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 P/T is equal to

• A. $\frac{P_{1}}{T_{1}} + \frac{P_{2}}{T_{2}}$
• B. $\frac{P_{1}T_{1} + P_{2}T_{2}}{(T_{1} + T_{2})^{2}}$
• C. $\frac{P_{1}T_{2} + P_{2}T_{1}}{(T_{1} + T_{2})^{2}}$
• D. $\frac{P_{1}}{2T_{1}} + \frac{P_{2}}{2T_{2}}$

Answer 1

Answer: (D)

$\frac{P_{1}}{2T_{1}} + \frac{P_{2}}{2T_{2}}$

Answer 2

Number of moles in first vessel $\mu_{1} = \frac{P_{1}V}{RT_{1}}$ and number of

moles in second vessel $\mu_{2} = \frac{P_{2}V}{RT_{2}}$

If both vessels are joined together then quantity of gas

remains same i.e $\mu = \mu_{1} + \mu_{2}$

$\frac{P(2V)}{RT} = \frac{P_{1}V}{RT_{1}} + \frac{P_{2}V}{RT_{2}}$

$\frac{P}{T} = \frac{P_{1}}{2T_{1}} + \frac{P_{2}}{2T_{2}}$