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  4. A closed container is fully insulated from outside. One half of it is filled with an ideal gas X separated by a plate P from the other half Y which contains a vacuum as shown in figure. When P is removed, X moves into Y. Which of the following statements is correct?

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Q. A closed container is fully insulated from outside. One half of it is filled with an ideal gas $X$ separated by a plate $P$ from the other half $Y$ which contains a vacuum as shown in figure. When $P$ is removed, $X$ moves into $Y$. Which of the following statements is correct?Physics Question Image

Solution:

Free Expansion
So, $\Delta W =0 \Delta Q =0] \Rightarrow \Delta U =0$
$\Rightarrow \Delta T =0$
and $P_{1} V_{1}=P_{2}\left(2 V_{1}\right)$
$P_{2}=\frac{P_{1}}{2}$