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Two monconducting containers having volu...

Two monconducting containers having volume `V_(1)` and `V_(2)` contain monoatomic and dimatomic gases respectivley. They are connected as shown in figure. Pressure and temperature in the two containers are `P_(1), T_(1)` and `P_(2), T_(2)` respectively. Initially stop cock is closed, if the stop coc is opened find the final pressure and temperature.

Text Solution

Verified by Experts

`n_(1) = (P_(1) V_(1))/(RT_(1))` `n_(2) = (P_(2) V_(2))/(RT_(2))`
`n = n_(1) + n_(2)` (number of moles are conserved) Finally pressure in both parts and temperature of the both the gases will become equal
`(P(V_(1) + V_(2)))/(RT) = (P_(1) V_(1))/(RT_(2)) + (P_(2)V_(2))/(RT_(2))`
From energy conservation
`(3)/(2) n_(1) RT_(1) + (5)/(2) n_(2) RT_(2) = (3)/(2) n_(1) RT + (5)/(2) n_(2) RT`
`implies T = ((3 P_(1) V_(1) + 5 P_(2) V_(2)) T_(1) T_(2))/(3 P_(1) V_(1) T_(2) + 5 P_(2) V_(2) T_(1))`
`implies P = ((3 P_(1) V_(1) + 5 P_(2) V_(2))/(3 P_(1) V_(1) T_(2) + 5 P_(2) V_(2) T_(1))) ((P_(1) V_(1) T_(2) + P_(2) V_(2) T_(2))/(V_(1) + V_(2)))`
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