2 moles of a gaseous mixture having volume `V` and temperature `T` are compressed to `(1)/(4)th` of its initiall volume find the change in its adiabatic compressibility if `gamma=(3)/(2)`.

Explanation

Adiabatic compressibility, `C'_(adi)=(1)/(gammaP)`
`Delta'C=C'_(adi)-C'_(adi)=(1)/(gamma' P)-(1)/(gammaP)=(1)/(gamma)[(1)/(P')-(1)/(P)]`
In adiabatic process,
`PV^(gamma)=P'((V)/(4))^(gamma)` i.e., `P'=4^(gamma)P=(4)^((3)/(2))=8P`
`Delta'C=(1)/((3)/(2))[(1)/(8P)-(1)/(P)]=-(7)/(12P)=-(7)/((12nRT)/(V))`
`=-(7V)/(12xx2xx8.3T)=-0.035(V)/(T)(m^2)/(N)`