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  4. The molar heat capacity of a monoatomic ideal gas undergoing the process PV1 / 2=constant is

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Q. The molar heat capacity of a monoatomic ideal gas undergoing the process $PV^{1 / 2}=constant$ is

NTA AbhyasNTA Abhyas 2020

Solution:

For a polytropic process, specific heat of an ideal gas is given by,
$c=\frac{R}{\gamma - 1}+\frac{R}{1 - n} \, \, \left[n = \frac{1}{2} \, , \, f o r \, t h i s \, p o l y t r o p i c \, p r o c e s s\right]$
$c=\frac{R}{\frac{5}{3} - 1}+2R$
$=\frac{3 R}{2}+2R=\frac{7 R}{2}$