A small dog has thick fur, with a thermal conductivity of 0.040 W/(m K). The dog
ID: 2303099 • Letter: A
Question
A small dog has thick fur, with a thermal conductivity of 0.040 W/(m K). The dog's metabolism produces heat at a rate of 43 W, and its internal (body) temperature is 34C.
(a) If all of this heat flows out through the dog's fur, what is the outside temperature? Assume the dog has a surface area of 0.51 m2 and the length of the dog's hair is 1.2 cm.
C
(b) Now assume it is a hot summer day with an outdoor temperature of 33C (about 91F). What is the body temperature of the dog now? Your answer will explain why a dog can quickly overheat on a warm day.
C
Explanation / Answer
Use Fourier's law of heat conduction:
H = ?Q/?dt = k?A??T/dx
(H heat flow, k thermal conductivity, A area of the layer, ?T temperature difference, ?x thickness of the layer.
So the heat difference between dog's body and surrounding is:
?T = H??x / (k?A)
= 43W ? 0.012m / (0.04W/Km ? 0.51m