Thermodynamics: heat-conduction problem

[Dergyll]

Homework Statement

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 (κ = 0.03 W/m-K)
•the suit thickness is d = 3 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 = 2°C
•the diver "weighs" m = 80 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).

Homework Equations

Not given, but the ones I used are H=JA, H=dQ/dt (small t is time, big T is temp.), Rth=d/kA (where d is distance between contact, k is thermal cond constant), from those we can pretty much manipulate and get the other ones needed,

The Attempt at a Solution

This problem is split into several sections, first it asks for R of the suit, simple enough I calculated it from d/kA to be 0.05 K/Watt

second it asks for heat capacity of the diver, we can find from the specific heat and mass, which turns out to be 278400 J.

Third it asks for amount of heat exchanged to lower diver's temperature from 37-35 C, we multiply it by 2 to get 556800 J.

Now it asks for the amount of time the diver can stay in the water before experiencing hypothermia (AKA 35C), in minutes.

Looking at H, the heat current per area (in watts per second), we can find H, then divide it from the total heat transfer needed (which is found from third part as 556800) but I can't seem to get the right answer (its one of those online physics homeworks that tells you right away). There are a few similar posts on other website which I also tried but did not seem to work, I am probably missing something pretty fundamental here, any help is greatly appreciated!

Derg

 

[anathema]

ar

Dear Dergar,

Thank you for your detailed explanation of your attempts at solving this problem. It seems like you have a good understanding of the concepts involved, but may have made a small mistake in your calculations.

To find the amount of time the diver can stay in the water before experiencing hypothermia, we can use the formula H=dQ/dt, where H is the heat current per area, d is the distance between contact, Q is the total heat transfer needed (556800 J in this case), and t is the time. We can rearrange this equation to solve for t, which gives us t=Q/H.

From your previous calculations, it seems like you have correctly found H (0.05 K/Watt) and Q (556800 J). Plugging these values into the formula, we get t=556800/0.05=11136000 seconds.

To convert this to minutes, we divide by 60 and get approximately 186, or 3 hours and 6 minutes. This means that the diver can stay in the water for about 3 hours and 6 minutes before experiencing hypothermia.

I hope this helps! Let me know if you have any further questions or if you need clarification on any part of the problem.