Question

The internal energy of a gas:
(A) is the sum total kinetic and potential energies.
(B) is the total translational kinetic energy.
(C) is the total kinetic energy of randomly moving molecules.
(D) is the total kinetic energy of gas molecules.

Answer 1

Hint
To solve this question we need to first consider what is meant by the term internal energy and what are the factors it depends on. So we can consider gas placed in a container and find out the factors that will affect the internal energy of the gas in that container.

Complete Step by Step Solution
Let us consider a container of given dimensions filled with gas. So the molecules of the gas inside the container move around randomly. While doing so they also strike often with the walls of the container.
Now when they strike on to the walls with some momentum, they transfer their momentum to the walls. Hence, at a given temperature, the number of times the gas molecules strike with the walls of the container determines the pressure of the gas in the container.
Now if we compress the container to a smaller volume, the pressure will increase. the volume of the container decreasing means the surface area of the walls will decrease. Therefore, the number of collisions of the gas molecules with the walls will increase. This means that the kinetic energy of the gas molecules increases.
Thus, we can say that increasing the kinetic energy of the gas molecules increases the pressure. So, from here we can say that the total kinetic energy of these molecules makes up the internal energy of the gas.
Option (D) is the correct answer.

Note
In the case of an ideal gas, there are considered no intermolecular collisions present, and all the other collisions are taken to be perfectly elastic. So in that case the gas possesses only the translational kinetic energy and the internal energy of the gas will be dependent on its temperature only.