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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

Text Solution

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Number of moles before joining =
Number of mo]es after joining the vessels.
`n_(1) + n_(2) = n_(1)^(1) n_(2)^(1)`
i.e., `(P_(1)V)/(RT_(1)) + (P_(2)V)/(RT_(2)) = (PV)/(RT) + (PV)/(RT) `
(or) `(P_(2)V)/(RT_(1)) + (P_(2)V)/(RT_(2)) = (2PV)/(RT) `
`rArr (P_(1))/(T_(1)) + (P_(2))/(T_(2)) = (2P)/(T) " " therefore (P)/(T) = (1)/(2) [ (P_(1))/(T_(1)) + (P_(2))/(T_(2)) ] `
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