Enthalpy

Thermodynamic potential for constant-pressure processes; H = U + pV. Theory, formulas, worked examples and interactive graphs.

Conceptual context

Enthalpy $H$ is the thermodynamic potential designed for processes that occur at constant pressure, the most common condition in laboratory, chemical industry, and biology. When an open vessel allows the system to exchange expansion work with the atmosphere, internal energy alone does not describe the heat exchange: the push-work term $p$·$V$ must be added.

The concept arose from the practical need to tabulate reaction heats without measuring mechanical expansion work separately. Today, tables of standard enthalpies of formation allow prediction of the heat exchanged in thousands of reactions without performing any additional experiment.

Enthalpy sits in the tree of thermodynamic potentials alongside Gibbs free energy and Helmholtz free energy. Each potential governs a specific set of conditions: $H$ governs when $p$ is constant, Helmholtz free energy when volume is constant, and Gibbs free energy when both $p$ and $T$ are constant.

🟢 Essential level

Enthalpy $H$ answers a simple question: when a process occurs at constant pressure, how much heat does the system exchange with the surroundings? The answer is $\Delta H$. If $\Delta H$ is negative, the system releases heat and the process is exothermic; if positive, the system absorbs heat and the process is endothermic.

The intuition is as follows: internal energy $U$ measures all energy stored molecularly, but at constant pressure the system also performs mechanical expansion work to push against the atmosphere. Enthalpy incorporates that work into a single quantity, so $\Delta H$ captures both the change in internal energy and the expansion work exchanged with the surroundings.

That is why $\Delta H$ is best read as the useful thermal balance of a process open to the atmosphere. It does not simply say whether the microscopic energy goes up or down: it says how much heat the laboratory actually sees when the external pressure stays fixed. This distinction prevents confusing a heat-releasing reaction with a plain decrease in $U$ that ignores the accompanying volume change.

🔵 Formal level

Basic formulas

The definition of enthalpy combines internal energy with the pressure-volume product:

Definition of enthalpy

In a constant-pressure process, the enthalpy change equals the exchanged heat:

Heat at constant pressure equals ΔH

The first formula builds $H$ as a new state property; the second shows why that construction is useful in practice: it turns a direct calorimetric measurement into an enthalpy change.

Real student questions

Why use $\Delta H$ instead of $U$ for laboratory reactions? In the laboratory, vessels are open and atmospheric pressure remains constant. The system exchanges expansion work with the atmosphere without the experimenter controlling it. By using $\Delta H$, that work is automatically included and the calorimeter directly measures $\Delta H$ without separately measuring volumes or pressures.

What happens when $\Delta H$ is exactly zero? No heat is exchanged at constant pressure. Mechanical work may still occur, but the system temperature does not change if heat capacity is non-zero. A process with zero $\Delta H$ does not mean nothing happens; the system can still change its entropy and volume.

Does Hess's law always work? It works whenever $H$ is a state function, which holds for any thermodynamic system in equilibrium. The only practical condition is that all steps in the cycle are constant-pressure processes. If any step is at constant volume, the expansion work term must be included as a correction.

Why does reversing a reaction change the sign of $\Delta H$? Because $H$ is a state function: the path from A to B has the same $\Delta H$ in magnitude as from B to A, but with the opposite sign. If carbon combustion releases 394 kJ/mol, synthesizing carbon from carbon dioxide absorbs exactly 394 kJ/mol.

Final synthesis

$\Delta H$ is the heat of a constant-pressure process, the most common condition in chemistry and technology. Its additivity, guaranteed by Hess's law, allows computing enthalpies of reactions that cannot be measured directly from standard tables. Mastering its sign, its units, and the isobaric condition is mastering practical calorimetry.