Isothermal process

An isothermal process is a thermodynamic process in which the temperature of the system stays constant: Δ"T" = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and processes occur slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange. An alternative special case in which a system exchanges no heat with its surroundings ("Q" = 0) is called an "adiabatic process".

Consider an ideal gas, in which the temperature depends only on the internal energy, which is a function of the mean translational kinetic energy of the molecules, as given by a Boltzmann distribution; if the internal energy is constant, so is the temperature. Take the number of moles "n" as a constant.

: Delta U = n R Delta T = 0 ,

but this means, according to the ideal gas law, that

: Delta (P V) = 0 ,

so that

: P_i V_i = P V = P_f V_f ,

where P_i and V_i are the pressure and volume of the initial state, P_f and V_f are the pressure and volume of the final state, and the variables "P" and "V" stand for the pressure and volume of any intermediate state during an isothermal process.

Curves called "isotherms" appear as a hyperbolas on a "P"-"V" (pressure-volume) diagram ("T" = constant). Each one asymptotically approaches both the "V" (abscissa) and "P" (ordinate) axes. This corresponds to a one-parameter family of curves, a function of "T", whose equation is

: P = {n R T over V} ,

By the first law of thermodynamics, the isotherms of an ideal gas are also determined by the condition that

: Q = W ,

where "W" is work done "on" the system. (While "Q" and "W" are incremental quantities, they do not represent differentials of state functions.) This means that, during an isothermal process, all heat accepted by the system from its surroundings must have its energy entirely converted to work which it performs on the surroundings. That is, all the energy which comes into the system comes back out; the internal energy and thus the temperature of the system remain constant.

In a minute process of this process, the minute work "dW" can be shown as follow.

:dW=Fdx=PSdx=PdV

Therefore the entire work of the process from A to B is shown with the integration of the previous equation.

:W_{A o B}=int_{V_A}^{V_B}dW=int_{V_A}^{V_B}PdV

Here, by the ideal gas equation,

:W_{A o B}=int_{V_A}^{V_B}PdV=int_{V_A}^{V_B}frac{nRT}{V}dV=nRTln{frac{V_B}{V_A

Therefore in the isothermal process, the following equation is formed.

:W_{A o B}=Q=nRTln{frac{V_B}{V_A

Isothermal processes can occur in any kind of system, including highly structured machines, and even living cells. Various parts of the cycle of some heat engines are carried out isothermally and may be approximated by a Carnot cycle.


See also

* Adiabatic process
* Cyclic process
* Isobaric process
* Isochoric process
* Polytropic process


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • isothermal process —  Isothermal Process  Изотермический процесс   Процесс, происходящей в системе при постоянной температуре. На термодинамических диаграммах состояния изображается изотермой. Для осуществления такого процесса систему обычно помещают в термостат,… …   Толковый англо-русский словарь по нанотехнологии. - М.

  • isothermal process — izoterminis vyksmas statusas T sritis Standartizacija ir metrologija apibrėžtis Pastovioje temperatūroje vykstantis vyksmas. atitikmenys: angl. isothermal process vok. isotherme Zustandsänderung, f; isothermer Prozess, m rus. изотермический… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

  • isothermal process — izoterminis procesas statusas T sritis chemija apibrėžtis Pastovioje temperatūroje vykstantis procesas. atitikmenys: angl. isothermal process rus. изотермический процесс …   Chemijos terminų aiškinamasis žodynas

  • isothermal process — izoterminis procesas statusas T sritis Energetika apibrėžtis Termodinaminis procesas, vykstantis esant pastoviajai temperatūrai, pvz., chemiškai vienalytės medžiagos virimas, esant pastoviajam aplinkos slėgiui. atitikmenys: angl. isothermal… …   Aiškinamasis šiluminės ir branduolinės technikos terminų žodynas

  • isothermal process — Thermodynam. a process that takes place without change in temperature. * * * …   Universalium

  • isothermal process — /aɪsəˈθɜməl proʊsɛs/ (say uysuh thermuhl prohses) noun a process which takes place without change in temperature …   Australian English dictionary

  • isothermal process — Thermodynam. a process that takes place without change in temperature …   Useful english dictionary

  • isothermal process — Смотри изотермический процесс …   Энциклопедический словарь по металлургии

  • isothermal — 1. adjective a) Of or pertaining to a process that takes place at constant temperature b) Of or pertaining to an isotherm 2. noun An isotherm …   Wiktionary

  • isothermal — adjective of a process or change taking place at constant temperature (Freq. 1) • Similar to: ↑equal • Derivationally related forms: ↑isotherm …   Useful english dictionary


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.