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

Answer: (C)

$\frac{10}{3}R$

Given: Diatomic gas doing work of $W=\frac{Q}{4}$ when $△Q=Q$ heat is supplied.

Solution:

From first law of thermodynamics, we know that $△Q=△U+W$

Putting the given values in above equation,we get,

$△U=\frac{3Q}{4}$

We know that $△U=\frac{nR△T}{\gamma -1}$ $\to$ (1)

The value of $\gamma$ for a diatomic gas is$\frac{7}{5}$. Putting in equation (1), we get,

$n△T=\frac{3Q}{10R}$ $\to$ (2)

Also we know that $Q=nC△T$ $\to$ (3)

where $C$ is molar specific heat

Putting the value of $n△T$ from equation 2 in equation 3 we get,

$\frac{3CQ}{10R}=Q$

$\therefore C=\frac{10R}{3}$

Hence the correct option is C.