isothermal process

In thermodynamics, a process in which the temperature is constant while the system changes. Examples include melting and boiling.

An isothermal process is a thermodynamic process in which the temperature of the system stays constant: ΔT = 0.

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;

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

so that

where Pi and Vi are the pressure and volume of the initial state, Pf and Vf 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. 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.

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.

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.