Explain the internal energy of a system.

Explanation

Every bulk system consists of a large number of molecules.
Internal energy is the sum of the kinetic energies and potential energies of these molecules.
In thermodynamics the kinetic energy of the system is not relevant.
Thus the internal energy is the sum of molecular kinetic and potential energies in the frame of reference relative to which the centre of mass of the system is at rest. Thus, internal energy associated with random motion of molecules of the system. Internal energy U is simply macroscopic variable of the system.
It depends only on the state of the system, not on how that state was achieved.
Internal energy U of a system is an example of a thermodynamic state variable its value depends only on the given state of the system. But, not on the path taken to arrive at that state.
Thus, the internal energy of a given mass of gas depends on its state described by specific values of pressure, volume and temperature but it does not depend on how this state of the gas came about.
If we neglect the small intermolecular forces in a gas, the internal energy of a gas is just the sum of kinetic energies associated with various random motions of its molecules.

(a) Internal energy U of a gas is the sum of the kinetic and potential energies of its molecules when the box is at rest. Kinetic energy due to various types of motion (translational, rotational, vibrational) is to be included in U.
(b) If the same box is moving as a whole with some velocity the kinetic energy of the box is not to be included in U.
In figure (a), when box is at rest internal energy U of gas is the sum of the kinetic and potential energies of its molecules. Kinetic energy due to various types of motion like translational, rotational and vibrational is to be included in U. In figure (b), if the box is moving with some velocity, the kinetic energy of the box is not to be included in U.