Question

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 attains 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. $\frac{1}{2}(\frac{p_1}{T_1}+\frac{p_2}{T_2})$
• C. $\frac{p_1{T}_2+p_2{T}_1}{T_1+T_2}$
• D. $\frac{p_1+p_2}{T_1+T_2}$

Answer 1

The correct option is B $\frac{1}{2}(\frac{p_1}{T_1}+\frac{p_2}{T_2})$

After mixing of both the gases,

Total volume of the vessels = V+V =2V

Total number of moles $n=n_1+n_2$=constant

using ideal gas equation,

$\frac{P\left(2V\right)}{RT}=\frac{p_{1}V}{R{T}_1}+\frac{p_{2}V}{R{T}_2}\Rightarrow \frac{P}{T}=\frac{1}{2}(\frac{p_1}{T_1}+\frac{p_2}{T_2})$

Hence, Option B is correct.