Two cylinders \(A\) and \(B\) fitted with pistons, contain equal number of moles of an ideal monoatomic gas at \(400 \mathrm{~K}\). The piston of \(A\) is free to move while that of \(B\) is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in \(A\) is \(42 \mathrm{~K}\), the rise in temperature of the gas in \(B\) is \((\gamma=5 / 3)\)

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.