An ideal gas (cp/cv = γ) is taken through a process in which pressure and volume vary as

Question

An ideal gas \((\frac{C_p}{C_v}=γ)\) is taken through a process in which pressure and volume vary as P = aV^b . What is value of b for which the specific heat capacity in the process is zero?

(1) γ 

(2) -γ

(3) 1/γ

(4) -1/γ

Answer 1

(2) -γ

P = aV^b or PV^-b = constant .....(1)

Specific heat capacity C = \(\frac{ΔQ}{nΔT}\) will be zero when ΔQ = 0 and ΔT ≠ 0. The process is adiabatic. We know for adiabatic process

PV^γ =  constant .....(2)

From Eqns. (1) and (2) we have

γ = -b