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?

Question

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? (A) No work is done by X (B) X decreases in temperature (C) X increases in internal energy (D) X doubles in pressure.

Tardigrade Admin · Accepted Answer

Free Expansion So, Δ W =0 Δ Q =0] ⇒ Δ U =0 ⇒ Δ T =0 and P1 V1=P2(2 V1) P2=(P1/2)

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?

No work is done by X

X decreases in temperature

X increases in internal energy

X doubles in pressure.

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

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?