Question

4.0 g of a gas occupies 22.4L at NTP. The specific heat capacity of the gas at constant volume is 5.0 JK-1mol-1. If the speed of sound in the gas at NTP is 952 ms-1, then the heat capacity at constant pressure is.

(Take gas constant R=8.3 JK-1mol-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

Answer: (B)

7.5 JK-1mol-1

No of moles is 1 (given).
Molar mass of the gas $m=4gm=4\times {10}^{-3}kg$.
Speed of sound $v=\sqrt{\frac{\gamma RT}{m}}$
$\Rightarrow v^2=\frac{\gamma RT}{m}=\frac{\gamma \times 8.3\times 298}{4\times {10}^{-3}}$
$(952{)}^2=\frac{\gamma \times 8.3\times 298}{4\times {10}^{-3}}$
$\Rightarrow \gamma =\frac{7.5}{5}$
Thus, $\gamma =\frac{C_p}{C_v}=\frac{7.5}{5}$
where $C_v=5J{K}^{-1}mo{l}^{-1}$ (given)
$⟹$ $C_p=5\times \frac{7.5}{5}=7.5$ $J{K}^{-1}mo{l}^{-1}$