A) \[\frac{1}{\gamma }\left( \frac{\Delta V}{V} \right)\]
B) \[\frac{1}{{{\gamma }^{2}}}\left( \frac{\Delta V}{V} \right)\]
C) \[-\gamma \left( \frac{\Delta V}{V} \right)\]
D) \[\gamma \left( \frac{\Delta V}{V} \right)\]
Correct Answer: C
Solution :
For an adiabatic process\[P{{V}^{\gamma }}=\]constant. Differentiating both the sides \[dp{{V}^{\gamma }}+p\gamma {{V}^{\gamma -1}}dV=0\] \[\gamma p=\frac{dp}{-dV/V}\] \[\Rightarrow \] \[\frac{dp}{p}=\gamma \frac{dV}{V}\]
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