An ideal gas `(C_p // C_V = (gamma)` is taken through a process in which the pressure and the volume vary as `P = aV^b`. Find the values of (b) for which the specific heat capacity of the gas for the process is zero.

Explanation

`(C_p/C_v) = gamma` , `C_p-C_v=R`, `C_v=C_p=0`
`pdv = (1)/((b+1))(Rdt)`
implies `0=(b+1)C_vdT+(RdT)`
implies ` (1)/((b+1)) = (-C_v)/R`
implies `b+1= (-R)/(C_v) =(-(C_p-C_v))/(C_v)`
= `-gamma +1`
implies ` b = -gamma`