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 -

An ideal gas is expanded so that amount of heat given is equal to the

1.	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 -
Answer» <P>`(7)/(5P)` `(5)/(7P)` `(2)/(5P)` `(7)/(3P)` Solution :`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)`