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

Options

A. `P_1/T_1+P_2/T_2`
B. `(P_1T_1+P_2T_2)/((T_1+T_2)^2)`
C. `(P_1T_2+P_2T_1)/((T_1+T_2)^2)`
D. `P_1/(2T_1)+P_2/(2T_2)`

Answer

D

Explanation

`n_1=(P_1V)/(RT_1)" "("for "1^(st)" vessel")`
`n_2=(P_2V)/(RT_2)" "("for "2^(nd)" vessel")`
If both vessels are joined together
`n=n_1+n_2`
`rArr(P(2V))/(RT)=(P_1V)/(RT_1)+(P_2V)/(RT_2)`
`rArrP/T=P_1/(2T_1)+P_2/(2T_2)`