4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0JK^–1. If the speed of any quantity x 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)

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$7.5 {JK}^{- 1} {mol}^{- 1}$

$7.0 {JK}^{- 1} {mol}^{- 1}$

$8.5 {JK}^{- 1} {mol}^{- 1}$

$8.0 {JK}^{- 1} {mol}^{- 1}$

answer is D.

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Detailed Solution

Molar mass of the gas = 4g/mol

Speed of any quantity x

$\begin{array}{l} V = \sqrt{\frac{γRT}{m}} \Rightarrow 952 = \sqrt{\frac{γ \times 3 .3 \times 273}{4 \times 10^{- 3}}} \\ \Rightarrow γ = 1 .6 = \frac{16}{10} = \frac{8}{5} \end{array}$

Also, $Y = \frac{C_{P}}{C_{V}} = \frac{8}{5}$

So, $C_{P} = \frac{8 \times 5}{5} = 8 {JK}^{- 1} {mol}^{- 1}$

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