Enthalpy of Moist Air

Enthalpy of moist air ($h$) is the total heat content of 1 kg of dry air together with the water vapor it carries (humidity ratio $x$). It is expressed in kJ per kg of dry air.

Components of enthalpy

$$h = c_{pa} \cdot t + x \cdot (r_0 + c_{pv} \cdot t)$$

where:

• $c_{pa}$ = 1.006 kJ/(kg·K) — specific heat of dry air
• $c_{pv}$ = 1.860 kJ/(kg·K) — specific heat of water vapor
• $r_0$ = 2501 kJ/kg — latent heat of vaporization of water at 0 °C
• $t$ — temperature [°C]
• $x$ — humidity ratio [kg/kg dry air]

Enthalpy in the Mollier diagram

In the h–x diagram the axes are $h$ and $x$ themselves, so the diagram lets you read the enthalpy of any air state directly. Lines of constant enthalpy run parallel to the oblique $h$-axis.

Duty from a change in enthalpy

Cooling or heating duty [kW]:

$$\Phi = \dot{m} \cdot (h_1 - h_2)$$

where $\dot{m}$ is the mass flow of dry air [kg/s] (also written $q_m$ per ISO 80000) and $h_1$, $h_2$ are the inlet and outlet enthalpies.

Sensible and latent heat

• Sensible heat — changes temperature, with no phase change of water
• Latent heat — the energy of the phase change of water (condensation/evaporation)

Enthalpy includes both. A cooling coil must also remove the latent heat of the water vapor whenever it cools the air below its dew point.