The change in the internal energy of 3 moles of a gas heated at constant volume from $20^{\circ} \mathrm{C}$…
The change in the internal energy of 3 moles of a gas heated at constant volume from $20^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ is $1080 \mathrm{~J}$. The molar specific heat of the gas at constant volume is $\mathrm{J} \mathrm{mol}^{-1}$ $\mathrm{K}^{-1}$ is.
$21$
$18$
$24$
$12$
Solution
Change of internal energy at a constant volume is
$
\begin{aligned}
\Delta U & =n C_V \Delta T \\
C_V & =\frac{\Delta U}{n \Delta T}
\end{aligned}
$
Here,
$
\begin{aligned}
\Delta U & =1080 \mathrm{~J} \\
n & =3 \text { moles } \\
\Delta T & =40-20=20^{\circ} \mathrm{C} \text { or } 20 \mathrm{~K}
\end{aligned}
$
Hence, $C_V=\frac{1080}{3 \times 20}=18 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$