Physics of heat flow or should I wear a sweater inside or insulate my walls?

Question

This is a theoretical question about heat flow…just phrased in terms of everyday life. On first approximation, in terms of home heat loss, which makes a bigger difference or are they equivalent:

a) decreasing the temperature gradient between inside and outside or

b) changing the thermal resistance of the walls proportionally to (a)

In other words, say if you double your wall R value by insulating more, would that decrease heat loss the same as if you do nothing with insulation, but decrease the temperature gradient difference by a factor of 2 between inside and outside (eg if it’s 0C outside, you’d decrease the inside temp from 20C to 10C, thus halving the temp gradient).

I realize a lot more variable go into this and I’m not exactly asking a practical question, but a more theoretical one having to do with heat flux. Instead of an actual house, let’s assume we’re talking about a uniform-walled hermetically sealed box.

Answer 1

The total rate of heat flow is given by (see R-value): $$ \phi=\frac{\Delta T A}{R} $$ Thus, either increasing $R$ by a factor of 2 or decreasing $\Delta T$ by a factor of two result in the two-fold decrease of heat flow. Doing both would reduce the heat flow by a a factor of 4.

In practice, one is limited in how much one can reduce $\Delta T$ - the standard room temperature is supposed to be $18^\circ$C (which many people find still quite chilly, but tolerable with a sweater), whereas the outside temperature may well go beyond the freezing point (i.e., below $0^\circ$C.) Doubling $R$ might be technically difficult and costly, but it remains the more realistic option nonetheless.

Before insulating walls one should however deal with various thermal leaks, as the main heat losses occur not through the bulk walls, but via various holes, imperfect junctions (poorly insulated corners, doors and window frames), as well as through surfaces with potentially lower R, like windows.

Another useful wikipedia article: Building insulation

Answer 2

Energy-wise, they will be the same in the first approximation. However, there are 2 significant issues with "oh, I will just grab sweater, it helps the same and it is a much cheaper and easier solution":

1.) You still feel cold air - breathing, on exposed parts of your skin (eg hands), after a shower ... It will be way less comfortable in that house.

2.) When/if temperatures outside get low enough, you still need to maintain warm enough walls to avoid freezing of water inside pipes in those walls. If water freezes you are in a lot of trouble and with higher costs than if you simply heated uninsulated house to comfortable temperatures.

There might be other issues I haven't experienced yet or paid much attention to (winter parties in an uninsulated weekend house).