A thermodynamic process that occurs at constant temperature is called an isothermal process. Heat slowly flows into the system or out of the system to maintain thermal equilibrium. Processes involving phase changes like water evaporation into steam or freezing water into ice at a constant temperature are examples of Isothermal Processes.

An ideal gas can also undergo isothermal expansion or compression.

For example, consider 1 mole of an ideal gas inside an isolated cylinder at initial volume V and pressure p. Suppose the heat added to the system causes a quasistatic expansion of the gas at a constant temperature of 300 K. If the volume of the gas changes to 2V, what is the amount of heat added to the system?

Here the known quantities are the number of moles of the gas, initial and final volume of the gas. The unknown quantity, heat, is to be calculated.

According to the first law of thermodynamics,

As the temperature is constant, the change in internal energy for this process is zero. Thus, the heat added to the system equals the work done by the system.

Now, the work done by an ideal gas during isothermal expansion is given by,

Substituting for the number of moles, gas constant, temperature, initial volume, and the final volume of the gas, the work done is equal to 1728.85 J.

Since the work done by the system equals the heat added to the system, it is considered that 1728.85 J of heat is applied to the system to expand it isothermally to 2V.