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A monoatomic ideal gas undergoes thermodynamic process according to relation ${PT}^{2} =$ constant. If molar heat capacity of gas at constant volume is ‘ $C_{v}$ ’ then its molar heat capacity for given process is

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3 $C_{v}$

4 $C_{v}$

$\frac{5}{4}$ $C_{v}$

$\frac{3 C_{v}}{2}$

answer is A.

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Detailed Solution

$\begin{array}{l} P v^{x} = c o n s t \\ C = C v + \frac{R}{1 - x} \end{array}$

here ${PT}^{2} = constant \Rightarrow {PV}^{\frac{3}{2}} = constant$

So $C = 3 C_{v}$

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