Question

A box (thermally insulated) has two chambers separated by a membrane. One of volume $V$ contains an ideal gas at temperature $T$. The other of volume $\left(\frac{1}{2}V\right)$ is evacuated. If the membrane breaks down, the gas temperature will be

• A. $\frac{3}{2}T$
• B. $\frac{2T}{3}$
• C. $T$
• D. None of these

Answer 1

Answer: (C)

Free expansion is adiabatic process in which no work is performed on or by the system. Consider two vessels placed in a system which is enclosed with thermal insulation (asbestos covered).
One vessel contains a gas and the other is evacuated. When suddenly the stop cock is opened, the gas rushes into the evacuated vessel and expands freely.
$\Delta W=0$ (Because walls are rigid)
$\Delta Q=0$ (Because walls are insulated)
$\Delta U=U_f-U_i=0$
(Because $\Delta Q$ and $\Delta W$ are zero).
Thus, the final and initial internal energies are equal in free expansion.
The temperature remains $T$.