Two identical vessels contain the same gas at pressure `P_(1)` and `P_(2)` at absolute temperature `T_(1) and T_(2)`, respectively. On joining the vessels with a small tube as shown in the figure. The gas reaches a common temperature T and a common pressure P. Determine the ratio `P//T`

Options

A. `[(P_(1) T_(1) + P_(2) T_(2))/(T_(1) T_(2))]`
B. `(1)/(2)[(P_(1) T_(1) + P_(2) T_(2))/(T_(1) T_(2))]`
C. `(1)/(2)[(P_(1) T_(2) + P_(2) T_(1))/(T_(1) T_(2))]`
D. `[(P_(1) T_(2) + P_(2) T_(1))/(T_(1) T_(2))]`

Answer

C

Explanation

On combining the two vessels the total number of moes remains constant , `i.e., n = n_(1)+n_(2)`
Using gas equation, we can write , `n_(1) +(P_(1)V)/(RT_(1)), n_(2) = (P_(2)V)/(RT_(2))`
and `n=(P(2V))/(RT)`
where `V` is the volume of each vessel.
Thus `(P(2V))/(RT) = (P_(1)V)/(RT_1)+(P_(2)V)/(RT_2) or P/T = 1/2[(P_1)/(T_1)+(P_2)/(T_2)]` .