Question

Two containers of equal volume contain the same gas at pressures $P_1$ and $P_2$ and absolute temperatures $T_1$ and $T_2$ respectively. On joining the vessels, the gas reaches a common pressure $P$ and common temperature $T$. The ratio $\frac{P}{T}$ is equal to

• A. `(P_(1))/(T_(1)) + (P_(2))/(T_(2))`
• B. `(P_(1)T_(1) + P_(2) T_(2))/((T_(1) + T_(2))^(2))`
• C. `(P_(1)T_(2) + P_(2) T_(1))/((T_(1) + T_(1))^(2))`
• D. `(P_(1))/(2T_(1)) + (P_(2))/(2T_(2))`

Answer 1

The correct option is D `(P_(1))/(2T_(1)) + (P_(2))/(2T_(2))`

Number of moles in the first vessel `mu_(1) = (P_(1) V)/(RT_(1))`
Number of moles in the second vessel `mu_(2) = (P_(2) V)/(RT_(2))`
If both vessels are joined together, then quantity of gas remains same, i.e., `mu = mu_(1) + mu_(2)`
`(P(2V))/(RT) = (P_(1)V)/(RT_(1)) + (P_(2)V)/(RT_(2))` `(P)/(T) = (P_(1))/(2T_(1)) + (P_(2))/(2T_(2))`