Question

Internal energy of an ideal gas depends upon
(A). Temperature only
(B). Volume only
(C). Both volume and temperature
(D). Neither volume nor temperature

Answer 1

Hint: Intermolecular forces are assumed to be absent in ideal gases and the collisions are perfectly elastic. We need to find which kinetic energy is associated with the collisions of the molecules in an ideal gas to decide the factors affecting internal energy of an ideal gas.

Complete step by step answer:
Ideal gas is considered as a hypothetical gas whose molecules occupy negligible space and have no interactions. An ideal or perfect gas is a theoretical gas which is composed of many randomly moving point particles that are not subject to inter particle interactions. An ideal gas always obeys ideal gas law. Ideal gas molecules never attract or repel each other and they themselves take up no volume.
The internal energy of a system is described as the energy contained within the system. It is the amount of energy necessary to create or prepare in any given state, but does not contain the kinetic energy of motion of particles of the system in any given state. The internal energy changes in an ideal gas can be described solely by changes in its kinetic energy. Kinetic energy is simply considered as the internal energy of the perfect gas and depends entirely on its pressure, volume and thermodynamic temperature. In an ideal gas, intermolecular forces are assumed to be absent and all the collisions are perfectly elastic. Thus, the gas possesses only the translational kinetic energy and hence the internal energy of the ideal gas depends only on temperature.

Hence, the correct option is A.

Note: The meaning of ‘depend only on temperature’ means that the internal energy of the gas does not change when it is allowed to expand into a vacuum. In that sense, the internal energy is independent of pressure and volume, and therefore depends only on temperature. Temperature is a measure of the average kinetic energy of the particles of an ideal gas. When temperature increases, the kinetic energy also increases.