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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 J K⁻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 J K⁻¹ mol⁻¹)

1. 7.5 J K⁻¹ mol⁻¹
2. 7.0 J K⁻¹ mol⁻¹
3. 8.5 J K⁻¹ mol⁻¹
4. 8.0 J K⁻¹ mol⁻¹

Correct answer: 7.5 J K⁻¹ mol⁻¹

Solution

The speed of sound in a gas is given by v = sqrt(γRT/M), where γ = Cp/Cv. Using the given data, γ can be calculated as γ = v²M/(RT). Substituting γ = Cp/Cv, we find Cp = γ * Cv. After calculations, Cp = 7.5 J K⁻¹ mol⁻¹.

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