Heat Exchanger Duty
Q = ṁ·cp·ΔT for one stream — the first number of every exchanger problem.
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The engineering
Sensible heat only — the energy to change a stream's temperature, not its phase. The cp values are fixed representative numbers: water 4186 J/kg·K (liquid, near ambient), air 1005 (at roughly room temperature and constant pressure), and 'light oil' a nominal 1900 — real oils run anywhere from 1700 to 2500 and vary with temperature, so treat that one as an estimate.
In a real exchanger this equation is written twice — once per stream — and the two duties must match; the mismatch is your heat loss or your measurement error. Any condensation or boiling adds latent heat on top (water's ~2,260 kJ/kg of vaporization dwarfs its sensible term), which this card deliberately does not include.
Where this math comes from
Specific heat is Joseph Black's idea from the 1760s — he noticed different substances need different amounts of heat for the same temperature rise, and separated heat from temperature for the first time. James Joule's paddle-wheel experiments of the 1840s nailed the exchange rate between mechanical work and heat, which is why cp carries his name in its units.
The ṁ·cp·ΔT habit became industrial with steam power and was codified by the heat-exchanger industry — TEMA sheets since 1941 begin with the duty balance, and a process engineer's first sanity check on any datasheet is still whether the two streams' Q agree.
- 1760Joseph BlackSpecific and latent heat distinguished (circa).
- 1843James Prescott JouleMechanical equivalent of heat — energy accounting unified.
- 1941TEMADuty balance formalized on every exchanger datasheet.
See the full timeline of the math behind every calculator →
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