Why does the I.E of an ideal gas only depend on K.E/T

Answer 1

While examining the internal energy of the molecules in an ideal gas we need to remember that it is dependent on the kinetic energy which is dependent on temperature.

In an ideal gas, the gas molecules gain their energy essentially perfectly elastic collisions and motion of the molecules themselves. This increases their kinetic energy.

As observed through the ideal gas laws, if the temperature rises, the molecules move faster resulting in a higher kinetic energy. Since the gas molecules themselves do not possess any intermolecular forces, the internal energy they possess is determined by the kinetic energy of the molecules.

We can also take a look at the equation, which demonstrates Internal Energy's dependency on Temperature and essential Kinetic Energy as well.

U = (3/2)*n*R*T