An ideal gas with adiabatic exponent $(\gamma=1.5)$ undergoes a process in which work done by the gas is same as increase in internal energy of the gas. The molar heat capacity of gas for the process is -
A$C =4 R$
B$C =0$
C$C =2 R$
D$C = R$
Medium
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A$C =4 R$
a (a)
$\Rightarrow \Delta Q =\Delta U+\Delta W$
$\Delta U=\Delta W$
$\Rightarrow \Delta Q =2\Delta U$
$\Rightarrow nC\Delta T =2 nC _{ v } \Delta t $
$\Rightarrow C =2 C _{ v }=\frac{2 R }{\gamma-1}$
$\Rightarrow C =\frac{2 R }{1.5-1}=4 R$
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