Energy and Human Ambitions on a Finite Planet, 2021a

6 Putting Thermal <strong>Energy</strong> to Work 86
To perform computations using specific heat capacity, try an intuitive
approach rather than some algorithmic formula. 7 The following should
just make a lot of sense to you, <strong>and</strong> can guide how to put the pieces
together: it takes more energy to heat a larger mass or to raise the temperature
by a larger amount. It’s all proportional. The units also offer a hint.
To go from specific heat capacity in J/kg/ ◦ C to energy in J, we need to
multiply by a mass <strong>and</strong> by a temperature change.
Example 6.2.2 To compute the amount of energy it will take to heat
a 30 kg piece of furniture 8 by 8 ◦ C, we will multiply the specific heat
capacity by the mass—to capture the “more mass” quality—<strong>and</strong> then
multiply by the temperature change—to reflect the “more temperature
change” element. In this case, we get 240 kJ.
7: Although, this would be a good opportunity
for a student to make up their own
formula, driving home the concept <strong>and</strong> the
fact that equations simply capture a concept.
Also, the choice of symbols is arbitrary,
which the experience would reinforce.
8: . . . assuming 1,000 J/kg/ ◦ C
6.3 Home Heating/Cooling
Our personal experience with thermal energy is usually most connected
to heating a living space <strong>and</strong> heating water or food. Indeed, about
two-thirds of the energy used in residential <strong>and</strong> commercial spaces 9
relate to thermal tasks, like heating or cooling the spaces, heating water,
refrigeration, drying clothes, <strong>and</strong> cooking.
9: . . . in the form of natural gas, electricity,
<strong>and</strong> fuel oil
When it comes to heating (or cooling) a home, we might care about two
things:
◮ how long will it take to change its temperature by some certain
amount; <strong>and</strong>
◮ how much energy it will take to keep it at the desired temperature.
The first depends on how much stuff is in the house, 10 how much ΔT
you want to impart, <strong>and</strong> how much power is available to create 11 the heat.
The energy required is mass times ΔT times the catch-all 1,000 J/kg/ ◦ C
specific heat capacity. The time it takes is then the energy divided by the
available power.
Example 6.3.1 How long will it take to heat up the interior of a mobile
home from 0 ◦ C to 20 ◦ C using two 1,500 W space heaters? We’ll assume
that we must heat up about 6,000 kg of mass. 12
The first job is to find the energy required <strong>and</strong> then divide by power
to get a time. We’ll use the good-for-most-things specific heat capacity
of 1,000 J/kg/ ◦ C.
10: . . . including walls, furniture, air
11: ...ortoremove, if cooling
12: Only 300 kg is in the form of air: most of
the mass to be heated is in the walls, floor,
<strong>and</strong> ceiling.
Multiplying the specific heat capacity by mass <strong>and</strong> temperature change
results in 120 MJ of energy. At a rate of 3,000 W, it will take 40,000 s to
inject this much energy, which is about 11 hours.
How much it takes to maintain temperature depends on how heat flows
out of (or into) the house through the windows, walls, ceiling, floor,
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.