Editing Second law of thermodynamics (section)

== Direction of spontaneous processes ==
The second law determines whether a proposed physical or chemical process is forbidden or may occur spontaneously. For [[isolated system]]s, no energy is provided by the surroundings and the second law requires that the entropy of the system alone cannot decrease: Δ''S'' ≥ 0. Examples of spontaneous physical processes in isolated systems include the following: 
* 1) [[Heat transfer|Heat can be transferred]] from a region of higher temperature to a lower temperature (but not the reverse).
* 2) Mechanical energy can be converted to thermal energy (but not the reverse).
* 3) A solute can move from a region of higher concentration to a region of lower concentration (but not the reverse).

However, for some non-isolated systems which can exchange energy with their surroundings, the surroundings exchange enough heat with the system, or do sufficient work on the system, so that the processes occur in the opposite direction. In such a case, the reverse process can occur because it is ''coupled'' to a simultaneous process that ''increases'' the entropy of the surroundings. The coupled process will go forward provided that the total entropy change of the system and surroundings combined is nonnegative as required by the second law: Δ''S''<sub>tot</sub> = Δ''S'' + Δ''S''<sub>R</sub> ≥ 0. For the three examples given above:
* 1) Heat can be transferred from a region of lower temperature to a higher temperature by a [[refrigerator]] or [[heat pump]], provided that the device delivers sufficient mechanical work to the system and converts it to thermal energy inside the system.
* 2) Thermal energy can be converted by a heat engine to mechanical work within a system at a single temperature, provided that the heat engine transfers a sufficient amount of heat from the system to a lower-temperature region in the surroundings.
* 3) A solute can travel from a region of lower concentration to a region of higher concentration in the biochemical process of [[active transport]], if sufficient work is provided by a concentration gradient of a chemical such as [[Adenosine triphosphate|ATP]] or by an [[electrochemical gradient]].

=== Second law in chemical thermodynamics ===
For a [[spontaneous process|spontaneous chemical process]] in a closed system at constant temperature and pressure without non-''PV'' work, the Clausius inequality Δ''S'' > ''Q/T''<sub>surr</sub> transforms into a condition for the change in [[Gibbs free energy]]
: <math>\Delta G < 0 </math>
or d''G'' < 0. For a similar process at constant temperature and volume, the change in [[Helmholtz free energy]] must be negative, <math>\Delta A < 0 </math>. Thus, a negative value of the change in free energy (''G'' or ''A'') is a necessary condition for a process to be spontaneous. This is the most useful form of the second law of thermodynamics in chemistry, where free-energy changes can be calculated from tabulated enthalpies of formation and standard molar entropies of reactants and products.<ref name="Oxtoby8th"/><ref name="MortimerBook" /> The chemical equilibrium condition at constant ''T'' and ''p'' without electrical work is d''G'' = 0.