Energy and Human Ambitions on a Finite Planet, 2021a

6 Putting Thermal <strong>Energy</strong> to Work 100
of 1.25 kg/m 3 . Express your answer as an approximate number in
minutes.
3. When you put clothes on in the morning in a cool house at 15 ◦ C,
you warm them up to something intermediate between your skin
temperature (35 ◦ C) <strong>and</strong> the ambient environment. 60 If your clothes
have a mass of 2 kg, how much energy must be deposited into the
clothes? If you are emitting power at 100 W, how long will this
take?
60: The inside surface of the clothing will
be near skin temperature, <strong>and</strong> the outside
will be near ambient temperature.
4. You score this massive 1 kg burrito but decide to put it in the
refrigerator to eat later. It comes out at 5 ◦ C, <strong>and</strong> you want to heat
it in the microwave up to 75 ◦ C before eating it. If the microwave
puts energy into the burrito at a rate of 700 W. 61 How long should
61: i Note that a microwave oven might
you run the microwave for a high-water-content burrito having an
effective specific heat capacity of 3,000 J/kg/ ◦ C?
be rated for 1,500 W, but not all the energy
ends up in the burrito, so we pick 700 W to
be realistic.
5. Let’s say you come home from a winter vacation to find your
house at 5 ◦ C <strong>and</strong> you want to heat it to 20 ◦ C. Let’s say the
house contains: 500 kg of air; 62 1,000 kg of furniture, books, <strong>and</strong> 62: . . . appropriate for a 150 m 2 footprint
other possessions; plus walls <strong>and</strong> ceiling <strong>and</strong> floor that amount
to 6,000 kg of effective 63 mass. Using the catch-all specific heat
63: i We only count half-thickness of exterior
walls since they are not heated to
capacity for all of this stuff, how much energy will it take, <strong>and</strong> how
long to heat it up at a rate of 10 kW? Express in useful, intuitive the interior temperature all the way to the
outside.
units, <strong>and</strong> feel free to round, since it’s an estimate, anyway.
6. In a house achieving a heat loss rate of 200 W/ ◦ C equipped only
with two 1,500 W space heaters, what is the coldest it can get
outside if the house is to maintain an internal temperature of
20 ◦ C?
7. In a house achieving a heat loss rate of 200 W/ ◦ C equipped a
5,000 W heater, what will the internal temperature be if the outside
temperature is −10 ◦ C <strong>and</strong> the heater is running 100% of the time?
8. In a super-tight house achieving 100 W/ ◦ C equipped with a
5,000 W heater, what percentage of the time will the heater need
to run in order to keep the internal temperature at 20 ◦ C if the
temperature outside is at the freezing point? 64
9. How much will it cost per day to keep a house at 20 ◦ C inside when
the external temperature is steady at −5 ◦ C using direct electric
heating 65 if the house is rated at 150 W/ ◦ C <strong>and</strong> electricity costs
$0.15/kWh?
10. Provide at least one example not listed in the text in which heat
flows into some other form of energy. 66 In the text, we mentioned
hot air over a car, wind, internal combustion, <strong>and</strong> a steam turbine
plant.
64: Hint: compute the average power that
would be needed in this case.
65: ...noheat pump: just straight energy
deposition at 100% efficiency
66: Think about motion deriving from or
caused by heat or thermal release.
11. What is the only form of significant electricity production in the
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.