Three samples of the same gas A , B and C ( γ = 3 2 ) have equal volume initially. Now, the volume of each sample is doubled. For A , the process is adiabatic; for B , it is isobaric and for C , the process is isothermal. If the final pressures are equal for all the three samples, the ratio of their initial pressures is

Step-by-step solution

Let P A , P B , P C be the initial pressures of the three samples and P be the final pressure of each. For A process is adiabatic, P V γ   =   constant ∴     P A ( V ) 3 / 2   =   P   ( 2 V ) 3 / 2   ⇒   P A   =   2 3 / 2   P For B, the process is isobaric ∴     P B   =   P For C, the process is isothermal, P V   = constant ∴     P C ( V ) =   P ( 2 V )   ⇒   P C =