Energy and Human Ambitions on a Finite Planet, 2021a

5 <strong>Energy</strong> <strong>and</strong> Power Units 81
10. If a 70 kg person (weight: 700 N) is capable of putting out energy
at a rate of 500 W in short bursts, how long will it take the person
to race up a flight of stairs 4 m high, considering only the vertical
energy 42 required?
11. If asked to compute the power associated with performing a
pull-up, 43 what specific information would you need to solve the
problem (<strong>and</strong> what are the units of each)? Write out the math that
would give the final answer.
42: Ignoring inefficiencies of moving legs,
rounding flights, etc.
43: ...orchin-up, lifting your entire body
up to a bar using your arms
12. How many kcal will it take to heat 1 liter of water (e.g., in a pot)
from room temperature (20 ◦ C) to boiling (100 ◦ C)? How many
Joules is this?
13. If a microwave operates at a power of 1,600 W (1,600 J/s), how
long will it take to heat 0.25 L of water from room temperature to
boiling (changing temperature by 80 ◦ C)if50% of the microwave
energy is absorbed by the water?
14. A smaller or less active person may require only 1,300 kcal per day
of food intake, while a larger or more active person might dem<strong>and</strong>
3,000 kcal per day. Approximately what range of power does this
spread translate to, in Watts?
15. If a typical metabolic intake is 2,000 kcal each day, approximately
how much energy does this translate to for one day, in units of
kWh? Compare this to a typical American household’s electricity
usage of 30 kWh in a day.
i 50% is typical for microwave efficiency.
i The result can help inform your sense
for the typical range of human metabolic
power.
Hint: it may be convenient to first get power
in Watts <strong>and</strong> round to a nice number before
proceeding.
16. The chapter banner image (page 68) shows food labels for peanut
butter <strong>and</strong> Nutella. The former indicates 188 Calories in a 32 g
serving, while Nutella is 539 kcal in 100 g. To compare, we must
adjust to the same serving size. Using 100 g as a sensible reference,
which of the two is more energetic for the same serving size, <strong>and</strong>
by how much (as a percentage)?
17. Based on the peanut butter label in the chapter banner image
(page 68), showing 188 Cal per 32 g serving, how much mass of
peanut butter would need to be consumed daily to constitute a
2,000 kcal/day diet? If a baseball has a mass of 145 g, how many
baseballs of peanut butter would need to be consumed each day?
18. A generic $10 pizza might contain about 2,500 kcal. What is this i Comparable to a full day’s intake.
in kWh? Electricity typically costs $0.15 per kWh, 44 so how much
would a pizza’s amount of energy cost in electrical terms? Which
44: . . . regionally variable
of the two is a cheaper form of energy?
19. A refrigerator cycles on <strong>and</strong> off. Let’s say it consumes electrical
power at a rate of 150 W when it’s on, <strong>and</strong> (essentially) 0 W when
it’s off. If it spends half of its time in the on-state, what is its average
power? How much energy does it consume in a 24-hour day, in
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.