`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

Options

A. 7.5J `K^(-1)" mol"^(-1)`
B. 7.0 J `K^(-1)" mol"^(-1)`
C. 8.5 J `K^(-1)" mol"^(-1)`
D. 8.0 J `K^(-1)" mol"^(-1)`

Answer

D

Explanation

Velocity
`V= sqrt((gamma R T)/(m)) implies 952xx952 implies (gammaxx3.3xx273)/(4xx10^(-3))`
`implies gamma=1.6=(16)/(10)=(8)/(5)`
Now, `gamma= (C_P)/(C_V)=8/5 implies C_P=(8xx5)/(5) = 8 JK^(-1)"mol"^(-1)`.