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Comprehension VI
An ideal gas with the adiabatic exponent \( \gamma \) undergoes a process in which its internal energy relates to the volume as \( U=a . V^{\alpha} \), where \( a \) and \( \alpha \) are constants.
What is the magnitude of work performed by the gas to increase its internal energy by \( \Delta U ? \)
(a) \( \frac{R \cdot \Delta U}{\alpha(\gamma-1)} \)
(b) \( \frac{\Delta U}{\alpha(\gamma-1)} \)
(c) \( \frac{\Delta U \cdot(\gamma-1)}{\alpha} \)
(d) \( \frac{\Delta U \cdot \alpha}{(\gamma-1)} \)
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