A) \[T{{V}^{\gamma }}\] = constant
B) \[{{T}^{\gamma }}V\] = constant
C) \[T{{V}^{1-\gamma }}\] = constant
D) \[T{{V}^{\gamma -1}}\] = constant
Correct Answer: D
Solution :
In an adiabatic process \[PV{{}^{\gamma }}=\text{constant}\] Using ideal gas equation, PV = RT \[\therefore \] \[\left( \frac{RT}{V} \right){{V}^{\gamma }}=\text{constant}\] or \[T{{V}^{\gamma -1}}=\text{constant}\](as R is a gas constant)
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