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 _____ `(R=8.3 "JK"^(1) "mol"^(-1))`

Options

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

Answer

B

Explanation

Velocity of sound ,
`v=sqrt((gammaRT)/M)`
`therefore gamma=(mv^2)/(RT)`
`=(4xx10^(-3)xx(952)^2)/(8.3xx273)`
`=3625.2/2265.9`
`therefore gamma=1.599`
`therefore gamma approx` 1.6
`therefore` The heat capacity at constant pressure ,
`C_P=gammaC_V=1.6xx5.0=8.0 "JK"^(1) "mol"^(-1)`