
Enthalpy is a thermodynamic quantity representing the total heat content of a system at constant pressure.Energy that a substance stores as heat and the ability to push or expand. By heating a pot of water, you increase its enthalpy: part goes to heating, part to expansion. It's like a battery: it's not just hot, but also exerts pressure on the pipes to heat the room.
The roots of the concept go back to the work of Hermann Helmholtz and Rudolf Clausius (1850s), who called it 'heat content'. In 1909, Heike Kamerlingh Onnes introduced the modern name from the Greek 'to heat'. Later, with the development of statistical physics, enthalpy received a microscopic foundation as the average energy of a system at fixed pressure and temperature.
From the first law of thermodynamics: dU = δQ - P dV. At constant pressure, dH = dU + P dV = δQ. Therefore, the heat effect of a reaction at P=const equals ΔH. The second law of thermodynamics, through the Gibbs free energy G = H - TS, determines the direction of spontaneous processes. In engineering, the enthalpy of steam or refrigerant allows calculation of cycle efficiencies.
Melting ice absorbs 334 J per gram without raising the temperature — its enthalpy jumps. That's why a handful of snow thrown into a fire hisses and cools down faster than it seems.
| \epsilon | variable | energy density — energy density joule per cubic metre |
| n | variable | particle number density — number density per cubic metre |
| p | variable | pressure — pressure pascal |
| \frac{d}{dn} | operator | derivative with respect to particle number density — derivative with respect to number density |
| EIRP | variable | Effective isotropic radiated power — power watt |
| d | variable | Distance from source — distance metre |
| S | variable | Power flux density — power flux density watt per square metre |
| 4πd² | operator | Surface area of a sphere of radius d — sphere surface area |
| ΔH_f | variable | Formation enthalpy change — enthalpy joule per mole |
| H_compound | variable | Enthalpy of the compound — enthalpy joule per mole |
| x_i | variable | Stoichiometric coefficient of element i — stoichiometric coefficient |
| H_i^element | variable | Enthalpy of element i in its standard state — enthalpy joule per mole |
| Σ | operator | Sum over constituent elements — summation |
| \Delta H_{\text{hull | variable | Hull enthalpy, energy above convex hull — enthalpy joule per mole |
| \Delta_f H | variable | Formation enthalpy of the compound — enthalpy joule per mole |
| E_{\text{hull}} | variable | Convex hull energy at the composition — energy joule per mole |
| S | variable | entropy of the system — entropy joule per kelvin |
| Ω | variable | number of microstates corresponding to the macrostate — number of microstates |
| k_B | constant | relates temperature to energy per degree of freedom — boltzmann constant = 1.380649e-23 joule per kelvin |
| ln | operator | natural logarithm — natural logarithm |
| C_P | variable | Heat capacity at constant pressure — heat capacity joule per kelvin |
| H | variable | Enthalpy — enthalpy joule |
| T | variable | Temperature — temperature kelvin |
| P | variable | Pressure (held constant) — pressure pascal |
| ∂/∂T | operator | Partial derivative with respect to temperature — partial derivative |
















