- Isothermal process
An isothermal process is a
thermodynamic process in which thetemperature of thesystem staysconstant : 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 throughheat exchange. An alternative special case in which a system exchanges no heat with itssurroundings ("Q" = 0) is called an "adiabatic process ".Consider an
ideal gas , in which the temperature depends only on theinternal energy , which is a function of the mean translationalkinetic energy of themolecule s, as given by aBoltzmann distribution ; if the internal energy is constant, so is the temperature. Take the number of moles "n" as a constant.:
but this means, according to the
ideal gas law , that:
so that
:
where and are the pressure and volume of the initial state, and are the pressure and volume of the final state, and the
variable s "P" and "V" stand for the pressure and volume of any intermediate state during an isothermal process.Curves called "isotherms" appear as a
hyperbola s 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:
By the
first law of thermodynamics , the isotherms of an ideal gas are also determined by the condition that:
where "W" is work done "on" the system. (While "Q" and "W" are incremental quantities, they do not represent differentials of
state function s.) This means that, during an isothermal process, all heat accepted by the system from its surroundings must have itsenergy 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.
:
Therefore the entire work of the process from A to B is shown with the integration of the previous equation.
:
Here, by the ideal gas equation,
:
Therefore in the isothermal process, the following equation is formed.
:
Isothermal processes can occur in any kind of system, including highly structured
machines , and even living cells. Various parts of the cycle of someheat engine s are carried out isothermally and may be approximated by aCarnot cycle .See also
*
Adiabatic process
*Cyclic process
*Isobaric process
*Isochoric process
*Polytropic process
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