Kinetic Theory - Result Question 27
27. $\quad 4.0 g$ of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is $5.0 JK^{-1}$. If the speed of sound in this gas at NTP is $952 ms^{-1}$, then the heat capacity at constant pressure is (Take gas constant $R=$ $8.3 JK^{-1} mol^{-1}$ )
[2015 RS]
(a) $7.5 JK^{-1} mol^{-1}$
(b) $7.0 JK^{-1} mol^{-1}$
(c) $8.5 JK^{-1} mol^{-1}$
(d) $8.0 JK^{-1} mol^{-1}$
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Answer:
Correct Answer: 27. (d)
Solution:
- (d) Molar mass of the gas $=4 g / mol$ Speed of sound
$v=\sqrt{\frac{\gamma RT}{m}} \Rightarrow 952=\sqrt{\frac{\gamma \times 3.3 \times 273}{4 \times 10^{-3}}}$
$\Rightarrow \gamma=1.6=\frac{16}{10}=\frac{8}{5}$
Also, $\gamma=\frac{C_P}{C_V}=\frac{8}{5}$
So, $C_P=\frac{8 \times 5}{5}=8 JK^{-1} mol^{-1}$
$ [C_V=5.0 JK^{-1} \text{ given }] $
