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Name: _____________________________
Homework One
Due date: Friday, January 15, 2021 by 11:59pm Pacific Standard Time
Show all calculations. Set up all equations with variable symbols/letters first, then substitute numbers to do the
calculations. Define in words each variable symbol/letter and their units (example: T stands for air temperature
measured in Kelvin)
1. [25 points] This exercise illustrates the importance of size to endothermic organisms. We are going to
abstract two example organisms as being spherical in shape. Consider both the Etruscan shrew (~7 mm
radius) and an African Elephant (~1 m radius). Assume the maximum metabolic energy that each of these
mammals can produce is -100 W kg-1. This is a reasonable assumption since mammalian biochemistries
and metabolisms are very similar across all species. Note the negative sign—the greater the metabolic
production, the more negative the metabolic energy would be.
Remember that the sign of G is negative when energy flows to the surface, as it does for metabolism. If the
magnitude of energy losses from the animals’ surfaces exceeds the metabolic energy production magnitude
for too long, then the mammals cannot survive as they would eventually succumb to hypothermia.
In the example below, the magnitude of energy losses/gains from an animal is H + LE –Rn. The magnitude
(magnitudes are always positive) of the maximum metabolic production energy flux density is -Gmetab. We
assume that that the mammals can lower their metabolic rate magnitude if necessary to survive, specifically
that they can only change that metabolic rate to the maximum of -100 W kg-1.
a. Calculate the volume of each mammal, and then the mass of each animal, assuming their density is the
same as water.
Calculate the maximum metabolic production of each mammal in Watts (W).
Calculate the surface area of each mammal, again assuming they are both spherical.
Calculate the maximum metabolic energy flux density of each mammal in W m-2.
Can these mammals survive if they are levitating (floating) in a cave/burrow (meaning that there is no
external conduction loss to the walls), when the net radiation Rn is -100 W m-2, the sensible heat H is +
100 W m-2, and the latent energy LE is +100 W m-2? Discuss and justify your answer.
(Hint: rearrange the energy budget to arrive at an equation G = …; To survive, the mammal would need
the magnitude of G to be less than your answer in (d).)
f. Now consider a spherical human with a radius of 25 cm. Following the same steps above and showing
your work and answers throughout, with the same assumed maximum metabolic rate, would the human
survive under the conditions in (e)? Discuss and justify your answer.
g. Discuss the importance of surface area to volume ratios to mammals of different sizes.
b.
c.
d.
e.
2. [25 points] Consider the diagram below, for an energy budget.
a) Write down the maximum and minimum values of net radiation, sensible heat, latent energy, and
conduction flux densities. Compare their maximum magnitudes: which is greatest, which is least, and
which is in between?
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b) At which time(s) is the net radiation flux density positive? When is it negative? Discuss your answer,
explaining why the net radiation is positive when it is and why it is negative when it is.
c) Is this energy budget likely for a human sitting in a classroom, or a crop ecosystem? Justify your answer
using what you’ve learned so far about electromagnetic radiation.
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