One mole of an ideal diatomic gas undergoes an expansion in which the ratio V / T² remains constant throughout. If the temperature of the gas rises by 50 K during this process, find the heat transferred to the gas.

225R
125R
100R
None of the above

Correct answer: 225R

Solution

Since V/T² = constant, V proportional to T². Using pV = nRT, we get p proportional to T⁻¹. This is polytropic with index n = 1/2. Work done W = nR * delta_T / (1 - n) = R * 50 / (1/2) = 100R. Change in internal energy delta_U = Cv * delta_T = (5R/2)(50) = 125R. Total heat Q = 125R + 100R = 225R.

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