Question

$24\text{J}$ of heat is added to a diatomic gas in a process in which the gas performs $8\text{J}$ of work. Find the molar heat capacity of the gas during the process.

• A. $4\text{R}$
• B. $\frac{6R}{5}$
• C. $3\text{R}$
• D. $\frac{15R}{4}$

Answer 1

The correct option is D $\frac{15R}{4}$

Given,
Heat added to the gas $Q=24\text{J}$
work done by the gas $W=8\text{J}$
According to first law of thermodynamics
$Q=\Delta U+W$
$\Rightarrow 24=\Delta U+8$
$\Rightarrow \Delta U=16\text{J}$
But we know that, $\Delta U=n{C}_V\Delta T$
$\Rightarrow n{C}_V\Delta T=16\text{J}...........\left(1\right)$
Also, $Q=nC\Delta T$
Thus, $nC\Delta T=24\text{J}.........\left(2\right)$
from $\left(1\right)$ & $\left(2\right)$ we get,
$\frac{C}{C_V}=\frac{3}{2}\Rightarrow C=\frac{3C_V}{2}$
For a diatomic gas we know that,$C_V=\frac{5R}{2}$
$\therefore C=\frac{3}{2}\times \frac{5R}{2}$
$\Rightarrow C=\frac{15R}{4}$
Thus, option (d) is the correct answer.