Two containers, each of volume VO' 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)

Two containers, each of volume VO' joined by a small pipe initially co

1.	Two containers, each of volume VO' 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)
Answer» Solution :Let `n_(1) and n_(2)` be the initial NUMBER of moles of gas and `n_(1)^(1) and n_(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))/(R2 T_(0))` `(or) (2P_(0)V_(0))/(RT_(0)) + (P_(0)V_(0))/(RT_(0)) [ (3)/(2)] rArr P = (4P_(0))/(3)` From gas equation PV = nRT, we have `(4P_(0))/(3) V_(0) = n_(2)^(1) R (2T_(0))` `therefore n_(2)^(1) = (4P_(0)V_(0))/(3R (2 T_(0))) rArr n_(2)^(1) (4P_(0)V_(0))/(6RT_(0)) = (2P_(0)V_(0))/(3RT_(0)) `