Heat lost from face due to black body radiation

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Homework Help Overview

The problem involves calculating the net rate of heat loss from a skier's head due to black body radiation, modeled as a cylinder. The scenario is set on a cold day, and the discussion centers around the parameters of the problem, including temperature and emissivity.

Discussion Character

  • Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formula for heat loss and question the surface area calculation for the cylindrical model. There is confusion regarding whether to include the bottom surface in the area calculation.

Discussion Status

Some participants have offered corrections and clarifications regarding the surface area formula. There is an acknowledgment of errors in the initial calculations, and a participant indicates they have arrived at a correct answer after revisiting their approach.

Contextual Notes

Participants are working under the assumption that the head is modeled as a cylinder without a bottom, which influences the surface area calculation. The discussion reflects a learning process with adjustments based on peer feedback.

nlingraham
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Homework Statement



Much of the of heat lost from a cross-country skier's body is radiated from the head, since it is often uncovered. Treat a head as a 20-cm-diameter, 20-cm-tall cylinder with a flat top. If the surface temperature of a body is 35 C, what is the net rate of heat loss on a frosty 5 C day? All skin, regardless of color in the visible wavelengths of light, is effectively black in the infrared where the radiation occurs. Therefore, assume an emissivity of 0.97.

Homework Equations



Q/Δt = eσA(T4-T04)

where:
e=.97
σ=5.76*10-8 W/m2k4
A=Surface area of cylinder, SA=2∏r2+2∏rh, = .188 m2
T=308 K
T0=278K

The Attempt at a Solution



Seems like straight plug n' chug.

Q/Δt = (.97)(5.67*10-8)(.188)(3084-2784)
=31.29 W

However, this isn't right. Can anyone tell me what I did wrong?
 
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Why 2\pi r^2?
 
So would the SA just be SA=2∏r+2∏rh since the cylinder doesn't have a bottom? Which would make the SA = .754 m2, Which would give an answer of 125.5 W?
 
So I think sometimes I may be retarded. So it should have been ∏r2+2∏rh. I got the correct answer now. Thank you
 

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