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An ideal gas, having ratio of specific heat \( \gamma \) undergoes a process in which its internal energy relates to the volume as \( \mathrm{U}=\alpha \sqrt{\mathrm{V}} \), where \( \alpha \) is a constant. If the gas is expanded from volume \( \mathrm{V}_{1} \) to \( \mathrm{V}_{2} \).
The work performed by gas is :
(A) \( 2 \alpha(\gamma-1)\left[\sqrt{\mathrm{V}_{2}}-\sqrt{\mathrm{V}_{1}}\right] \)
(B) \( \alpha(\gamma-1)\left[\sqrt{\mathrm{V}_{2}}-\sqrt{\mathrm{V}_{1}}\right] \)
(C) \( 2 \alpha(\gamma-1)\left[\mathrm{V}_{2}-\mathrm{V}_{1}\right] \)
(D) \( \alpha(\gamma-1)\left[\mathrm{V}_{2}-\mathrm{V}_{1}\right] \)
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