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The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable, a thermodynamic potential, and an extensive property. [5] Thermodynamics defines internal energy macroscopically, for the body as a whole.
It is defined only up to an arbitrary additive constant of integration, which can be adjusted to give arbitrary reference zero levels. This non-uniqueness is in keeping with the abstract mathematical nature of the internal energy. The internal energy is customarily stated relative to a conventionally chosen standard reference state of the system.
The principle of minimum energy is essentially a restatement of the second law of thermodynamics. It states that for a closed system, with constant external parameters and entropy, the internal energy will decrease and approach a minimum value at equilibrium. External parameters generally means the volume, but may include other parameters which ...
The concept of internal energy and its relationship to temperature. If a system has a definite temperature, then its total energy has three distinguishable components, termed kinetic energy (energy due to the motion of the system as a whole), potential energy (energy resulting from an externally imposed force field), and internal energy. The ...
They are uniquely determined by the thermodynamic state as it has been identified by the original state variables. There are many such state functions. Examples are internal energy, enthalpy, Helmholtz free energy, Gibbs free energy, thermodynamic temperature, and entropy. For a given body, of a given chemical constitution, when its ...
That is, when a system is described by stating its internal energy U, an extensive variable, as a function of its entropy S, volume V, and mol number N, i.e. U = U (S, V, N), then the temperature is equal to the partial derivative of the internal energy with respect to the entropy [61] (essentially equivalent to the first TdS equation for V and ...
An example of a system that does not have a unique ground state is one whose net spin is a half-integer, for which time-reversal symmetry gives two degenerate ground states. For such systems, the entropy at zero temperature is at least k B ln(2) (which is negligible on a macroscopic scale).
Since the total change in entropy must always be larger or equal to zero, we obtain the inequality W ≤ − Δ F . {\displaystyle W\leq -\Delta F.} We see that the total amount of work that can be extracted in an isothermal process is limited by the free-energy decrease, and that increasing the free energy in a reversible process requires work ...