Please Return Stolen Jacket!

In my EMT training we learned about the different kinds of treatments we would need to perform for conditions that occur due to extreme environmental factors, such as hypothermia. Right now, people, and especially college students who may have altered judgment, need to be extremely careful about dressing appropriately for the weather when going outside. Every year we hear about college students freezing to death after leaving parties in the winter. I decided to look into the net rate of heat flow from a human who is scantily clad vs. the heat flow when wearing a thick down coat on a night like tonight, which will feature a temperature of 20°F (-6.7° C, 266.3 K) at midnight.

For the scantily clad person we need to consider radiation using this equation for the net rate of heat flow:

Q/t= eσA(T₁⁴ –T₂⁴)

Given the A of a person=1.7m², the e_{human skin}= 0.98, and the human body temperature of 310 K

Q= (0.98)(5.67 x 10^-8 W/m²K⁴)(1.7m²)((310K)⁴-(266.3K)⁴)

Q=397 W

When wearing a coat the person is insolated by the air contained within the ~2in (.05m) of down (assume the coat covers the whole body).  

We can find the heat transfer based on conduction:

Q/t= KA((T₁ –T₂)/l)

Given the cross-sectional area of a person is ~0.5m², the thermal conductivity constant of air is 0.024 W/mK, and the distance between the two temperatures is the thickness of the coat

Q=(0.024 W/mK)( 0.5m²)((310K-266.3K)/.05m)

Q=10.4 W

Obviously, the cross sectional area of a person is less than the total surface area used in the calculation of radiation. However, one can still see that much less heat is transferred to the environment when wearing a coat. Jacket thieves run rampant at Colgate, as evidenced by the frequent pleas for the return of coats on the class Facebook pages. We can see here how important coats are for maintaining body heat, and should be more careful to bring our own outerwear and not steal that of others!

References:

http://onlinelibrary.wiley.com/store/10.1256/wea.29.02/asset/2002571103_ftp.pdf?v=1&t=iwidutfm&s=018b03ff369ae002c3a08fb1b7b4b7b8a8ff3287

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