Energy balances

Energy is conserved like mass. For a process running at steady state, the heat added minus the shaft work done by the process (a turbine) equals the change in enthalpy of the streams, plus any change in their speed and height: Q − W = ΔH + ΔKE + ΔPE. In most chemical units the speed and height terms are tiny, so Q − W ≈ ΔH. For heaters and coolers with no shaft work, Q = ΔH: the heat added equals the outlet enthalpy minus the inlet enthalpy.

Sensible heat changes temperature: Q = ṁ × cp × ΔT, where ṁ is the mass flow and cp the specific heat. Heating 1000 kg/h of water from 20 to 80 °C takes 1000 × 4.18 × 60 = 250,800 kJ/h. Divide by 3600 to get kJ/s, which are kilowatts: about 70 kW.

Latent heat changes phase at constant temperature. Plants usually heat with steam, which gives up its latent heat as it condenses: about 2257 kJ/kg at 1 atm (less at higher pressures). To supply that 250,800 kJ/h with condensing steam needs 250,800 ÷ 2257 = 111 kg/h.

Reactions add a term: the heat of reaction. An exothermic reactor has to be cooled to hold its temperature, and the cooling duty is the heat of reaction times the reaction rate, adjusted for any temperature change of the streams. Making 10 mol/s of product with ΔH = −100 kJ/mol releases 1000 kW that a jacket or coil must carry away.

If nothing removes it, the heat goes into the stream: the adiabatic temperature rise. That's how engineers size cooling and check what happens if it fails, a big part of reactor safety and the subject of the Reaction engineering course.