The Internal Energy as a State Function

The Internal Energy as a State Function

  • Internal energy, U, represents the total energy of a system, including chemical, electrical, mechanical or any other type of energy.
  • Internal energy can change when heat passes into or out of the system, work is done on or by the system, or matter enters or leaves the system.
  • Internal energy is a state function, meaning it is characteristic of the state of the system.


  • Internal energy can also change by transfer of heat from the surroundings to the system or vice-versa, without the expenditure of work.
  • Heat, q, is the exchange of energy resulting from a temperature difference.
  • Heat can be measured in terms of the temperature difference between the system and the surroundings.
  • When no work is done at constant volume, the change in internal energy, ∆U, is equal to the heat absorbed by the system, q.
  • The sign of q depends on the direction of heat transfer; positive when heat is transferred from the surroundings to the system and negative when heat is transferred from the system to the surroundings.

First law of thermodynamics

  • The change in internal energy of a system during a change of state can be expressed as the sum of the heat transferred to or from the system and the work done on or by the system: ∆U = q + w.
  • The values of q and w can vary depending on how the change is carried out, but the sum q + w = ∆U is independent of the process and depends only on the initial and final states of the system.
  • For an isolated system where no energy is transferred as heat or work, the change in internal energy is zero: ∆U = 0.
  • The first law of thermodynamics is a mathematical expression of the principle of conservation of energy, which states that the energy of an isolated system is constant and cannot be created or destroyed.