A container with rigid walls is covered with perfectly insulating… - Vidyadip

MCQ

A container with rigid walls is covered with perfectly insulating material. The container is divided into two parts by a partition. One part contains a gas while the other is fully evacuated (vacuum). The partition is suddenly removed. The gas rushes to fill the entire volume and comes to equilibrium after a little time. If the gas is not ideal, then

✓
the initial internal energy of the gas equals its final internal energy
B
the initial temperature of the gas equals its final temperature
C
the initial pressure of the gas equals its final pressure
D
the initial entropy of the gas equals its final entropy

✓

Answer

Correct option: A.

the initial internal energy of the gas equals its final internal energy

a
(a)

Expansion is in vacuum, so work done by expanding gas is $\Delta W=0$.

Container is insulated, so heat exchanged with surroundings is $\Delta Q=0$.

Now, from first law of thermodynamics, we have

$\Rightarrow \Delta Q=\Delta U+\Delta W$

$\Rightarrow \Delta U=0$

$\Rightarrow U_i=U_f$

Hence, initial and final internal energies of gas are equal.

As, the gas is not ideal expansion results in reduction of pressure, so intermolecular potential energy increases. This results in reduction of kinetic energy, so temperature reduces.

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