An ideal gas undergoes a process where its molar heat capacity is given by C = C_v + alpha/T, where alpha is a constant. If the gas expands from volume V0 to 2V0 at a constant temperature T0, what is the work done by the gas?

JEE Main · PhysicsHard

$An ideal gas undergoes a process where its molar heat capacity is given by C = C_{v} + \frac{α}{T}, where α is a constant. If the gas expands from volume V_{0} to 2 V_{0} at a constant temperature T_{0}, what is the work done by the gas?$

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Correct answer: A — $R T_{0} ln (2)$

The work done by an ideal gas during an isothermal expansion depends only on the temperature and the change in volume. Since the process is isothermal at T_{0}, the work done is simply n R T_{0} ln (V_{f} / V_{i}), which simplifies to R T_{0} ln (2) for one mole.