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Comprehension IV
An ideal gas whose adiabatic exponent equals \( \gamma \) is expanded according to the law \( P=\alpha V \), where \( \alpha \) is a constant. The initial volume of the gas is equal to \( V_{0} \). As a result of expansion, the volume increases 4 times.
What is the magnitude of work performed by the gas?
(a) \( \frac{15 \alpha V_{0}^{2}}{\gamma-1} \)
(b) \( \frac{\alpha V_{0}^{2}}{\gamma-1} \)
(c) \( \frac{15 \alpha V_{0}^{2}}{2} \)
(d) \( \frac{15 \alpha(\gamma+1) V_{0}^{2}}{2(\gamma-1)} \)
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