Question

The internal energy of an ideal gas depends upon
A) only its pressure
B) only its volume
C) only its temperature
D) its pressure and volume

Answer 1

Hint
The 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 molecules in an ideal gas to decide the factors affecting internal energy of the ideal gas.

Complete Step by step solution
Ideal gas is considered to be the hypothetical gas whose molecules occupy negligible space and have no interactions. An ideal gas is considered as a theoretical gas which is composed of many random moving particles and there are no interparticle interactions between them. An ideal gas obeys an ideal gas law. An ideal gas molecules either attract or repel to each other and they themselves take no volume.
The internal energy of the system is described as the energy contained within the system. It is the amount of energy required to create any given state, but does not contain the kinetic energy of the particles of the system in any given state. The internal energy changes in an ideal gas can be described solely by change in its kinetic energy. Kinetic energy is simply considered as the internal energy of the perfect gas and depends entirely on its pressure, volume, temperature. In an ideal gas, the intermolecular forces are assumed to be absent and all the collisions are perfectly elastic. Thus, the gas possesses only translational kinetic energy and hence the internal energy of the ideal gas depends only on the temperature.
Hence, option (C) is correct.

Note
The meaning of only depends upon the temperature of the gas is that the internal energy of the gas does not change when it is allowed to expand in the vacuum, in that sense the internal energy only depends upon the temperature not depends upon the pressure and volume. Temperature is the measure of average kinetic energies of the particles of an ideal gas. When temperature increases the kinetic energy is also increased.