Question

What is the rate of heat conduction through the 3.00-cm-thick fur of a large animal having a 1.40 m2 surface area? Assume that the animal’s skin temperature is 32.0

Answer 1

What is the rate of heat conduction through the 3.00-cm-thick fur of a large animal having a 1.40 m2 surface area? Assume that the animal’s skin temperature is 32.0°C, that the air temperature is −5.00∘C, and that fur has the same thermal conductivity as air. (b) What food intake will the animal need in one day to replace this heat transfer?

a) = 39.7kW

b) = 819kcal

Step-by-step explanation:

Given that

d = 3.00cm = 3.0 × 10⁻²m

k(fur)=k(air) = 0.023 w/m °C

A = 1.4m²

T₁(animal) = 32 °C

T₂(air) = -5 °C

Δt = 1day =86400s

The rate of conduction heat transfer through a material

=
`(kA(T_1 - T_2))/(d)`

=
`(0.023 * 1.40 * (32 (-5)))/(3.0 * 10^-^2)`

= 39.7W

b) P = Q / Δt

Q = P × Δt

= 39.7 × 86400

Q = 3.43 × 10⁶J

1kcal = 4186J

Q(intake) = 3.43 × 10⁶J × (1kcal / 4186J)

= 819kcal