Editing Enthalpy (section)

===Characteristic functions and natural state variables===

The enthalpy {{nobr|{{math|''H''(''S''[''p''], ''p'', {{mset|''N{{sub|i}}''}})}}}} expresses the thermodynamics of a system in the ''energy representation''. As a [[State function|function of state]], its arguments include one intensive and several extensive [[state variable]]s. The state variables {{nobr|{{math|''S''[''p'']}},}} {{mvar|p}}, and {{math|{{mset|''N{{sub|i}}''}}}} are said to be the [[Thermodynamic potential#Natural variables|''natural state variables'']] in this representation. They are suitable for describing processes in which they are determined by factors in the surroundings. For example, when a virtual parcel of atmospheric air moves to a different altitude, the pressure surrounding it changes, and the process is often so rapid that there is too little time for heat transfer. This is the basis of the so-called [[adiabatic approximation]] that is used in [[meteorology]].<ref>
{{cite book
 |last1=Iribarne |first1=J. V.
 |last2=Godson   |first2=W. L.
 |year=1981
 |title=Atmospheric Thermodynamics |edition=2nd
 |publisher=Kluwer Academic Publishers
 |place=Dordrecht, NL
 |isbn=90-277-1297-2
 |pages=235–236
}}
</ref>

Conjugate with the enthalpy, with these arguments, the other characteristic function of state of a thermodynamic system is its entropy, as a function {{nobr|{{math|''S''[''p''](''H'', ''p'', {{mset|N{{sub|i}}}})}}}} of the same list of variables of state, except that the entropy {{math|''S''[''p'']}} is replaced in the list by the enthalpy {{mvar|H}}. It expresses the ''entropy representation''. The state variables {{mvar|H}}, {{mvar|p}}, and {{math|{{mset|''N{{sub|i}}''}}}} are said to be the ''natural state variables'' in this representation. They are suitable for describing processes in which they are experimentally controlled. For example, {{mvar|H}} and {{mvar|p}} can be controlled by allowing heat transfer, and by varying only the external pressure on the piston that sets the volume of the system.<ref>
{{cite book
 |last=Tschoegl |first=N. W.
 |year=2000
 |title=Fundamentals of Equilibrium and Steady-State Thermodynamics
 |publisher=Elsevier
 |place=Amsterdam, NL
 |isbn=0-444-50426-5
 |page=17
}}
</ref><ref>
{{cite book
 |last=Callen |first=H. B.
 |orig-date=1960 |year=1985
 |title=Thermodynamics and an Introduction to Thermostatistics |edition=1st (1960), 2nd (1985)
 |publisher=John Wiley & Sons
 |place=New York, NY
 |isbn=0-471-86256-8
 |at=Chapter&nbsp;5
}}
</ref><ref>
{{cite book
 |last=Münster |first=A.
 |year=1970
 |title=Classical Thermodynamics
 |translator-first=E. S. |translator-last=Halberstadt
 |publisher=Wiley–Interscience
 |place=London, UK
 |isbn=0-471-62430-6
 |page=6
}}
</ref>