Question

An insulated container is divided into two equal parts. One part contains an ideal gas at pressure P and temperature T, while the other part is a perfect vacuum. If a hole is opened between the two parts, find the change in the temperature of the gas.

Answer 1

As the system is thermally insulated,

$\Delta Q=0$

Further as the gas is expanding against vacuum (surroundings), the process is called free expansion and for it

$\Delta W=\int PdV=0$

So in accordance with first law of thermodynamics,

i.e., $\Delta Q=\Delta U+\Delta W$

we have

$0=\Delta U+0$,

$\Delta U=0$ or U = constant

For an ideal gas

$U=n{C}_{v}T$

or, $U\infty T$

$\therefore$ $\Delta T=0$