An open container of volume $V$ contains air at temperature $27^{o} C$ or $300 K$ . The container is heated to such a temperature so that amount of gas coming out is $2 / 3$ of
(a) amount of gas initially present in the container.
(b) amount of gas finally remaining in the container.
Find the temperature to which the container should be heated.

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Solution

(a) Here, $P$ & $V$ are constant, $n$ & $T$ are changing. Let, initially the amount of gas present be $n$ & temp is $27^{o} C$ or $300 K$ . Finally amount of gas present in container $= n - \frac{2}{3} n = (\frac{1}{3} \times n)$ & final temperature be $T$ .
Then using $n_{1} T_{1} = n_{2} T_{2}$ , we have, $n \times 300 = \frac{n}{3} \times T_{2} \Rightarrow T_{2} = 900 K$ i.e., final temp $= 900 K$
(b) Let there be $x$ moles of gas remaining in the container, $\frac{2}{3}$ of $x$ come out
$∴ (\frac{2}{3} x + x) = n \Rightarrow \frac{5 x}{3} = n$ $∴ x = \frac{3 n}{5}$
$∴$ Using $n_{1} T_{1} = n_{2} T_{2}$ $n \times 300 K = \frac{3 n}{5} \times T_{2}$
$∴ T_{2} = 500 K$
Final temperature $= 500 K$

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