Three samples A, B and C of the same gas `(gamma = 1.5)` have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for A, adiabtic for B and isobaric for C. If the final pressures are equal for the three samples, Find the ratio of the initial pressures.

Explanation

`V_A = V_B =V_C` `T_A = T_B= T_C`
For A the process is isothermal
`P_AV_A = P'_A2V_A`
implies `P'_A = P_A xx (1)/(2)`
For B, the process is adiabatic
`P_BV_B^gamma = P_B'(2V_B)^gamma`
implies `P_B' = (P_B)/(2^1.5)`
For C the process is adiabatic
`(V_c)/(T_c) = (V'_c)/(T'_c) implies (V_c)/(T_c) = (2V_c)/(T'_c)`
implies `T_c' = 2 T_c`
Final Pressure are equal
`(P_A)/(2) = (P_B)/(2.15)=P_c`
implies `P_A:P_B :P_C = 2:2^1.5:1`