`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. 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

A

Explanation

`M=4gm`
`V=22.4`litre
`C_(V)=5(J)/("Mole K")`
`V_("sound")=952m//sec`
`C_(P)=?`
`V_("sound")=sqrt((gammaPV)/(M))`
`gamma=(M)/(PV)V_("sound")^(2)=(C_(P))/(C_(V))`
`C_(P)=C_(V)((M)/(PV))V_("sound")^(2)`
`=5[(4xx10^(-3))/(10^(-5)xx22.4xx10^(-3))](952)^(2)`
`=(20)/(22.4)xx(952)^(2)xx10^(-5)`
`=809,200xx10^(-5)=8.09J//"moles k"`