Question

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

Answer 1

`(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`