MHT CET · Chemistry · Thermodynamics (C)

At the same conditions of pressure, volume and temperature, work done is maximum for which gas if all gases have equal masses?

A \(\mathrm{NH}_{3}\)
B \(\mathrm{N}_{2}\)
C \(\mathrm{Cl}_{2}\)
D \(\mathrm{H}_{2} \mathrm{~S}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\mathrm{NH}_{3}\)

Step-by-step Solution

Detailed explanation

When \(p, V\) and \(T\) are same and mass is also same, work done depends only upon molecular mass. \(W \propto \frac{1}{M}(\) where, \(M=\) molecular mass \()\)
Among the given gases, \(\mathrm{NH}_{3}\) has lowest molecular mass, so work done is maximum for it.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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