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The ratio of pressure of the same gas in...

The ratio of pressure of the same gas in two containers in `(n_(1) T_(1))/(n_(2) T_(2))` where `n_(1)` & `n_(2)` are the number of moles and `T_(1)` & `T_(2)` are respective temperatures. If the containers are now joined find the ratio of pressure to the pressure :

A

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

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
a. Given `(P_(1))/(P_(2)) = (n_(1) T_(2))/(n_(2) T_(2))`
`P prop nT`. It implies that volume of both containers is same. After mixing.
`P (2V) = (n_(1) + n_(2)) RT = ((P_(1) V)/(RT_(1)) + (P_(2) V)/(RT_(2))) RT`
`P//T = (1)/(2) ((P_(1))/(T_(1)) + (P_(2))/(T_(2))) = (1)/(2) ((P_(1) T_(2) + P_(2) T_(2))/(T_(1) T_(2)))`
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