Suppose you stand with one foot on ceramic flooring and one on a wool carpet, ma

Question

Suppose you stand with one foot on ceramic flooring and one on a wool carpet, making contact over a 65.2 cm^2 area with each foot. Both the ceramic and the carpet are 1.75 cm thick and are 10.0 degree C on their bottoms. At what rate must each foot supply heat to keep the top of the ceramic and carpet at 33.0 degree C? the thermal conductivity of ceramic is 0.84 J/(s middot m middot degree C) and that of wool is 0.04 J/(s middot m middot degree C). What is the rate of heat conduction through the 3.30-cm-thick fur of a large animal having a 1.33-m^2 surface area? Assume that the animal's skin temperature is 32.0 degree C, that the air temperature is -5.00 degree C, and that fur has the same thermal conductivity as air w What food intake will the animal need in one day to replace this heat transfer?

Explanation / Answer

Here we have Fourier equation as

Q/t = -kAdT/dx

For ceramic tile , rate at which foot should supply the heat

Q/t = 0.84*65.2*10-4*(33 - 10)/1.75*10-2 = 7.2 W

For wool carpet , rate at which foot should supply the heat

Q/t = 0.04*65.2*10-4*(33 - 10)/1.75*10-2 = 0.342 W

2) a)similarly

Q/t = 0.023*1.33*{32 - (-5)}/3.3*10-2 = 34.3 W

b) food intake is 34.3 J/s = 34.3/4.2 cal/s = 8.17 cal/s = 8.17*24*3600 Cal per day = 705600 Cal per day

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