Enthalpy
Enthalpy (H) is a thermodynamic state function defined as H = U + pV, the internal energy plus the product of pressure and volume. For a process at constant pressure in which the only work is expansion work, the change in enthalpy equals the heat absorbed, ΔH = Qp, which makes enthalpy the natural energy bookkeeping quantity for chemistry, phase changes and open flow systems.
Curious
Most everyday processes, such as boiling a kettle, burning fuel or dissolving salt, happen at roughly constant atmospheric pressure. If a system expands, it must push back the surrounding air, which costs work. Enthalpy packages internal energy together with that “room-making” term pV, so the heat you supply at constant pressure equals the change in enthalpy (see First Law).
Chemists tabulate reaction enthalpies: burning one mole of methane releases about 890 kJ (ΔH = −890 kJ/mol, with liquid water as product). Negative ΔH means heat is released (exothermic); positive means it is absorbed (endothermic).
Exploring
| Quantity | Natural use | Equals heat when |
|---|---|---|
| Internal energy U | Closed, rigid systems | Volume is constant |
| Enthalpy H = U + pV | Chemistry, flow systems, phase changes | Pressure is constant |
| Gibbs energy G = H − TS | Spontaneity at constant T and p | (not a heat; gives maximum non-expansion work) |
Deep Dive
Differential form. From dU = T dS − p dV, dH = T dS + V dp, so H is naturally a function of entropy and pressure, and Cp = (∂H/∂T)p. The name “enthalpy” was proposed by Heike Kamerlingh Onnes in the early twentieth century (see Heike Kamerlingh Onnes); Gibbs had used the quantity, calling it the heat function for constant pressure.
Open systems and throttling. For steady flow through a device, the first law becomes Δh + Δ(v²/2) + gΔz = q − wshaft per unit mass, which is why turbines, compressors and nozzles are analysed with specific enthalpy h. In a throttling process (gas forced through a valve without heat exchange), enthalpy is conserved; the resulting temperature change, the Joule–Thomson effect, is zero for an ideal gas but is used to liquefy real gases such as nitrogen and helium (see Superconductivity for why cryogenics matters).
Hess's law. Because H is a state function, the enthalpy change of a reaction is independent of the path, so reaction enthalpies can be combined additively from tabulated standard enthalpies of formation. Tabulated values depend on the chosen standard state (since 1982 IUPAC uses 1 bar), a common source of small discrepancies between data sources.
Concept Relationship Map
Requires: first law, internal energy
Enables: latent heat, Gibbs free energy, flow-system analysis
Commonly confused with: entropy; “heat content”
Sources
- Gibbs, J.W. (1876, 1878). Transactions of the Connecticut Academy, 3, 108–248, 343–524.
- Atkins, P., de Paula, J. (2014). Atkins' Physical Chemistry (10th ed.). Oxford University Press.
- Callen, H.B. (1985). Thermodynamics and an Introduction to Thermostatistics (2nd ed.). Wiley.