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Two containers, each of volume V(0), joi...

Two containers, each of volume `V_(0)`, joined by a small pipe initially contain the same gas at pressure `P_(0)` and at absolute temperature `T_(0)`. One container is now maintained at the same temperature while the other is heated to `2T_(0)`. Find(1) commom pressure of the gas, and(2) the number of moles of gas in the container at temperature `2T_(0)`

Text Solution

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Let `n_(1)andn_(2)` be the initial number of moles of gas and `n_(1)^(1)andn_(2)^(1)` be the final number of moles of gas in the two containers.
Then `n_(1)+n_(2)=n_(1)^(1)+n_(2)^(1)`
(or) `(P_(0)V_(0))/(RT_(0))+(P_(0)V_(0))/(RT_(0))=(PV_(0))/(RT_(0))+(PV_(0))/(R2T_(0))`
(or) `(2P_(0)V_(0))/(RT_(0))+(P_(0)V_(0))/(RT_(0))[3/2]rArrP=(4P_(0))/3`
From gas equation PV = nRT,
we have `(4P_(0))/3V_(0)=n_(2)^(1)R(2T_(0))`
`thereforen_(2)^(1)=(4P_(0)V_(0))/(3R(2T_()))rArrn_(2)^(1)=(4P_(0)V_(0))/(6RT_(0))=(2P_(0)V_(0))/(3RT_(0))`
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