The isothermal change of state is a thermodynamic change of state in which the temperature remains unchanged:
There denote and the temperatures before and after the change of state. When a gas is compressed, the heat of compression has to be dissipated, and when it is expanded, heat has to be added ( diabatic change of state ) . This can be achieved approximately by a heat bath .
According to Boyle-Mariotte's law and the caloric equation of state of an ideal gas , the product of pressure and volume as well as the internal energy remain constant at constant temperature :
From this it follows that the pressures are inversely proportional to the corresponding volumes:
For the work done, the following applies to isothermal compression or expansion of moles of an ideal gas:
where denotes the universal gas constant .
Because is . According to the first law of thermodynamics ( ) it follows that the added or extracted heat corresponds directly to the work performed ( ).