Kinetic Theory - Result Question 37
37. For a certain gas the ratio of specific heats is given to be $\gamma=1.5$. For this gas
(a) $C_V=3 R / J$
(b) $C_P=3 R / J$
(c) $C_P=5 R / J$
(d) $C_V=5 R / J$
[1990]
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Answer:
Correct Answer: 37. (b)
Solution:
(b) $\gamma=\frac{C_P}{C_V}=\frac{15}{10}=\frac{3}{2} \Rightarrow C_V=\frac{2}{3} C_P$
$C_P-C_V=\frac{R}{J} \Rightarrow C_P-\frac{2}{3} C_P=\frac{R}{J}$
$\Rightarrow \frac{C_P}{3}=\frac{R}{J} \Rightarrow C_P=\frac{3 R}{J}$
38 .
(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 $Q_p=207 J \Rightarrow Q_v \cong 124 J$
