An isothermal process is a thermodynamic process, in which the temperature of the system remains constant (T = const). The heat transfer into or out of the system typically must happen at such a slow rate in order to continually adjust to the temperature of the reservoir through heat exchange. In each of these states the thermal equilibrium is maintained.
Isothermal Process and the First Law
The classical form of the first law of thermodynamics is the following equation:
dU = dQ – dW
In this equation dW is equal to dW = pdV and is known as the boundary work.
In isothermal process and the ideal gas, all heat added to the system will be used to do work:
Isothermal process (dU = 0):
dU = 0 = Q – W → W = Q (for ideal gas)
Isothermal Process of the Ideal Gas
The isothermal process can be expressed with the ideal gas law as:
pV = constant
p1V1 = p2V2
On a p-V diagram, the process occurs along a line (called an isotherm) that has the equation p = constant / V.
See also: Boyle-Mariotte Law