An isothermal process is any process in which the temperature stays constant from start to finish. The word itself breaks down simply: “iso” means same, “thermal” means heat. In thermodynamics, this constant-temperature condition has powerful consequences for how energy moves through a system, and isothermal processes show up in everything from melting ice to the theoretical engines that define the upper limits of efficiency.
How Temperature Stays Constant
For a gas to expand or compress without its temperature changing, two conditions need to be met. First, the gas must be in contact with a heat reservoir, something large enough to absorb or supply heat without its own temperature shifting. Think of a massive body of water or the surrounding atmosphere. Second, the process must happen slowly enough that the gas and the reservoir stay in thermal equilibrium at every moment. If you compress a gas too quickly, it heats up before heat can flow out to the reservoir, and the process stops being isothermal.
In practice, perfectly isothermal processes are an idealization. Real compressions and expansions always involve some temperature fluctuation. But many natural and engineered processes come close enough that the isothermal model is extremely useful.
What Happens to Energy
The first law of thermodynamics says that the change in a system’s internal energy equals the heat added minus the work done by the system. For an ideal gas, internal energy depends only on temperature. So if the temperature doesn’t change, the internal energy doesn’t change either.
That creates a clean relationship: all the heat flowing into the system gets converted directly into work, and all the work done on the system gets released as heat. During an isothermal expansion, the gas absorbs heat from its surroundings and uses that energy entirely to push outward. During an isothermal compression, the work you put in by squeezing the gas gets expelled entirely as heat into the reservoir. No energy gets “stored” as a temperature increase or decrease. It passes straight through.
The Math Behind It
For an ideal gas undergoing an isothermal process, pressure and volume follow a simple inverse relationship. As volume increases, pressure decreases proportionally, and their product stays constant. This is expressed as PV = constant, which you might recognize as a form of Boyle’s Law.
The work done during an isothermal expansion from one volume to another is calculated using a natural logarithm: W = nRT × ln(V₂/V₁), where n is the amount of gas, R is a constant, T is the temperature, and V₁ and V₂ are the starting and ending volumes. The logarithm captures the fact that as the gas expands and pressure drops, each additional bit of expansion does less work than the last. For compression, the formula gives a negative value, reflecting that work is being done on the gas rather than by it.
What It Looks Like on a Graph
On a pressure-volume (PV) diagram, the standard graph used in thermodynamics, an isothermal process traces a smooth curve that sweeps from upper left to lower right. This curve is called an isotherm. Higher temperatures produce curves that sit farther from the origin, while lower temperatures sit closer. The shape is a hyperbola, reflecting that inverse relationship between pressure and volume.
This is visually distinct from an adiabatic process (where no heat is exchanged), which produces a steeper curve on the same diagram. The difference matters because the area under each curve represents the work done, and isothermal processes at a given temperature always do more work during expansion than adiabatic ones starting at the same point.
Phase Changes Are Isothermal
Some of the most familiar isothermal processes have nothing to do with engines or gas cylinders. When ice melts at 0°C, the temperature holds steady even though you’re adding heat. All that incoming energy goes toward breaking the bonds that hold water molecules in their solid structure, not toward raising the temperature. The same thing happens during boiling: water sits at 100°C (at standard pressure) until it has fully converted to steam, no matter how much heat you pour in during the transition.
Sublimation works the same way. Dry ice (solid carbon dioxide) converts directly from solid to gas at a constant temperature. Even the slow shrinking of ice cubes in your freezer is a sublimation process, with solid water molecules gradually escaping into the air inside the freezer. Freezer burn on meat is another example: it’s not a burn at all, but the result of solid water slowly sublimating away from the food’s surface.
The Role in Heat Engines
Isothermal processes are central to the Carnot cycle, the theoretical gold standard for heat engine efficiency. The Carnot cycle consists of four steps: two isothermal and two adiabatic. During the isothermal expansion step, the gas absorbs heat from a high-temperature reservoir and does work. During the isothermal compression step, the gas rejects heat into a low-temperature reservoir.
The efficiency of this ideal engine depends entirely on the temperatures of those two isothermal steps. Specifically, the efficiency equals 1 minus the ratio of the cold temperature to the hot temperature (both measured on an absolute scale). This means no heat engine operating between two given temperatures can ever be more efficient than a Carnot engine, and the isothermal steps are where all the heat exchange happens. Real engines, from car engines to power plants, fall short of Carnot efficiency because their processes are never perfectly isothermal or perfectly adiabatic, but the Carnot cycle sets the ceiling.
Industrial and Practical Uses
In gas compression, which is essential in refrigeration, manufacturing, and energy storage, isothermal compression represents the ideal case because it requires the least amount of work. When gas is compressed without removing heat (adiabatically), the temperature spikes and you end up fighting against increasing pressure. Isothermal compression avoids this by continuously removing heat during the process, keeping pressure lower at every step. Real compressors use intercoolers between compression stages to approximate this, reducing the energy needed and saving on operating costs.
Chemical reactions run at constant temperature in water baths or temperature-controlled reactors also approximate isothermal conditions. Maintaining a steady temperature lets chemists isolate the effects of concentration and catalysts without temperature acting as a variable, which is why isothermal conditions are a default assumption in much of chemistry lab work.