Three samples of the same gas A,B and C (gamma=3//2) have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for A. Isobaric for B and isothermal for C. If the final pressures are equal for all three samples, find the ratio of their initial pressures

Three samples of the same gas A,B and C (gamma=3//2) have initially eq

1.	Three samples of the same gas A,B and C (gamma=3//2) have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for A. Isobaric for B and isothermal for C. If the final pressures are equal for all three samples, find the ratio of their initial pressures
Answer» `2:1:SQRT(2)` `2sqrt(2):1:2` `sqrt(2):1:2` `sqrt(2):2:1` 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, the process is ADIABATIC `P_(A)(V)^(3//2)=P(2V)^(3//2), P_(A)=P2^(3//2)` For B, the process is isobaric `P_(B)=P` for C, the process is isothermal `P_(C )(V)=P(2V),2P` Hence `P_(A):P_(B):P_(C )=2^(2//3):1:2=2sqrt(2):1:2`