Question

Two containers of the equal volume contain the same gas at pressure $P_1$ 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. $\frac{P_1}{T_1}+\frac{P_2}{T_2}$
• B. $\frac{P_1{T}_1+P_2{T}_2}{\left(T_1+T_2\right)}$
• C. $\frac{P_1{T}_2+P_2{T}_1}{{\left(T_1+T_2\right)}^2}$
• D. $\frac{P_1}{2T_1}+\frac{P_2}{2T_2}$

Answer 1

Answer: (D)

Number of moles in the first vessel
${\mu }_1=\frac{{\text{P}}_1\text{V}}{{\text{RT}}_1}$
Number of moles in the second vessel
${\mu }_2=\frac{{\text{P}}_2\text{V}}{{\text{RT}}_2}$

If both vessels are joined together, then the quantity of gas remains the same, i.e., $\mu ={\mu }_1+{\mu }_2$
$\frac{\text{P}\left(2\text{V}\right)}{\text{RT}}=\frac{{\left(\text{P}\right)}_1\text{V}}{{\left(\text{RT}\right)}_1}+\frac{{\left(\text{P}\right)}_2\text{V}}{{\left(\text{RT}\right)}_2}$
$\frac{\text{P}}{\text{T}}=\frac{{\text{P}}_1}{2{\text{T}}_1}+\frac{{\text{P}}_2}{2T_2}$