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An ideal gas is expanded so that amount ...

An ideal gas is expanded so that amount of heat given is equal to the decrease in internal energy. The gas undergoes the process `TV^(1//5)=` constant. The adiabatic compressibility of gas when pressure is P, is -

A

`(7)/(5P)`

B

`(5)/(7P)`

C

`(2)/(5P)`

D

`(7)/(3P)`

Text Solution

Verified by Experts

The correct Answer is:
B
`dQ= -dU`
`C= -C_(V) = (-R)/(gamma-1)=(+R)/(gamma-1)+(P)/(n) (dV)/(dT)`
`-(P)/(n) (dV)/(dT)= (2R)/(gamma-1)`
`T^(5)V=` const.
`V=("const.")/(T^(5))`
`(dV)/(dT)= -5("const")/(T^(6))`
`PV=nRT`
`P//n=RT//V`
`+ (RT)/("const.")T^(5) xx (-5 ("const")/(T^(6)))=(2R)/(gamma-1)`
`(5)/(2)=(1)/(gamma-1) rArr gamma-1 =2//5`
`gamma=7//5`
adiabatic compressibility
`beta=(1)/(gammaP)=(5)/(7P)`
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