Question

4.0 g of a gas occupies 22.4 litres 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 = 8.3 $J{K}^{-1}mo{l}^{-1}$ )

• A. $7.0J{K}^{-1}mo{l}^{-1}$
• B. $8.5J{K}^{-1}mo{l}^{-1}$
• C. $8.0J{K}^{-1}mo{l}^{-1}$
• D. $7.5J{K}^{-1}mo{l}^{-1}$

Answer 1

The correct option is C

$8.0J{K}^{-1}mo{l}^{-1}$

Since 4 g of a gas occupies 22.4 litres of volume at NTP.

$\Rightarrow \text{Mass of 1 mol}=4g$

$\therefore M=4g/mol$
Speed of sound in gas is given as,

$V=\sqrt{\frac{\gamma RT}{M}}$

$\Rightarrow \gamma =\frac{M{V}^2}{RT}$

$\text{On substituting}M=4\times {10}^{-3}kg/mol,V=952m/s$

$R=8.3J/Kmol,T=273K\left(NTP\right)$

$\Rightarrow \gamma =\frac{(4\times {10}^{-3}){\left(952\right)}^2}{\left(8.3\right)\left(273\right)}=1.599\approx 1.6$

From definition of $\gamma$

$\gamma =\frac{Cp}{Cv}$

Given,

$C_v=5J/K.mol$

$\therefore C_p=\gamma C_v=1.6\times 5J/K-mol$

Why this question? Caution: Always remember to put molecular weight and all other parameters in S.I units in formula $V_{sound}=\sqrt{\frac{\gamma RT}{M}}$