Mixed Air Temperature

A mixing box is a weighted average and nothing more: mass fractions of two airstreams, blended. Because the weights sum to one, the arithmetic works in any temperature scale: °F, °C or K all give the same answer, which is a rare licence in thermodynamics and comes from the offsets cancelling. Twenty-five percent outdoor air at 35 °F mixed with return air at 75 °F leaves the box at 0.25 × 35 + 0.75 × 75 = 65 °F.

Commissioning agents run this backwards as a damper check. Measure outdoor, return and mixed temperatures on a cold morning, solve for f, and compare it to what the control system claims: if the building automation says minimum outdoor air is 20 % and the temperatures say 55 %, someone's linkage has slipped or an economizer is stuck open, and you are paying to heat the outdoors. The trap is stratification: outdoor and return air do not blend instantly, so a single-point sensor in the mixing plenum can read 10 °F off. Use an averaging sensor or take a nine-point traverse. In winter the same stratification is what freezes preheat coils, one row of tubes at a time.