Two different ideal diatomic gases `A` and `B` are initially in the same state. `A` and `B` are then expanded to same final volume through adiabatic and isothermal process respectively. If `P_(A), P_(B)` and `T_(A), T_(B)` represents the final pressure and temperature of `A` and `B` respectively then.

Options

A. `P_(A) lt P_(B)` and `T_(A) lt T_(B)`
B. `P_(A) gt P_(B)` and `T_(A) gt T_(B)`
C. `P_(A) gt P_(B)` and `T_(A) lt T_(B)`
D. `P_(A) lt P_(B)` and `T_(A) gt T_(B)`

Answer

A

Explanation

a. For adiabatic process `P V_(1)^(gamma) = P_(A) V_(2)^(gamma)`
`P_(A) = P ((V_(1))/(V_(2)))^(gamma)`
For isothermal process
`P V_(1) = P_(B) V_(2)`
`P_(B) = P (V_(1))/(V_(2))`
Form (i) and (ii),
`P_(A) lt P_(B)`
and by `PV = nRT T_(A) lt T_(B)`