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4.0 g of a gas occupies 22.4 L at NTP. T...

4.0 g of a gas occupies `22.4 L` at NTP. The specific heat capacity of the gas at constant volume is `50 KJ^(-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 JK^(-1) mol^(-1)` )

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)`

Text Solution

Verified by Experts

The correct Answer is:
A
`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"`
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