Energy and Human Ambitions on a Finite Planet, 2021a

6 Putting Thermal <strong>Energy</strong> to Work 87
<strong>and</strong> air gaps. But it also depends linearly on ΔT—the difference between
inside <strong>and</strong> outside temperatures—that is being maintained. A house
can be characterized by its heat loss rate in units of Watts per degree
Celsius. 13 This single number then indicates how much power is needed
to maintain a certain ΔT between inside <strong>and</strong> outside. Box 6.1 explores an
example of how to compute the heat loss rate for a house, <strong>and</strong> Example
6.3.2 applies the result to practical situations.
13: ...or equivalently, Watts per degree
Kelvin
0°C
0.15 W/m 2 /°C
12 m
0.8 W/m 2 /°C
20°C
2.5 m
2 m 2
12 m
Figure 6.1: External walls <strong>and</strong> windows for
the house modeled in Box 6.1. The floor
<strong>and</strong> ceiling are not shown. The numbers in
W/m 2 / ◦ C are U-values, <strong>and</strong> in this case
represent the very best engineering practices.
Most houses will have larger values
by factors as high as 2–6. Don’t forget the
door in a real house!
Box 6.1: House Construction
The very best practices result in a snugly-built house qualified as
a “Passive House,” achieving 0.15 W/ ◦ C for each square meter of
external-interfacing surface 14 <strong>and</strong> 0.8 W/ ◦ C per square meter of
windows.
Let’s imagine a house having a square footprint 12 m by 12 m, walls
2.5 m high, each of the four walls hosting two windows, <strong>and</strong> each
window having an area of 2 m 2 (Figure 6.1). The floor <strong>and</strong> the ceiling
are both 144 m 2 , <strong>and</strong> the wall measures (perimeter times height)
48×2.5 120 m 2 . But we deduct 16 m 2 for the eight windows, leaving
104 m 2 for the walls. The resulting heat loss measure for the house is
13 W/ ◦ C for the windows (0.8W/m 2 / ◦ C × 16 m 2 ), plus 59 W/ ◦ C for
the walls/floor/ceiling for a total of 72 W/ ◦ C.
The loss rate for a decently-constructed house might be about twice
this, while a typically-constructed house (little attention to efficiency)
might be 3–6 times this—several hundred W/ ◦ C. Of course, smaller
houses have smaller areas for heat flow <strong>and</strong> will have smaller loss
rates.
14: . . . outer walls, ceiling-to-unconditioned
attic, floor-to-crawl-space
The numbers used to characterize heat loss
properties of walls <strong>and</strong> windows are called
U-values, in units of W/m 2 / ◦ C, where low
numbers represent better insulators. In the
U.S., building materials are described by
an inverse measure, called the R-value, in
ugly units of ◦ F ·ft 2 · hr/Btu. The two are
numerically related as R 5.7/U, so that
our Passive House wall has R ≈ 38 <strong>and</strong> the
windows have R ≈ 7—both rather impressive
<strong>and</strong> hard to achieve.
Example 6.3.2 Let’s compare the requirements to keep three different
houses at 20 ◦ C while the temperature outside is 0 ◦ C (freezing point).
The first is a snugly-built house as described in Box 6.1, where we
round the heat loss rate to a more convenient 75 W/ ◦ C. We’ll then
imagine a decently built house at 150 W/ ◦ C, <strong>and</strong> a more typical 15
house at 300 W/ ◦ C.
15: ...not“thermally woke"
The temperature difference, ΔT,is20 ◦ C, so that our super-snug house
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.