A gas in container `A` is in thermal equilibrium with another gas in container `B`. Both contain equal masses of the two gases. Which of the following can be true ?

Options

A. `P_(A) V_(A) = P_(B) B_(B)`
B. `P_(A) = P_(B), V_(A) != V_(B)`
C. `P_(A) != P_(B), V_(A) = V_(B)`
D. `(P_(A))/(V_(A)) = (P_(B))/(V_(B))`

Answer

B, C

Explanation

Accroding to the problem, mass of gases is equal so number of moles will not be equal,` i.e., mu _(A)!= mu _(B)`
From ideal gas equation, `PV=mu RT`
`:. (P_(A)V_(A))/(mu_(A))=(P_(B)V_(B))/( mu_(B))(` as temperatures of the containers are equal `)`
From this relation it is clear that if `P_(A) = P_(B),` then
`(V_(A))/(V_(B))=(mu_(A))/( mu_(B)) != 1`
`i.e., V_(A)!= V_(B)`
Similarly, if `V_(A)=V_(B)`
`(P_(A))/( P_(B))=( mu_(A))/( mu_(B))!= 1`
`i.e., P_(A)!= P_(B)`