Pressuretemperature

Pressure and temperature are fundamental thermodynamic state variables. Their relationship controls the behavior of gases, liquids, and solids, and governs phase transitions, chemical reactions, and many engineering processes. Pressure–temperature relationships are described by simple laws for idealized systems or by more complex models for real substances.

In gases, the ideal gas law PV = nRT relates P, V, and T for a fixed amount of gas. At fixed volume, pressure varies with temperature; at fixed pressure, volume varies with temperature. Under heating at constant pressure, both temperature and volume rise; under heating at constant volume, pressure rises as temperature increases. These are the isobaric and isochoric processes.

Phase diagrams plot pressure against temperature to show where solid, liquid, and gas phases exist for a substance. The curved lines mark phase equilibria and define saturated pressure at a given temperature. The triple point is where all three phases coexist, and the critical point marks the end of distinct liquid and gas phases. Along these boundaries, latent heat drives phase changes even without large temperature changes.

Real substances deviate from ideal behavior, especially at high pressures or low temperatures. Equations of state such as the van der Waals model or more accurate cubic EOS adjust for molecular size and intermolecular forces to predict P–T behavior.

Applications span meteorology, HVAC, chemical engineering, materials science, and cooking. Temperature is measured on scales such as kelvin, and pressure is expressed in pascals, bars, or atmospheres. Understanding pressure–temperature relations supports design, safety, and analysis of systems that involve heating, compression, phase changes, and gas handling.