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  4. Two monoatomic ideal gases A and B occupying the same volume V, are at the same temperature T and pressure p. If they are mixed, the resultant mixture has volume V and temperature T. The pressure of the mixture is

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Q. Two monoatomic ideal gases $A$ and $B$ occupying the same volume $V$, are at the same temperature $T$ and pressure $p$. If they are mixed, the resultant mixture has volume $V$ and temperature $T$. The pressure of the mixture is

J & K CETJ & K CET 2009Kinetic Theory

Solution:

$\frac{p_{1} V_{1}}{T_{1}}=\frac{p_{mix} \times V_{mix}}{T_{mix}}$
Here, $T_{1}=T_{m i x}=T$
$ V_{1}=V+V$
$ V_{mix}=V$
$\therefore \frac{p \times 2 V}{T}=\frac{p_{mix \times V}}{T}$
$\Rightarrow p_{mix}=2 p$