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  4. A monoatomic gas performs a work of (Q/4) where Q is the heat supplied to it. The molar heat capacity of the gas will be R during this transformation. Where R is the gas constant.

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Q. A monoatomic gas performs a work of $\frac{Q}{4}$ where $Q$ is the heat supplied to it. The molar heat capacity of the gas will be _______$R$ during this transformation.
Where $R$ is the gas constant.

JEE MainJEE Main 2022Kinetic Theory

Solution:

$\Delta Q =\Delta E + WD \Rightarrow Q =\Delta E +\frac{ Q }{4}$
$\Rightarrow n \frac{3 R }{2} \Delta T =\Delta E =\frac{3 Q }{4}$
$\therefore n \Delta T =\frac{ Q }{2 R }$
$\therefore C =2 R$