`3` moles of a gas mixture having volume V and temperature `T` is compressed to `1/5`th of the initial volume. Find the change in its adiabatic compressibility if the gas obeys `PV^(19//13)`contant`[R=8.3J//mol-K]`

Explanation

Bulk modulus`B=gammaP`
`compressibilityC=(1/B)=1/(gammaP)`
` and DeltaC=C-C`
`or DC=1/(gamma)[1/p-1/p]`
`PV^(gamma)=p'(V/5)^(gamma)`
` With gamma=19/13andP'=5^(gamma)P,11`
`DeltaC=1/(gammaP)[1/5^(gamma)-1/1]=(13xx0.905)/(19P)`
`But PV=nRT orP=(nRT)/V`
`DeltaC=(13.(0905)V)/(19xx3xx8.317T)=(-0.0248V)/T`