Isotherm

An isotherm is a curve or line of equal temperature. In thermodynamics, it is a curve on a pressure–volume diagram along which the temperature remains constant. For an ideal gas, the equation PV = nRT relates pressure P, volume V, amount n, and temperature T, so at fixed n and T an isotherm is a hyperbola given by P = nRT / V.

During an isothermal process, the temperature does not change. For an ideal gas this implies the internal energy depends only on temperature, so dU = 0 and all heat added or removed appears as work; the work for a reversible isothermal expansion from V1 to V2 is W = nRT ln(V2/V1).

In adsorption science, an isotherm describes how much adsorbate a surface holds as a function of pressure at a fixed temperature. Common models include Langmuir, Freundlich, and the Brunauer–Emmett–Teller (BET) equation. These models help characterize surface area, porosity, and interaction strength between adsorbate and substrate.

In meteorology and geography, isotherms are lines of equal temperature on maps. They reveal spatial temperature patterns, gradients, and can indicate air masses, fronts, and climatic zones.

Overall, isotherms provide a simple, widely used tool to represent how temperature interacts with pressure or abundance in physical systems and environmental data.