Question

An ideal gas undergoing expansion in vacuum shows

$$A.\;\Delta E = 0 \\\ B.\;W = 0 \\\ C.\;Q = 0 \\\ D.\;All\;of\;these \\\$$

Answer 1

An ideal gas is the one which obeys all the gas laws and does not show any interaction whereas vacuum is space where no matter is present. In order to answer this question, we need to find out how different parameters like internal energy, heat energy, enthalpy etc get affected under vacuum.

Complete answer:
As I mentioned that no matter is present in the vacuum, the pressure inside it would be negligible because pressure is mainly due to collisions between the molecules and the wall of a container. In vacuum, as no particles are present, the pressure would be low or almost zero. So even if a gas is said to be expanding in vacuum, it can be considered as free expansion as there is no pressure in and around it. Now let us find out the work done by ideal gas which is given by the equation
$\Rightarrow W = {P_{external}}\int {dV}$
As I mentioned that there is no external pressure, the net work done by the idea gas also becomes zero $\Rightarrow W = 0$ By this we can conclude that the second option is correct.
Now coming to heat energy, as vacuum is just an empty space, heat exchange cannot take place because for any energy interaction to happen, surroundings must be present. As it is a vacuum, no surrounding is present so heat exchange is zero and hence $Q = 0$ . This says that the third option is also correct.
Now we need to find$\Delta E$, from the first law of thermodynamics we can derive the relation between E, W and Q. The equation is written as
$\Rightarrow Q = U + \Delta W$
We came to know that $Q = \Delta W = 0$
After substituting the values we get$U = 0$ . This says first option is also correct

This means all the three options are correct and hence the correct answer is D.

Note:
In vacuum, the temperature is also said to be zero because temperature is the kinetic energy of the particles, since a vacuum does not have any particles, temperature is also said to be zero. But according to the third law of thermodynamics, zero temperature does not exist and hence it says there is no perfect vacuum.