Answer to Question #114360 in Physics for Phoebe

Question

An arctic fox with surface area of 0.2 m2
and a core body temperature of 38◦C has a 1 cm
thick layer of fat (kfat = 0.2 W m−1 K and a 4 cm layer of insulating fur
(kfur = 0.16 W m−1 K) If the outside temperature of the fox’s fur is −5
◦C then what is the skin temperature of the fox (in ◦C)?

Answer 1

$$k_1A\frac{T_c-T}{d_1}=k_2A\frac{T-T_o}{d_1}$$

$$0.2\frac{38-T}{1}=0.16\frac{T+5}{4}$$

$$T=31\degree C$$