Editing Entropy (section)

=== Entropy of a system ===
[[File:system boundary.svg|thumb|A [[thermodynamic system]]]]

[[File:Temperature-entropy chart for steam, imperial units.svg|thumb|A [[temperature–entropy diagram]] for steam. The vertical axis represents uniform temperature, and the horizontal axis represents specific entropy. Each dark line on the graph represents constant pressure, and these form a mesh with light grey lines of constant volume. (Dark-blue is liquid water, light-blue is liquid-steam mixture, and faint-blue is steam. Grey-blue represents supercritical liquid water.)]]

In a [[thermodynamic system]], pressure and temperature tend to become uniform over time because the [[equilibrium state]] has higher [[probability]] (more possible [[combination]]s of [[microstate (statistical mechanics)|microstates]]) than any other state. As an example, for a glass of ice water in air at [[room temperature]], the difference in temperature between the warm room (the surroundings) and the cold glass of ice and water (the system and not part of the room) decreases as portions of the [[thermal energy]] from the warm surroundings spread to the cooler system of ice and water. Over time the temperature of the glass and its contents and the temperature of the room become equal. In other words, the entropy of the room has decreased as some of its energy has been dispersed to the ice and water, of which the entropy has increased.

However, as calculated in the example, the entropy of the system of ice and water has increased more than the entropy of the surrounding room has decreased. In an [[isolated system]] such as the room and ice water taken together, the dispersal of energy from warmer to cooler always results in a net increase in entropy. Thus, when the "universe" of the room and ice water system has reached a temperature equilibrium, the entropy change from the initial state is at a maximum. The entropy of the [[thermodynamic system]] is a measure of how far the equalisation has progressed.

Thermodynamic entropy is a non-conserved [[state function]] that is of great importance in the sciences of [[physics]] and [[chemistry]].<ref name="McH" /><ref name="Wiley91">{{cite book|last1=Sandler|first1=Stanley I.|title=Chemical, biochemical, and engineering thermodynamics|url=https://archive.org/details/chemicalbiochemi00sand|url-access=limited|date=2006|publisher=John Wiley & Sons|location=New York|isbn=978-0-471-66174-0|page=[https://archive.org/details/chemicalbiochemi00sand/page/n104 91]|edition=4th}}</ref> Historically, the concept of entropy evolved to explain why some processes (permitted by conservation laws) occur spontaneously while their [[T-symmetry|time reversals]] (also permitted by conservation laws) do not; systems tend to progress in the direction of increasing entropy.<ref name="McQuarrie817">{{cite book|last1=Simon|first1= John D. |first2=Donald A. |last2=McQuarrie |title=Physical chemistry : a molecular approach|date=1997|publisher=Univ. Science Books|location=Sausalito, Calif.|isbn=978-0-935702-99-6|page=817|edition=Rev.}}</ref><ref>{{Cite book|last=Haynie|first=Donald T.|title=Biological Thermodynamics|publisher=[[Cambridge University Press]]|year=2001|isbn=978-0-521-79165-6}}</ref> For [[isolated system]]s, entropy never decreases.<ref name="Wiley91" /> This fact has several important consequences in science: first, it prohibits "[[perpetual motion]]" machines; and second, it implies the [[Entropy (arrow of time)|arrow of entropy]] has the same direction as the [[arrow of time]]. Increases in the total entropy of system and surroundings correspond to irreversible changes, because some energy is expended as waste heat, limiting the amount of work a system can do.<ref name="McH" /><ref name="Sethna78">{{cite book|last1=Sethna|first1=James P.|title=Statistical mechanics : entropy, order parameters, and complexity.|url=https://archive.org/details/statisticalmecha00seth_912|url-access=limited|date=2006|publisher=Oxford University Press|location=Oxford|isbn=978-0-19-856677-9|page=[https://archive.org/details/statisticalmecha00seth_912/page/n97 78]|edition=[Online-Ausg.]}}</ref><ref name="OxSci">{{cite book|last1=Daintith|first1=John|title=A dictionary of science|date=2005|publisher=Oxford University Press|location=Oxford|isbn=978-0-19-280641-3|edition=5th}}</ref><ref>{{Cite book|last=de Rosnay|first=Joel|title=The Macroscope&nbsp;– a New World View (written by an M.I.T.-trained biochemist)|publisher=Harper & Row, Publishers|year=1979|isbn=978-0-06-011029-1|title-link=M.I.T.}}</ref>

Unlike many other functions of state, entropy cannot be directly observed but must be calculated. Absolute [[standard molar entropy]] of a substance can be calculated from the measured temperature dependence of its [[heat capacity]]. The molar entropy of ions is obtained as a difference in entropy from a reference state defined as zero entropy. The [[second law of thermodynamics]] states that the entropy of an [[isolated system]] must increase or remain constant. Therefore, entropy is not a conserved quantity: for example, in an isolated system with non-uniform temperature, heat might irreversibly flow and the temperature become more uniform such that entropy increases.<ref>{{cite web|last=McGovern|first=J. A.|title=Heat Capacities|url=http://theory.phy.umist.ac.uk/~judith/stat_therm/node50.html|url-status=dead|archive-url=https://web.archive.org/web/20120819175243/http://theory.phy.umist.ac.uk/~judith/stat_therm/node50.html|archive-date=19 August 2012|access-date=27 January 2013}}</ref> Chemical reactions cause changes in entropy and system entropy, in conjunction with [[enthalpy]], plays an important role in determining in which direction a chemical reaction spontaneously proceeds.

One dictionary definition of entropy is that it is "a measure of thermal energy per unit temperature that is not available for useful work" in a cyclic process. For instance, a substance at uniform temperature is at maximum entropy and cannot drive a heat engine. A substance at non-uniform temperature is at a lower entropy (than if the heat distribution is allowed to even out) and some of the thermal energy can drive a heat engine.

A special case of entropy increase, the [[entropy of mixing]], occurs when two or more different substances are mixed. If the substances are at the same temperature and pressure, there is no net exchange of heat or work – the entropy change is entirely due to the mixing of the different substances. At a statistical mechanical level, this results due to the change in available volume per particle with mixing.<ref>{{cite journal|last1=Ben-Naim|first1=Arieh|title=On the So-Called Gibbs Paradox, and on the Real Paradox|journal=Entropy|date=21 September 2007|volume=9|issue=3|pages=132–136|doi=10.3390/e9030133|url=http://www.mdpi.org/entropy/papers/e9030132.pdf|bibcode=2007Entrp...9..132B|doi-access=free}}</ref>