Internal Energy and Formulation of the First Law

In thermodynamics, energy is used to describe and predict the behavior of physical systems. The internal energy (U) of a system is the sum of all microscopic forms of energy within the system, including molecular kinetic and potential energies, as well as contributions from electronic and nuclear energy levels. Although the individual components of internal energy cannot be measured directly, the internal energy of any system is well defined within thermodynamic theory.

The first law of thermodynamics states that for an isolated system, the total energy remains constant, meaning that energy cannot move in or out of the system. This does not mean that the system itself is static or unchanging, but that the total energy of the system does not change. Mathematically, this can be expressed as ΔU = q + w, where q is the heat added to the system, and w is the work done on the system during the process. A change in internal energy occurs only when work or heat (or both) is involved.

In an adequately insulated system, heat will be unable to get into or leave the system. Such systems are called adiabatic, and in these cases, q = 0. For adiabatic processes, ΔU = w, where w represents the work done on the system.

The internal energy of a system is an extensive state function dependent on the amount of matter in the system, while the molar internal energy is an intensive property dependent on pressure and temperature.

The internal energy is a state function that depends only on the initial and final states of the system and is independent of the path taken to reach those states. In cyclic processes, where the final state of the system is identical to the initial state, the change in internal energy is zero.