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12.Kinetic Theory of Gases
normal
Two containers of equal volume contain identical gases at pressures $P_1$ and $P_2$ and absolute temperatures, $T_1$ and $T_2$ respectively. The vessels are joined and the gas reaches a common pressure $P$ and a common temperature $T$. Then
A
$P = \left( {\frac{{{P_1}}}{{{T_1}}} + \frac{{{P_2}}}{{{T_2}}}} \right)T$
B
$P = \frac{1}{2}\left( {\frac{{{P_1}}}{{{T_1}}} + \frac{{{P_2}}}{{{T_2}}}} \right)T$
C
$T = \frac{{P{T_1}{T_2}}}{{{P_1}{T_2} + {P_2}{T_1}}}$
D
$T = \frac{{2P{T_1}{T_2}}}{{{P_1}{T_1} + {P_2}{T_2}}}$
Solution
Total number of moles will remain same
$\frac{P_{1} V}{R T_{1}}+\frac{P_{2} V}{R T_{2}}=\frac{P(2 V)}{R T}$
$\Rightarrow P=\frac{1}{2}\left(\frac{P_{1}}{T_{1}}+\frac{P_{2}}{T_{2}}\right) T$
Standard 11
Physics
