Editing Isothermal process (section)

== Examples ==
Isothermal processes can occur in any kind of system that has some means of regulating the temperature, including highly structured [[machines]], and even [[life|living]] cells. Some parts of the cycles of some [[heat engine]]s are carried out isothermally (for example, in the [[Carnot cycle]]).<ref>{{cite book|last=Keenan |first=J. H. |date=1970 |title=Thermodynamics |chapter=Chapter 12: Heat-engine cycles |publisher=MIT Press |location=Cambridge, Massachusetts}}</ref> In the thermodynamic analysis of [[Chemical thermodynamics|chemical reactions]], it is usual to first analyze what happens under isothermal conditions and then consider the effect of temperature.<ref name=":Rock">{{cite book|last=Rock |first=P. A. |date=1983 |title=Chemical Thermodynamics |chapter=Chapter 11: Thermodynamics of chemical reactions |publisher=University Science Books |location=Mill Valley, CA |isbn=0-935702-12-1}}</ref> [[Phase changes]], such as [[melting]] or [[evaporation]], are also isothermal processes when, as is usually the case, they occur at constant pressure.<ref name="Petrucci">{{cite book |last1=Petrucci |first1=R. H. |first2=W. S. |last2=Harwood |first3=F. G. |last3=Herring |first4=J. D. |last4=Madura |date=2007 |title=General Chemistry |chapter=Chapter 12 |publisher=Pearson |location=Upper Saddle River, NJ |isbn=978-0-13-149330-8 |url-access=registration |url=https://archive.org/details/generalchemistry0000petr }}</ref> Isothermal processes are often used as a starting point in analyzing more complex, non-isothermal processes.

Isothermal processes are of special interest for ideal gases. This is a consequence of [[Joule–Thomson effect#Joule's second law|Joule's second law]] which states that the [[internal energy]] of a fixed amount of an ideal gas depends only on its temperature.<ref name="Klotz">{{cite book|last1=Klotz |first1=I. M. |first2=R. M. |last2=Rosenberg |date=1991 |title=Chemical Thermodynamics |chapter=Chapter 6, Application of the first law to gases |publisher=Benjamin |location=Meno Park, CA}}{{ISBN missing}}</ref> Thus, in an isothermal process the internal energy of an ideal gas is constant. This is a result of the fact that in an ideal gas there are no [[intermolecular forces]].<ref name="Klotz"/> Note that this is true only for ideal gases; the internal energy depends on pressure as well as on temperature for liquids, solids, and real gases.<ref>{{cite book|last=Adkins |first=C. J. |date=1983 |title=Equilibrium Thermodynamics |publisher=Cambridge University Press |location=Cambridge}}{{ISBN missing}}</ref>

In the isothermal compression of a gas there is work done on the system to decrease the volume and increase the pressure.<ref name="Klotz"/> Doing work on the gas increases the internal energy and will tend to increase the temperature. To maintain the constant temperature energy must leave the system as heat and enter the environment. If the gas is ideal, the amount of energy entering the environment is equal to the work done on the gas, because internal energy does not change. For isothermal expansion, the energy supplied to the system does work on the surroundings.  In either case, with the aid of a suitable linkage the change in gas volume can perform useful mechanical work.  For details of the calculations, see [[Isothermal process#Calculation of work|calculation of work]].

For an [[adiabatic process]], in which no heat flows into or out of the gas because its container is well insulated, ''Q''&nbsp;=&nbsp;0. If there is also no work done, i.e. a [[Joule expansion|free expansion]], there is no change in internal energy. For an ideal gas, this means that the process is also isothermal.<ref name="Klotz"/> Thus, specifying that a process is isothermal is not sufficient to specify a unique process.