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Temperature and pressure are fundamental state variables that describe a system's thermodynamic state. Temperature measures average molecular energy, while pressure is the force per unit area exerted by particles on their surroundings. Together, they influence phase, density, and chemical potential. Temperature is measured in kelvin or Celsius; pressure in pascals, kilopascals, bars, or atmospheres.

For an ideal gas, PV = nRT. At fixed n and V, P is proportional to T (Gay-Lussac's law). At fixed T, P is inversely proportional to V (Boyle's law). The combined gas law describes how P, V, and T change together. Real gases deviate at high pressure or low temperature; van der Waals corrections account for molecular size and interactions.

In liquids and solids, temperature affects pressure through thermal expansion and density changes. Liquids have vapor pressure that rises with T, enabling evaporation and boiling. In closed rigid vessels, heating raises internal pressure; in open systems, vapor may escape.

Applications span meteorology, HVAC, manufacturing, and materials science, where temperature–pressure effects are essential for design and safety. Instruments include thermometers and pressure sensors; distinctions exist between absolute and gauge pressure, with common units such as Pa, kPa, bar, and atm.

In summary, the temperature–pressure relationship governs phase behavior and material properties, and is described by thermodynamics, kinetics, and empirical correlations for real materials.