Isothermal process

The isothermal state change is a thermodynamic change of state, in which the temperature remains unchanged. At a compression of a gas so the compression heat must be dissipated or supplied at a heat expansion. This can be achieved by a heating bath approximately. According to the law of Boyle -Mariotte and the equation of state of an ideal gas, the product of pressure and volume at constant temperature T is also constant:

It also follows that the pressures are inversely proportional to the corresponding volumes:

For the work performed is valid for an isothermal compression or expansion of moles of an ideal gas:

Wherein the universal gas constant. According to the first law of thermodynamics () follows with (and therefore ) that the supplied or heat extracted directly is the work done (). It follows, where is the internal energy.