Question

The temperature of $5$ moles of a gas at constant volume is changed from $100 \,{}^\circ C$ to $120 \,{}^\circ C$ . The change in internal energy is $80 \, J$ . The total heat capacity of the gas at constant volume (in $J \, K^{- 1}$ ) is

• A. $8$
• B. $4$
• C. $0.8$
• D. $0.4$

Answer 1

Answer: (B)

Number of moles $n=5 \, mol, \, T_{1}=100^\circ C$
$T_{2}=120^\circ C,\Delta U=80 \, J$
Rise in temperature $\Delta T=120-100=20^\circ C$
$\Delta U=ms\Delta T$
$\frac{80}{5}=1\times s\times 20$
$s=\text{0.8} \, J$
$\therefore $ For $5$ mol, $s=\text{0.8}\times 5 \, JK^{- 1}=4 \, JK^{- 1}$