concept

enthalpy

Enthalpy is a thermodynamic quantity representing the total heat content of a system at constant pressure.
57 related articles · 6 formulas · 1 who worked here

Description

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.

History

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.

How it works

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.

Fun fact

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.

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Formulas

$$\frac{d\epsilon}{dn} = \frac{\epsilon + p}{n}$$
The energy gradient per particle equals enthalpy per particle.
What is in the formula
\epsilonvariableenergy density — energy density joule per cubic metre
nvariableparticle number density — number density per cubic metre
pvariablepressure — pressure pascal
\frac{d}{dn}operatorderivative with respect to particle number density — derivative with respect to number density
\frac{dε}{dn}=\frac{ε+p}{n} · 2605.08584v2
$$\mathrm{EIRP} = 4\pi d^2 S$$
EIRP is the power needed for an isotropic radiator to produce flux density S at distance d.
What is in the formula
EIRPvariableEffective isotropic radiated power — power watt
dvariableDistance from source — distance metre
SvariablePower flux density — power flux density watt per square metre
4πd²operatorSurface area of a sphere of radius d — sphere surface area
{eirp}=4πd^2s_{\min}δν · 2607.01666v1
$$\Delta H_f = H_{\text{compound}} - \sum x_i H_i^{\text{element}}$$
Energy difference between compound and its elements.
What is in the formula
ΔH_fvariableFormation enthalpy change — enthalpy joule per mole
H_compoundvariableEnthalpy of the compound — enthalpy joule per mole
x_ivariableStoichiometric coefficient of element i — stoichiometric coefficient
H_i^elementvariableEnthalpy of element i in its standard state — enthalpy joule per mole
ΣoperatorSum over constituent elements — summation
e_{{hull}}=e_{a}-\sum_ix_ie_i^{{stable}} · 2607.01713
$$\Delta H_{\text{hull}} = \Delta_f H - E_{\text{hull}}$$
Positive hull enthalpy indicates thermodynamic instability.
What is in the formula
\Delta H_{\text{hullvariableHull enthalpy, energy above convex hull — enthalpy joule per mole
\Delta_f HvariableFormation enthalpy of the compound — enthalpy joule per mole
E_{\text{hull}}variableConvex hull energy at the composition — energy joule per mole
δ_{{hull}}h({x}_\varphi)=δ_fh({x}_\varphi)-e_{{gs}}({x}_\varphi) · 2607.04502
$$S = k_B \ln \Omega$$
Entropy equals Boltzmann constant times log of states.
What is in the formula
Svariableentropy of the system — entropy joule per kelvin
Ωvariablenumber of microstates corresponding to the macrostate — number of microstates
k_Bconstantrelates temperature to energy per degree of freedom — boltzmann constant = 1.380649e-23 joule per kelvin
lnoperatornatural logarithm — natural logarithm
s=k_b\lnω · 2505.02040v2
s=k\logw · 2604.06450
$$C_P = \left( \frac{\partial H}{\partial T} \right)_P$$
Heat capacity at constant pressure is the derivative of enthalpy with respect to temperature.
What is in the formula
C_PvariableHeat capacity at constant pressure — heat capacity joule per kelvin
HvariableEnthalpy — enthalpy joule
TvariableTemperature — temperature kelvin
PvariablePressure (held constant) — pressure pascal
∂/∂ToperatorPartial derivative with respect to temperature — partial derivative
c_p(t)=(\frac{\partialh}{\partialt})_p · 2607.08957

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