Energy balances: sensible heat, latent heat, duty

Energy is conserved on the same terms as mass: around an envelope, the energy in minus the energy out equals the energy accumulated, and at steady state the two flows balance. For most process heating and cooling the energy of interest is thermal, and the energy balance becomes the tool that sizes every heater, cooler, exchanger, condenser and reboiler in the plant. Two kinds of heat appear, and telling them apart is the heart of the topic.

Sensible heat: changing temperature

Sensible heat is the energy that changes a material’s temperature without changing its phase. For a flowing stream the rate is Q̇ = ṁ × Cp × ΔT — the mass flow times the specific heat capacity times the temperature change. It is "sensible" because you can sense it as a temperature change. The specific heat is the property that says how much energy a kilogram of the material soaks up per degree, and it is supplied from property data, not assumed — a point this site is built around. Raise a stream by a known number of degrees at a known flow and specific heat, and the sensible duty follows directly.

Latent heat: changing phase

Latent heat is the energy that changes phase at constant temperature — boiling a liquid to vapour, condensing it back, melting or freezing. Here the relation is Q̇ = ṁ × λ, the mass flow times the latent heat of the phase change, with no temperature term because the temperature does not move while the phase does. Latent heats are large compared with sensible heats over modest temperature ranges, which is why evaporators, condensers and reboilers — the equipment that boils and condenses — carry the heaviest duties in many plants, and why a process that can avoid a phase change often saves more energy than one that merely trims a temperature.

Duty: the rate the plant must handle

The duty is the total rate of heat the process must supply or reject at a point — the sum of the sensible and latent contributions for whatever the stream is doing. A reboiler that heats a feed to its boiling point and then boils part of it has a sensible duty followed by a latent one; the total is what sizes the heat source and, downstream, the cooling that rejects it again. The duty is the number that connects this module to the heat-transfer module later in the path: once the duty is known, an exchanger is sized from it, the temperature driving force and an overall coefficient giving the area. Energy balance first, equipment second.

The calculator below computes the sensible duty Q̇ = ṁ × Cp × ΔT for a stream, the canonical first term of any heating or cooling load. Supply the flow, the specific heat and the temperature change, and it returns the duty — the rate the plant must provide or carry away.