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$J{K}^{-1} mo{l}^{-1}.$ 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}$$mo{l}^{-1}$)

detailed solution

Correct option is C

Since 4.0g of a gas occupies 22.4 litres at NTP, so the molecular mass of the gas isM=4.0 g mol-1As the speed of the sound in the gas isv=γRTMwhere γ is the ratio of two specific heats, R is the universal gas constant and T is the temperature of the gas.∴γ=Mv2RT Here, M=4.0 g mol-1=4.0×10-3 kg mol-1v=952 ms-1,R=8.3JK-1 mol-1 and T=273 K (at NTP) ∴  γ=4.0×10-3 kg mol-1952 ms-128.3JK-1 mol-1(273 K)=1.6By definition, γ=CpCv   or   Cp=γCv But γ=1.6 and Cv=5.0JK-1 mol-1∴  Cp=(1.6)5.0JK-1 mol-1                  =8.0JK-1 mol-1