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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...
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 = 1.5 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 = 5°C
- the diver "weighs" m = 70 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 thermal resistance of the suit?
2) What is the heat capacity of the diver?
3) What is the total amount of heat flow needed to change the diver's temperature from 37°C to 35°C?
4) Estimate how long (in minutes) the diver can stay in the water (before feeling the effects of hypothermia).
5) What would the time be if the suit were 8-mm thick instead?
6) 1 calorie is the energy needed to raise the temperature of 1 gram of water by 1 degree Celcius, i.e., the specific heat of water is 1 calorie/g-°C. How many joules is 1 calorie?
1 cal =
7) A food Calorie (note the capitalization!) is defined as 1000 'physics' calories: 1 Cal = 1 kcal (kilocalorie). How many Calories would our diver have to consume (assuming they all went to heating him) in order to make up for the thermal energy lost in cooling from 37°C to 35°C? (This assumes that he leaves the cold water, or that he consumes this many Calories every t minutes, where t is the time calculated above.)