Kinetic Theory Ques 1
1. One mole of an ideal monoatomic gas requires $207 \mathrm{J}$ heat to raise the temperature by $10 \mathrm{K}$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10 \mathrm{K}$, the heat required is
[Given the gas constant $R=8.3 \mathrm{J} / \mathrm{mol}$. K]
[1990]
(a) $198.7 \mathrm{J}$
(b) $29 \mathrm{J}$
(c) $215.3 \mathrm{J}$
(d) $124 \mathrm{J}$
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Answer:
Correct Answer: 1.(d)
Solution: (d) $C_p=\frac{5}{2} R$ and $C_v=\frac{3}{2} R$
We know that $Q_v=n C_v \Delta T$ and $Q_p=n C_p \Delta T$ $\Rightarrow \frac{Q_v}{Q_p}=\frac{3}{5}$.
Given $Q_p=207 \mathrm{J} \Rightarrow Q_v \cong 124 \mathrm{J}$
BETA
