Thermodynamic equations

Thermodynamic equations relate measurable state variables and energy transfers in systems at equilibrium or during changes. They include laws, state equations, and relations for heat, work, and entropy.

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Thermodynamic state: A thermodynamic state is specified by macroscopic properties such as temperature, pressure, and volume. Equations connect the variables used to describe a system's state.
Equation of state: An equation of state relates thermodynamic variables such as pressure, volume, and temperature. It gives explicit constraints among a system's state variables.
Clapeyron equation: The Clapeyron equation relates the slope of a phase boundary to the latent heat and volume change. It predicts how transition pressure changes with temperature.
Ideal gas law: The ideal gas law is the relation PV = nRT for an ideal gas. Its simple equation of state contrasts with broader, interacting-fluid models.
Sadi Carnot: Sadi Carnot was a French engineer whose analysis of heat engines helped establish the foundations of thermodynamics. His cycle analysis preceded the modern mathematical statement of the second law.
State variable: A state variable is a macroscopic property determined by a system's current thermodynamic state. These are the quantities appearing in thermodynamic relations.
Fundamental thermodynamic relation: The fundamental thermodynamic relation connects changes in internal energy with entropy, volume, and particle number. It generates many relations among equilibrium properties.
Kirchhoff's law of thermochemistry: Kirchhoff's law relates a reaction's enthalpy change at different temperatures to heat-capacity differences. It extends measured reaction enthalpies to other temperatures.
Van der Waals equation: The van der Waals equation modifies the ideal gas law to account approximately for molecular attraction and finite molecular size. It illustrates how an equation of state can correct ideal-gas assumptions.
Rudolf Clausius: Rudolf Clausius was a German physicist who formulated foundational statements of thermodynamics and introduced entropy. His work shaped the equations for entropy and reversible heat.