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The temperature of 5 moles of a gas at constant volume is changed from $100^{\circ} \mathrm{C}$ to $120^{\circ} \mathrm{C}$. The change in internal energy is $80 \mathrm{~J}$. The total heat capacity of the gas at constant volume will be in $\mathrm{J} / \mathrm{K}$ is :
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The correct answer is:
4
$n=5$ moles, $T_1=100^{\circ} \mathrm{C}$
$T_2=120^{\circ} \mathrm{C}, \Delta U=80 \mathrm{~J}$
Rise in temperature $\Delta t=120-100=20^{\circ} \mathrm{C}$
$\Delta U=m s \Delta t$
$\frac{80}{5}=1 \times s \times 20$
$s=0.8 \mathrm{~J}$
$\therefore \quad$ For 5 moles, $s=0.8 \times 5 \mathrm{~J} / \mathrm{K}$
$=4 \mathrm{~J} / \mathrm{K}$
$T_2=120^{\circ} \mathrm{C}, \Delta U=80 \mathrm{~J}$
Rise in temperature $\Delta t=120-100=20^{\circ} \mathrm{C}$
$\Delta U=m s \Delta t$
$\frac{80}{5}=1 \times s \times 20$
$s=0.8 \mathrm{~J}$
$\therefore \quad$ For 5 moles, $s=0.8 \times 5 \mathrm{~J} / \mathrm{K}$
$=4 \mathrm{~J} / \mathrm{K}$
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