The change in internal energy when $20 \mathrm{~g}$ of a gas is heated from $25^{\circ} \mathrm{C}$ to…
The change in internal energy when $20 \mathrm{~g}$ of a gas is heated from $25^{\circ} \mathrm{C}$ to $35^{\circ} \mathrm{C}$ at constant volume is (Specific heat capacity of the gas at constant volume
$74 \mathrm{~J}$
$336 \mathrm{~J}$
$136 \mathrm{~J}$
$168 \mathrm{~J}$
Solution
Mass of gas, $\mathrm{m}=20 \mathrm{~g}$
Change in temperature, $\Delta \mathrm{T}=35^{\circ} \mathrm{C}-25^{\circ} \mathrm{C}=10^{\circ} \mathrm{C}$
Specific heat capacity of the gas. $\mathrm{C}_{\mathrm{v}}=0.2 \mathrm{cal} \mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1}$
The change in internal energy is given by
$
\begin{aligned}
& \mathrm{Q}=\Delta \mathrm{U}=\mathrm{mC}_{\mathrm{v}} \Delta \mathrm{T} \\
& (\Delta \mathrm{V}=0 ; \mathrm{W}=0) \\
& =20 \times 0.2 \times 10 \times 4.200=168 \mathrm{~J}
\end{aligned}
$