Question

4.0 g of a gas occupier 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J/K mol. If the speed of sound in this gas at NTP is 952 1/ ms, then the heat capacity at constant pressure is
(Take gas constant R = 8.3 J/K mol)

• A. 8.5 J/K mol
• B. 8.0 J/K mol
• C. 7.5 J/K mol
• D. 7.0 J/K mol

Answer 1

The correct option is B 8.0 J/K mol

given, mass(m)= 4 g

Volume(V) = 22.4 liters

Specific heat capacity of gas at constant volume ($C_v$) = 5.0 J/K mol

Velocity of sound ($v_{sound}$)=952 m/s

As we know that,

Velocity of sound, $v_{sound}=\sqrt{\frac{\gamma PV}{m}}$

$\Rightarrow \gamma =\frac{m{v_{sound}}^2}{PV}$ .......................equation(1)

Also,

$\gamma =\frac{C_p}{C_v}$

So, equation (1) becomes,

$\frac{C_p}{C_v}=\frac{m{v_{sound}}^2}{PV}$

$\Rightarrow C_p=C_v\frac{m{v_{sound}}^2}{PV}$

by substituting the values we get,

$\Rightarrow C_p=\frac{5\times 4\times {10}^{-3}\times {952}^2}{{10}^5\times 22.4\times {10}^{-3}}$

$\Rightarrow C_p$=8.09 J/K mol

$\Rightarrow C_p$ $\approx$8.00 J/K mol