Internal Energy and Formulation of the First Law

Internal energy is the sum of all microscopic forms of energy within a system, including molecular kinetic and potential energies, plus contributions from electronic and nuclear energy levels. Although individual components cannot be measured directly, the total internal energy is well-defined within thermodynamic theory and depends on the amount of matter present.

The first law states that change in internal energy equals heat added to the system plus work done on the system, expressed as ΔU = q + w. This means internal energy changes only when work or heat transfers occur. For isolated systems, total energy remains constant.

Internal energy is a state function because it depends only on the initial and final states of a system, not on the path taken between them. This path-independence means that regardless of how a system reaches a particular state, its internal energy value remains the same for those conditions.

In cyclic processes, the final state of the system is identical to the initial state, so the change in internal energy is zero. This occurs regardless of the work done or heat transferred during intermediate steps, since internal energy depends only on initial and final states.

In adiabatic systems, heat cannot enter or leave the system, so q = 0. This simplifies the first law to ΔU = w, meaning the change in internal energy equals only the work done on the system. These adequately insulated systems prevent heat transfer entirely.

Internal energy is an extensive state function that depends on the amount of matter in the system. Molar internal energy, by contrast, is an intensive property that depends on pressure and temperature but not on the quantity of substance present.

Work changes internal energy when pressure-volume changes occur, such as moving a piston up or down. Heat changes internal energy when thermal energy flows into or out of the system. Both mechanisms alter internal energy independently, and their combined effect determines the total change.