- Home
- Standard 11
- Physics
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
$\frac{{{P_1}}}{{{T_1}}} + \frac{{{P_2}}}{{{T_2}}}$
$\frac{{{P_1}{T_1} + {P_2}{T_2}}}{{{{({T_1} + {T_2})}^2}}}$
$\frac{{{P_1}{T_2} + {P_2}{T_1}}}{{{{({T_1} + {T_2})}^2}}}$
$\frac{{{P_1}}}{{2{T_1}}} + \frac{{{P_2}}}{{2{T_2}}}$
Solution
$P _{1} V = n _{1} R T _{1}$
$P _{2} V = n _{2} RT _{2}$
where $V$ is the volume of each vessel.
When the vessels are joined, $P (2 V )=\left( n _{1}+ n _{2}\right) RT$
$\therefore \frac{ P }{ T }=\frac{1}{2} \frac{\left( n _{1}+ n _{2}\right) R }{ V }=\frac{1}{2}\left(\frac{ P _{1}}{ T _{1}}+\frac{ P _{2}}{ T _{2}}\right)=\frac{ P _{1}}{2 T _{1}}+\frac{ P _{2}}{2 T _{2}}$
