I'm inventing my own physics problem for extra credit thermodynamics and fluids

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1. A man falls into a tank at 40 degrees C. His body temperature is 98.6 degrees Fahrenheit. I want to ask if the man will freeze to death, but I don't know at what temperature that happens. Can I ask them to figure out what his final body temperature is, if say he doesn't get rescued in 10 mins? Do I need to provide more information? I can always go off in a completely different direction...



2. Tc = (5/9)*(Tf-32)
Q=mL
Q=mCdeltaT




3. I'm looking for advise about how to write a problem!
 

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dynamicsolo
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1. A man falls into a tank at 40 degrees C. His body temperature is 98.6 degrees Fahrenheit. I want to ask if the man will freeze to death, but I don't know at what temperature that happens. Can I ask them to figure out what his final body temperature is, if say he doesn't get rescued in 10 mins? Do I need to provide more information? I can always go off in a completely different direction...



2. Tc = (5/9)*(Tf-32)
Q=mL
Q=mCdeltaT




3. I'm looking for advise about how to write a problem!
First off, do you mean the tank of water is 40º Fahrenheit? Water at 40º C (104º F) would be mighty uncomfortable, but you won't freeze to death in it...

In any case, hypothermia is a rather complicated physiological condition. People have been recovered with body core temperatures that had fallen below 65º F and been revived successfully. Likewise, the time of fatal exposure to near-freezing water varies pretty widely. But I'd say that ten minutes is rarely lethal, though half an hour generally is.

The difficulty in introducing time into your problem is that you need to include information about the rate at which heat is being lost from the person's body. Has your physics course covered problems in conductive heat transfer at all? The thermal equation you've given would need to be differentiated implicitly with respect to time to create a rate equation relevant to your problem. Have students in the course done problems like that before? You would have to provide at least a crude model of how heat would be lost from the body in those circumstances to give the problem enough of a "closed form" for students to solve it.

A related sort of problem would be to have students solve for the rate at which heat is removed from the body by perspiration. You'd need estimates for the surface area of the body (assuming perspiration is uniform over the surface -- which it isn't, really), a rate at which water is leaving the pores everywhere, and the latent heat of vaporization of water at skin temperature (around 85º F -- you could google up a table for such data, I believe).

You could even extend the problem to estimate how fast heat is also being removed by breathing, using the rate at which air at body core temperature (pretty much 98.6 F) is warmed and expelled; you could also include the water vapor content in the breath, which is probably picking up most of the heat. The results could be compared with the average rate at which metabolism generates heat in the body (around 100 W -- have them find this too!). The calculations still require certain assumptions, but I think it's a bit more tractable than trying to model the whole body. Just a suggestion...
 
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