In order to stay warm, divers often wear some sort of thermal protection, like a

Question

In order to stay warm, divers often wear some sort of thermal protection, like a "wetsuit". Often this is a neoprene "foamed" material, which traps gas bubbles as the insulating material. For this problem, assume: the thermal conductivity is that of air ( = 0.03 W/m-K) the suit thickness is d = 3.5 mm the area of the suit is A ~2 m2 the diver's initial body temperature is Td,i = 37°C (98.6°F) the water temperature is Tw = 3°C the diver "weighs" m = 50 kg the specific heat of the diver is cd = 3480 J/kg-K (this is slightly less than the specific heat of water 4184 J/kg-K due to the presence of protein, fat, and minerals) the diver will start to experience loss of motor skills due to hypothermia when his core temperature cools to below Td,f = 35°C (95°F). (Note: Throughout this problem we are also implicitly assuming that the diver is at a uniform temperature, which obviously is an over-simplification [since our bodies are evolutionarily engineered to maintain a stable core temperature, even if we have cold limbs...].)

1.What is the total amount of heat flow needed to change the diver's temperature from 37°C to 35°C?

2.Estimate how long (in minutes) the diver can stay in the water (before feeling the effects of hypothermia).

Explanation / Answer

k = 0.03
A = 2
d = 3.5*10^-3
Ti = 37
Tw = 3
m = 50
cd = 3480
cw = 4184

1. heat, Q = mcd*dT = 50*3480*2 = 348 kJ
2. let time be t
   heat rate = kA(dT/d) = 0.03*2*34/3.5*10^-3 = 582.85 s = 9.714 min

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