# What Is an Isothermal Process?

Isothermal process is a thermodynamic transformation at constant temperature. That is a variation of the state of a physical system during which the temperature of the system remains constant. Since the internal energy of an ideal gas depends only on temperature and, in an isothermal process, remains constant in expansion, the heat taken from the focus is equal to the work done by the gas: Q = W. According to the first law of thermodynamics

Thermostats are devices that can maintain a constant temperature value in this kind of thermodynamic process.

Boyle's law describes the isothermal transformation of a perfect gas. “The pressure exerted by a chemical force is inversely proportional to the gaseous mass, as long as its temperature remains constant. (If the volume increases the pressure decreases, and if the volume decreases the pressure increases).”

Isobaric process is the same but keeping the pressure constant.

## Examples of Isothermal Processes

Isothermal processes can occur in any type of system that has some means of regulating temperature. Below we list some examples:

• The phase changes of different liquids through the melting and evaporation process are isothermal.

• Certain cycles of heat engines; for instance, Carnot's machine. Part of the Carnot cycle is performed and the temperature remains constant.

• Reactions in the refrigerator are isothermal and a constant temperature is maintained.

• In biology, the interactions of a cell with its surrounding cells is done through isothermal processes.

## Isothermal Processes in Ideal Gases

In physics and thermodynamics, isothermal processes are of special interest for ideal gases. This is a consequence of Joule's second law. This law states that the internal energy of a fixed quantity of an ideal gas depends only on temperature.

Therefore, in an isothermal process, the internal energy of an ideal gas is constant. This is the result of the fact that in an ideal gas there are no intermolecular forces. Internal energy depends on temperature, pressure, and volume.

In this process, work is carried out that alters the volume and pressure. This work involves a variation of the internal energy and will tend to increase the temperature. Keeping the temperature constant requires heat exchange with the outside.

In an isothermal expansion, the heat energy is absorbed, in a compression the heat energy is released. The amount of heat transferred is the same as the work done. For the gas to expand, it must be supplied with heat.

## Comparison of the Work Between the Isothermal and the Adiabatic Process

The adiabatic process is taken as the "ideal" theoretical reference. It shows the behavior without thermal loss, which means an energy efficiency of exactly 100%.

### Work Required for Isothermal Compression

The work done on the system required for isothermal compression is greater than the work required for the same adiabatic compression. It means that the gas heated by compression is warmer than room temperature. In the isothermal case, heat energy can leave the system.

The additional work corresponds to the thermal energy of the system lost.

### Theoretical Energy Efficiency

Therefore, the theoretical energy efficiency of isothermal compression is less than using an adiabatic process (100%). It follows that the theoretical energy efficiency of an isothermal compression is less than 100%.

It is found, for example, in the study of the Carnot cycle.

### Work Resulting from an Expansion

The work resulting from an isothermal expansion is greater than the work resulting from the same adiabatic expansion. The gas-cooled by the expansion is colder than the ambient temperature. In the isothermal case, heat can enter the system. The additional work observed for the isothermal expansion corresponds to the thermal energy obtained by the system.

Consequently, the theoretical energy efficiency of an isothermal expansion is greater than the same expansion in an adiabatic process (100%). It follows that the theoretical energy efficiency of an isothermal expansion is greater than 100%, which is found, for example, in the study of a refrigeration machine.

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Published: March 8, 2018
Last review: June 23, 2020