Three samples X , Y , and Z of same gas have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for X, adiabatic for Y and isobaric for Z. If the final pressures are equal for the three samples, the ratio of the initial pressures is (r=3 / 2)

Step-by-step solution

Initial Pressures for Volume Expansion Processes Let V₀ be the initial volume and V_f = 2V₀ the final volume for all samples. Final pressure is P_f for each. Given = 3/2 . For the isothermal process (Sample X), since PV is constant: P_X V₀ = P_f (2V₀) P_X = 2P_f For the adiabatic process (Sample Y), as PV^ is constant: P_Y V₀^ 3/2 = P_f (2V₀)^ 3/2 P_Y = P_f 2^ 3/2 = 2 2 P_f In the isobaric process (Sample Z), pressure remains constant: P_Z = P_f The ratio of initial pressures is: P_X : P_Y : P_Z = 2P_f : 2 2 P_f :