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

The correct option is C

only its temperature

The explanation for the correct option:

Option(C):

1. In an ideal gas, the inter-molecular collisions are assumed to be absent and collisions occur with other molecules or with the walls of the container.
2. Hence the molecules do not lose any kinetic energy and these collisions are said to be perfectly elastic.
3. Thus, the gas possesses only translational kinetic energy, which can be given as: $\mathrm{K}.\mathrm{E}=\frac{3}{2}\mathrm{RT}$
4. As $\mathrm{R}\mathrm{and}3/2$are constants, thus the translation kinetic energy of gas molecules is directly proportional to the temperature of the gas $\mathrm{T}.$
5. Thus, the gas possesses only translational kinetic energy, and hence the internal energy of the ideal gas depends only on temperature.

The explanation for the incorrect option:

Option(A): only its pressure

1. The internal energy of an ideal gas does not depend upon its pressure.
2. Hence, the given option is the incorrect one.

Option(B):only its volume

1. The internal energy of an ideal gas is generally independent of its volume.
2. Hence, the given option does not represent the correct concept.

Option(D):its pressure and volume

1. The internal energy of an ideal gas is generally independent of its pressure and volume.
2. Hence, the given option does not coincide with the correct concept.

Hence, Option (C) is correct. the internal energy of an ideal gas depends upon only its temperature