRT = \frac{RT}{2} \Rightarrow n = \frac{1}{2}$$All three comparisons confirm $n = \frac{1}{2}$.Since the van der Waals equation applies to real gases, the given form is valid for $\frac{1}{2}$ mole of a real gas.Answer:Option D: $\frac{1}{2}$ mole of a real gas.