Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio V_a V_d and the ratio V_b V_c is:

Step-by-step solution

For adiabatic process TV ^ -1 = constant aligned & T _ a V _ a ^ -1 = T _ d V _ d ^ -1 & ( V _ a V _ d )^ -1 = T _ d T _ a & T _ b V _ b ^ -1 = T _ c V _ c ^ -1 & ( V _ b V _ c )^ -1 = T _ c T _ b & V _ a V _ d = V _ b V _ c ( array c T _ d = T _ c T _ a = T _ b array ) aligned