Thermodynamics & Heat Transfer · From R to U
The same wall, said the other way
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The same wall, said the other way

Insulation is sold in R-values; energy codes are written in U-factors. They are the same fact, upside down. U=1RtotU = \dfrac{1}{R_{tot}} — read aloud U equals one over R-total, where RtotR_{tot} is the assembly's total R-value in m²·K/W and UU is its U-factor in W/(m²·K): the watts that cross one square metre of it for every kelvin of difference.

Say what each direction means and you will never flip the wrong way. R is resistance — big is good, and a big R-value is a wall you are proud of. U is a conductance — big is bad, and a code that caps U at 0.28 W/(m²·K) is demanding an assembly of at least RSI 3.6. The reciprocal also flips the unit, which is the cheapest check in this chapter: m²·K/W turned over is W/(m²·K), and if your answer still wears the unit it went in with, you never inverted anything.

Then the wrong turn that costs marks and, occasionally, buildings. Resistances add; conductances do not. Faced with two layers, RSI 3.5 and RSI 0.5, the honest road is U=1R1+R2=14.0=0.25U = \dfrac{1}{R_1 + R_2} = \dfrac{1}{4.0} = 0.25. Adding the U-factors instead gives 0.286+2=2.290.286 + 2 = 2.29 — a wall nine times leakier than the truth, and worse than either layer on its own, which should be impossible on sight. Add the R's, invert once, at the end.

And the same reciprocal, with an area folded in, works for the K/W form: Q˙=ΔTR\dot{Q} = \dfrac{\Delta T}{R}Q-dot equals delta-T over R, with Q˙\dot{Q} the heat flow in watts, ΔT\Delta T the difference across the assembly in kelvin and RR its resistance in K/W. That is Ohm's law wearing a hard hat: heat for current, temperature difference for voltage, K/W for ohms. Once you see the analogy, every network trick you know comes with you.