## Isothermal Process

An **isothermal process** is a **thermodynamic process**, in which the **temperature** of the system **remains constant** (T = const). The heat transfer into or out of the system typically must happen at such a slow rate in order to continually adjust to the temperature of the reservoir through heat exchange. In each of these states the **thermal equilibrium** is maintained.

For an** ideal gas** and a polytropic process, the case ** n = 1 **corresponds to an

**isothermal**(constant-temperature) process. In contrast to

**adiabatic process**, in which

*n = κ**and*

*a system exchanges no heat with its surroundings (Q = 0;*

*∆T≠0*

*)*

*, in an isothermal process there is no change in the internal energy (due to ∆T=0) and therefore*

*ΔU = 0 (for ideal gases) and Q ≠ 0.*An adiabatic process is not necessarily an isothermal process, nor is an isothermal process necessarily adiabatic.

In engineering, phase changes, such as evaporation or melting, are isothermal processes when, as is usually the case, they occur at constant pressure and temperature.

## Isothermal Curve – Isotherm

On a pV diagram, the process occurs along a line called **isothermal curve** or an **isotherm**. This curve has the equation** p = constant / V**. It can be derived from ideal gas law.

In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume.

*pV = nRT*

where:

*p*is the absolute pressure of the gas*n*is the amount of substance*T*is the absolute temperature*V*is the volume*R*is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant,

In this equation the symbol R is a constant called the **universal gas constant** that has the same value for all gases—namely, R = 8.31 J/mol K.

The **isothermal process **can be expressed with the **ideal gas law** as:

*pV = constant*

and the** isotherm **can be expressed as:

*p = constant / V*

It corresponds to the **Boyle-Mariotte Law**, which states that:

*For a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure.*

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