Saturday, December 04, 2010

Feels warmer

Fourier's law for heat conduction says that if:

- ΔQ/Δt is the rate of heat loss by the house (in watts);
- k is the average heat conductivity of the house (in watts per metre per °K);
- A is the surface area of the house (square metres);
- ΔT is the difference between the inside and outside temperatures (°K = °C);
- Δx is the average width of the walls in metres;

then ΔQ/Δt = -kA ΔT/Δx.

Wrapping k, A and Δx into one constant c we have

ΔQ/Δt = c ΔT.

We tend to keep our house a toasting-warm 23°. When it was absolutely freezing a couple of days ago it was -5° outside giving a ΔT of 28°. Today, however, it's a balmy 2° outside giving a ΔT of 21°.

The ratio of (heat-lossfreezing)/(heat-lossbalmy) is therefore 28/21 = 4/3.

So to keep the house the same temperature, we're using 25% less power today. No wonder we had to turn the heating down.