During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of C p C v for the gas is :

Step-by-step solution

It is given that P ∝ T 3 ⇒ P T - 3 = constant . . . 1 For an adiabatic process, P V γ = constant . . . 2 Assuming the gas to be a perfect gas, it can be written from equation (2) that P n R T P γ = constant ⇒ P 1 - γ T γ = constant ⇒ P T γ 1 - γ = constant By comparing with equation(1), we get ⇒ γ 1 - γ = - 3 ⇒ γ = - 3 + 3 γ ⇒ 3 = 2 γ ⇒ γ = 3 2