Q122 / 160 · AP EAMCET 2003 · Physics

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 :

  • A
    8
  • Correct answer
    B
    4
  • C
    0.8
  • D
    0.4

Solution

$n=5$ 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, $s=0.8 \times 5 \mathrm{~J} / \mathrm{K}$ $=4 \mathrm{~J} / \mathrm{K}$

Hence, the correct answer is option: 'B'.

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