Question

$4.0g$ of a gas occupies $22.4L$ at NTP. The specific heat capacity of the gas at constant volume is $5.0J{K}^{-1}mo{l}^{-1}$. If the speed of sound in this gas at NTP is $952m{s}^{-1}$, then the heat capacity at constant pressure is.
(Take gas constant $R=8.3J{K}^{-1}mo{l}^{-1}$)

• A. $8.5J{K}^{-1}mo{l}^{-1}$
• B. $8.0J{K}^{-1}mo{l}^{-1}$
• C. $87.5J{K}^{-1}mo{l}^{-1}$
• D. $7.0J{K}^{-1}mo{l}^{-1}$

Answer 1

The correct option is B $8.0J{K}^{-1}mo{l}^{-1}$

No of moles is 1 (given).
Molar mass of the gas $m=4gm=4\times {10}^{-3}kg$.
Speed of sound $v=\sqrt{\frac{\gamma RT}{m}}$
$\Rightarrow v^2=\frac{\gamma RT}{m}=\frac{\gamma \times 8.3\times 273}{4\times {10}^{-3}}$
$(952{)}^2=\frac{\gamma \times 3\times 273}{4\times {10}^{-3}}$
$\Rightarrow \gamma =\frac{8}{5}$
Thus $\gamma =\frac{C_p}{C_v}=\frac{8}{5}$

where $C_v=5J{K}^{-1}mo{l}^{-1}$ (given)
$⟹$ $C_p=5\times \frac{8}{5}=8.0$ $J{K}^{-1}mo{l}^{-1}$