Question

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 $JK^{-1} \, mol^{-1}$. 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 $JK^{-1} \, mol^{-1}$ )

• A. $7.0 \, JK^{-1} \, mol^{-1}$
• B. $8.5 \, JK^{-1} \, mol^{-1}$
• C. $8.0 \, JK^{-1} \, mol^{-1}$
• D. $7.5 \, JK^{-1} \, mol^{-1}$

Answer 1

The Correct Option is C

Since 4.0 g of a gas occupies 22.4 litres at NTP, so the molecular mass of the gas is
$M = 4.0 \, g\, mol^{-1}$
As the speed of the sound in the gas is
$v=\sqrt{\frac{?RT}{M}}$
where $?$ is the ratio of two specific heats, R is the universal gas constant and T is the temperature of the gas.
$\therefore \, \gamma = \frac{Mv^2}{RT}$
Here, $ \, \, \, M = 4.0 \, g \, mol^{-1} = 4.0 \times 10^{-3}kg\, mol^{-1}$
$v=952 \, ms^{-1}, R = 8.3\, JK^{-1}\, mol^{-1}$,
$v= 952\, mol^{-1}, R = 8.3\,JK^{-1}\, mol^{-1} $
and T = 273 K (at NTP)
$\therefore \gamma= \frac{(4.0 \times 10^{-3} \,kg\, mol^{-1})(952\,ms^{-1})^2}{(8.3 JK^{-1} mol^{-1})(273\,K)}=1.6$
By definition,
$\gamma=\frac{C_P}{V_V}$ or $C_P = \gamma C_V$
But $\gamma=1.6$ and $C_V=5.0 \,JK^{-1} \, mol^{-1}$
$\therefore \, \, C_P = (1.6)(5.0 JK^{1} \, mol^{-1})$
$ \, \, \, \, =8.0 \,JK^{-1} mol^{-1}$

Answer 2

Ans: The relation between constant pressure of an ideal gas (Cp) and constant volume (Cv) for an idea gas can be  given by: 

Cp-Cv =R 

Here, R is the molar gas constant, with the value of R= 8.3 JK⁻¹mol⁻¹ 

In the question, the value of Cp is given as 5.0JK⁻¹mol⁻¹ 

Substituting the values in the formula, 

Cp = Cv + R 

Cp = 5.0JK⁻¹mol⁻¹  + 8.3JK⁻¹mol⁻¹ 

 Cp = 13.3JK⁻¹mol⁻¹