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Two containers of equal volume contain t...

Two containers of equal volume contain the same gas at pressure `P_(1)` and `P_(2)` and absolute temperature `T_(1)` and `T_(2)`, respectively. On joining the vessels, the gas reaches a common pressure `P` and common temperature `T`. The ratio `P//T` is equal to

A

`(P_(1))/(T_(1))+(P_(2))/(T_(2))`

B

`(1)/(2)[(P_(1))/(T_(1))+(P_(2))/(T_(2))]`

C

`(P_(1)T_(2)+P_(2)T_(1))/(T_(1)+T_(2))`

D

`(P_(1)T_(2)-P_(2)T_(1))/(T_(1)-T_(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
For a closed system, the total mass of gas or the number of moles remains constant.
Let `n_(1)` and `n_(2)` be number of moles of gas in container 1 and container 2 respectively. Then
`P_(1)V=n_(1)RT_(1)orn_(1)=(P_(1)V)/(RT_(1))`
`P_(2)V=n_(2)RT_(2)orn_(2)=(P_(2)V)/(RT_(2))`
`P(2V)=(n_(1)+n_(2))RT" "...(i)`
Substituting the values of `n_(1)andn_(2)` in equation (i), we get
`P(2V)=((P_(1)V)/(RT_(1))+(P_(2)V)/(RT_(2)))RTor(P)/(T)=(1)/(2)((P_(1))/(T_(1))+(P_(2))/(T_(2)))`
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