Q.Define the internal energy of the system.

The internal energy $U$ of a thermodynamic system is the sum of the kinetic and potential energies of all the molecules in the system, measured with respect to the centre of mass of the system: $U = E_K + E_P$, where $E_K$ (internal kinetic energy) comes from translational, rotational and vibrational molecular motion, and $E_P$ (internal potential energy, e.g. bond energy) comes from molecular interactions. For an ideal gas, molecules are assumed not to interact, so $U$ consists purely of kinetic energy, depending only on temperature and the number of particles, and not on volume; this is not true for real gases (e.g. van der Waals gases), where intermolecular interactions contribute to $E_P$. Internal energy is a state variable: it depends only on the system's initial and final states, never on the path taken to get there. Crucially, internal energy is associated only with the random molecular motion and the potential energy from molecular interactions -- the bulk kinetic energ …