Isothermal process

An isothermal process is a specific type of thermodynamic process where the temperature of a system remains constant. In scientific terms, this means the change in temperature, or delta T, is zero. This concept is vital because it provides a baseline for scientists to study more complex, non-isothermal processes. By understanding how systems behave when temperature is fixed, researchers can better analyze real-world changes.

The term itself comes from Ancient Greek roots, where "iso" means equal and "therm" means heat.

To achieve a constant temperature, a system must interact with its environment in a very specific way. Usually, the system stays in contact with an outside thermal reservoir. A thermal reservoir is a large source of heat that maintains a steady temperature. For the process to remain isothermal, the changes must occur slowly. This slow pace allows the system to continuously adjust to the reservoir through heat exchange. This is often referred to as quasi-equilibrium. This differs from an adiabatic process, where no heat is exchanged with the surroundings at all.

In an ideal gas, the mechanics of an isothermal process are governed by Joule's second law. This law states that the internal energy of a fixed amount of an ideal gas depends only on its temperature. Because the temperature does not change during an isothermal process, the internal energy also remains constant. This happens because there are no intermolecular forces between the particles in an ideal gas. However, this rule does not apply to liquids, solids, or real gases. For those substances, internal energy depends on both temperature and pressure.

When we look at the work performed during these processes, we see a direct link between energy and movement. In isothermal compression, work is done on the system to decrease its volume and increase its pressure. This work adds energy to the gas, which would normally raise the temperature. To prevent this rise, energy must leave the system as heat and enter the environment. In the case of an ideal gas, the amount of heat leaving is exactly equal to the work done on the gas.

Conversely, during isothermal expansion, the system does work on its surroundings by using energy supplied to it.

Scientists often visualize these processes using indicator diagrams, which are graphs of pressure versus volume. These diagrams were used by James Watt and other early engineers to monitor engine efficiency. Each curve on the graph is called an isotherm, representing a single, constant temperature.

For gases following Boyle's law, the product of pressure and volume remains constant during an isothermal process. This relationship is expressed by the ideal gas law, where the constant is determined by the number of moles, the ideal gas constant, and the absolute temperature. On these graphs, the temperature increases as you move from the lower left toward the upper right.

We can see a practical example of this through a piston in a cylindrical chamber. Imagine a working gas at 400 K in a chamber that is 1 meter high with a 1 meter squared area. If a piston allows the gas to expand from 2 atm to 1 atm, the gas performs mechanical work.

This expansion can be used to turn a crank-arm or a pulley to lift water from a mine. In this specific example, the total heat supplied is -140.5 kJ, while the usable mechanical work is -39.1 kJ. This means 27.9% of the heat was converted into useful work. The efficiency of this conversion depends on the specific temperature and pressure conditions.

Isothermal processes are also essential for calculating changes in entropy. Entropy is a measure of a system's state, and for a reversible isothermal process, the change in entropy is calculated by dividing the heat transferred by the absolute temperature. This is very useful during phase changes, such as when a substance melts or evaporates at a constant pressure. In these cases, the heat transferred is equal to the enthalpy of transformation. Because entropy is a state function, scientists can use these formulas to understand even irreversible processes, like the free expansion of a gas.