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 ${J K}^{- 1} {m o l}^{- 1}$ . If the speed of sound in this gas at NTP is 952 ${m s}^{- 1}$ , then the heat capacity at constant pressure is (Take gas constant R=8.3 ${J K}^{- 1} {m o l}^{- 1}$ )

8.5 {J K}^{- 1} {m o l}^{- 1}

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8.0 {J K}^{- 1} {m o l}^{- 1}

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7.5 {J K}^{- 1} {m o l}^{- 1}

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7.0 {J K}^{- 1} {m o l}^{- 1}

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Solution

The correct option is B $8.0 {J K}^{- 1} {m o l}^{- 1}$
No. Of moles, n=1 (since the gas occupies 22.4 l at NTP)
Molar mass of gas,m = 4g = $4 \times 10^{- 3} K g$
Speed of sound, v = $(\frac{γ R T}{m})^{\frac{1}{2}}$
$\Rightarrow v^{2} = \frac{γ R T}{m}$
$\Rightarrow γ = \frac{v^{2} m}{R T}$
$\Rightarrow γ = \frac{952 \times 952 \times 4 \times 10^{- 3}}{8.314 \times 273}$
$\Rightarrow γ = 1.6$
$γ = \frac{C_{p}}{C_{v}} = 1.6$
Since $C_{v} = 5 J / K m o l$ ,
$R i g h t a r r o w C_{p} = 1.6 \times 5 = 8 J / m o l K$
Hence, the correct option is B.

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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−1mol−1. If the speed of sound in this gas at NTP is 952ms−1, then the heat capacity at constant pressure is (Take gas constant R=8.3JK−1mol−1)