Question

The internal energy of a gram-molecule of an ideal gas depends on:
(A) Pressure alone
(B) Volume alone
(C) Temperature alone
(D) Both pressure as well as temperature

Answer 1

Hint
The internal energy of an ideal gas is given by: $U = cnT$ where $c$ is the molar heat capacity, $n$ is the number of moles of the gas and $T$ is the temperature.
$\Rightarrow U = cnT$ where $c$ is the molar heat capacity, $n$ is the number of moles of the gas and $T$ is the temperature.

Complete step by step answer
The internal energy $\left( U \right)$is the thermodynamic property of a system and is constituted by the potential and kinetic energies of the particles. But in an ideal gas system, the particles do not interact with each other and the system does not possess potential energy. Thus, the internal energy of such an ideal gas system is dependent only on the net kinetic energy of the particles. Since temperature is the measure of average kinetic energy of the system, we can conclude that the internal energy of an ideal gas depends on temperature.
We also know from the equation mentioned above that the internal energy of an ideal gas system depends on the number of moles and temperature only.
So, the correct answer option (C).

Note
There are many ways to change the temperature like changing the Pressure, Volume etc. So we may feel that the properties like Pressure, Volume etc. may also depend on the internal energy of the ideal gas system. But, fundamentally, temperature is the property which changes the energy, and all the other thermodynamic properties may help to change the temperature of the system.