Question

The molar heat capacity in a process of a diatomic gas, if it does a work of $\frac{Q}{4},$ when a heat of $Q$ is supplied to it is

• A. $\frac{2}{5}R$
• B. $\frac{5}{2}R$
• C. $\frac{10}{3}R$
• D. $\frac{6}{7}R$

Answer 1

The correct option is C $\frac{10}{3}R$

From first law of thermodynamics,
$Q=W+\Delta U$
$\Rightarrow Q=\frac{Q}{4}+\Delta U$ $(\because W=Q/4)$
$\Rightarrow \Delta U=\frac{3}{4}Q$
Let $C$ be the molar specific heat and $n$ be the number of moles
$\Rightarrow n{C}_v\Delta T=\frac{3}{4}nC\Delta T$
$(\because Q=nC\Delta T)$
$\Rightarrow C_v=\frac{3}{4}C$
$\Rightarrow C=\frac{4}{3}{C}_v=\frac{4}{3}\left(\frac{f}{2}R\right)$
For diatomic gas $f=$ 5
$C=\frac{4}{3}\times \frac{5}{2}R=\frac{10}{3}R$
Hence, option $\left(c\right)$ is the correct answer.