Question

In the free expansion of an ideal gas, its internal energy
A. remains constant
B. increases
C. decreases
D. sometimes increases, sometimes decreases

Answer 1

Hint: First law of thermodynamics is the law of conservation of energy in the case of thermodynamics (thermodynamic processes). It states that energy is always conserved. Using the equation of the first law of thermodynamics, the answer to this question can be obtained.

Formula used:
\[\Delta U=Q-W\]

Complete answer:
The free expansion of a gas is a process in which a gas is allowed to expand into the vacuum. This process happens within no time, as the gas doesn’t work while getting expanded. The reason for zero work done by the gas is that the gas doesn’t replace any other molecules while expanding, as the vacuum is a region with zero molecules.
The first law of thermodynamics is given by the formula as follows:
\[\Delta U=Q-W\]
Where \[\Delta U\]is the change in the internal energy, Q is the heat transferred and W is the work done.
As from the above explanation, it’s clear that the work done by the ideal gas while expanding is zero, the term W equals to 0.
When there will be no work done, there is no question of heat transfer, as the heat transfer only takes place where there is work done.
Thus, the term Q also equals to 0.
Substituting these obtained values in the equation of first law of thermodynamics, we will obtain the value of the internal energy of the ideal gas.
\[\begin{align}
  & \Delta U=Q-W \\
 & \Delta U=0-0 \\
 & \Delta U=0 \\
\end{align}\]
Thus, the change in the internal energy of the ideal gas in free expansion is zero.
As the change in the internal energy of an ideal gas in the free expansion is zero.

Thus, option (A) remains constant is correct.

Note:
The things to be on your finger-tips for further information on solving these types of problems are: As the question involves ideal gas – these gas molecules occupy negligible space and these molecules do not have interactions with each other and obey the gas laws.