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?