Enthalpy

Definition

Enthalpy ($H$) is a thermodynamic potential that represents the total heat content of a system. It is defined as the sum of the system’s internal energy and the energy required to make space for it (boundary work).

It is the preferred potential for analyzing open systems (flow processes) and constant-pressure processes.

Formula

$\boxed{H \equiv U + PV}$ In specific (per unit mass) terms: $h = u + Pv$

Relationships

• Related: Internal Energy, Steady-Flow Energy Equation, Entropy
• Is A: Thermodynamic Potentials
• Natural Variables: Entropy, Pressure

Physical Interpretation

Flow Energy (Open Systems)

In control volumes (like turbines or pumps), fluid carries not just internal energy ($u$), but also “flow work” ($Pv$)—the energy required to push the fluid across the boundary. Enthalpy conveniently groups these terms: $\theta = u + Pv = h$ This simplifies the Steady-Flow Energy Equation.

Heat at Constant Pressure (Closed Systems)

For a closed system undergoing a reversible isobaric process ($dP=0$): $dQ = dH$ This makes $\Delta H$ equivalent to the heat of reaction in chemistry or heat transfer in constant-pressure boilers.

Ideal Gases

For ideal gases, enthalpy depends only on temperature (since $Pv = RT$ and $u=u(T)$): $h(T) = u(T) + RT$ The change in enthalpy is simply: $\Delta h = \int_{T_1}^{T_2} c_p(T)\,dT$