Isothermal process

An isothermal process is a thermodynamic process in which the temperature of a system remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change in the system occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat transfer.

The term "isothermal" comes from the Greek words isos meaning "equal" and therme meaning "heat", indicating a process in which the heat level (temperature) stays the same. Isothermal processes can be contrasted with adiabatic processes, in which the system is insulated from its surroundings and no heat is transferred into or out of the system.

Thermodynamics of an Isothermal Process

In an isothermal process, because the temperature of the system remains constant, the internal energy (U) of an ideal gas also remains constant, due to the internal energy being a function of temperature only. According to the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system, for an isothermal process, this simplifies to Q = W, where Q is the heat transferred and W is the work done by or on the system.

For an ideal gas undergoing an isothermal expansion or compression, the work done can be expressed as W = nRT ln(Vf/Vi), where n is the number of moles of gas, R is the ideal gas constant, T is the absolute temperature, and Vf and Vi are the final and initial volumes, respectively.

Applications of Isothermal Processes

Isothermal processes have practical applications in various fields such as engineering, chemistry, and physics. For example, the isothermal expansion of gases is used in Carnot cycles, which are theoretical thermodynamic cycles that provide a template for the most efficient heat engines. In biotechnology and chemistry, isothermal processes are used in reactions that require constant temperature to ensure the stability of sensitive compounds.

Mathematical Representation

The mathematical representation of an isothermal process for an ideal gas is given by the equation PV = nRT, which is a form of the ideal gas law. This equation shows that, at constant temperature, the product of the pressure (P) and volume (V) of a gas is constant.

See Also

• Thermodynamic processes
• Adiabatic process
• Carnot cycle
• Heat transfer
• Thermal equilibrium