Question

A monoatomic gas performs a work of $\frac Q4$ 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.

Answer 1

According to the first law of thermodynamics,
$Δ U = Δ Q -\frac {Δ Q}{4}$

$Δ U = \frac 34Δ Q$

$⇒ nC_vΔT = \frac 34nCΔT$

$⇒ C = \frac {4C_v}{3}$
$= 2R$

So, the answer is $2$.