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Physics 333 Problem Set #2
Question 1 - A Cabin in the Woods
You still haven't fixed your time
machine , and you're still stuck in
your cabin. In a valiant attempt to
rescue you, your best friend has
teleported back in time, but their
machine broke as well. You're now
trying to survive in the cold together.
The cabin has a well insulated floor
and roof, and walls that are 15 cm
thick, 9 m long, 9 m wide and 3 m
high. (Kwood = 0.10 W/K m
a) Use the Mifflin equation below to find Basal metabolic rate of you and your
friend.
P =
10.0m
6.25h
5.0a
+
+ s
kcal
1 kg
1 cm
1 year
day
where s is -161 for females and +5 for males.
b) The only heat source you have in the cabin is the power generated by your
body. If the temperature outside is 4 C, what is the equilibrium temperature in
the cabin?
c) How the temperature change if both of you start pacing back and forth at 5
km/hr? What is the new equilibrium temperature?
d) You have to stop walking while you're sleeping, meaning you'll lose your heat
source when you fall to sleep. Find the characteristic cooling time of cabin.
What does the characteristic cooling time tell you? If you sleep for 5 hours to
morning, will you and your friend be OK?

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