The surface area of an adult human is about 1.8 m^2. Suppose a person with a ski

Question

The surface area of an adult human is about 1.8 m^2. Suppose a person with a skin temperature of 34 degrees C is standing nude in a room where the air is 25degrees C but the walls are 17 degrees C.

There is a "dead-air" layer next to your skin that acts as insulation. If the dead-air layer is 5.0 mm thick, what is the person's rate of heat loss by conduction?

What is the person's net radiation loss to the walls? The emissivity of skin is 0.97.

Does conduction or radiation contribute more to the total rate of energy loss?

If the person is metabolizing food at a rate of 160 W, does the person feel comfortable, chilly, or too warm?

Explanation / Answer

Here, P is power, which is the rate at which heat is lost. For radiation, P = sigma*A*e*(T^4-To^4) sigma is the constant 5.67x10^-8, A is the surface area of the object, e is the emissivity, T is the temperature of the skin (convert it to Kelvin), and To is the temperature of the background (walls, convert to Kelvin). For conduction, P=k*A*(Th-Tc)/L Here, L is the thickness of the dead air layer, Th is the hot temp (in Kelvin, probably), Tc is the cold temp, k is the coefficient of thermal conduction (your textbook probably gives this value for air, if not you can look it up) and A is the surface area again. Compare these 2 power numbers and this will answer the question about which contributes more. Then you add the power from conduction and radiation, and compare that number to 160W, and if they add up to less than 160 they feel cold, more they feel hot, close they feel comfortable, etc.

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