Internal Energy and Formulation of the First Law

The internal energy of a system is the sum of the kinetic and potential energies of all particles within the system.

This energy can be altered through both work and heat.

For instance, when gas in a container with a movable piston is heated, heat flows into the system, and it gains internal energy. But when cooled, heat flows out of the system, and it loses internal energy.

Similarly, moving the piston upward, where work is done on the gas, or downward, where work is done by the gas, also changes the internal energy of the system.

This relationship between the change in internal energy, heat transfer, and work done due to pressure-volume changes is defined by the first law of thermodynamics.

For any process, the internal energy is dependent only on the initial and final states of the system and is path-independent.

For cyclic processes, internal energy remains constant as the final state is identical to the initial state.

Adiabatic systems prevent heat from entering or leaving, with the change in internal energy being equal to the work done on the system.