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`, adiabatic for `B` and isobaric for `C`. If the final pressures are equal for the three samples, Find the ratio of the initial pressures.

Explanation

`(P_A,V,T)underset(A)overset("isothermal")to(P,2V,T_A)`
`(P_B,V,T)underset(B)overset("adiabatic")to(P,2V,T_B)`
`(P_C,V,T)underset(C)overset("isoba ric")to(P,2V,T_C)`
`A:P_AV=P.2VimpliesP_A=2P`
`B:P_BV^(gamma)=P(2V)^(gamma)impliesP_B=2^(gamma)P`
`C:P_C=P`
`P_A:P_B:P_C=2P:2^(gamma)P:P`
`=2:2^((3)/(2)):1`
`=2:2sqrt2:1`