1. The problem statement, all variables and given/known data 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 = 3.5 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 = 2°C the diver "weighs" m = 60 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...].) Values I have calculate so far: Thermal Resistance of wet suit Rth: 0.058333 K/Watt Heat Capacity of the diver: 208800 J/K τ: (time constant for differential equation): 12179.9 Estimate how long (in minutes) the diver can stay in the water (before feeling the effects of hypothermia). 2. Relevant equations The solution to a differential equation is as follows: TA(t) = TB + (TA0 - Tb)e^-t/τ 3. The attempt at a solution Solving everything symbolically yields τln( (TA - TB)/(TA0 - TB)) = -t TA0 = 37°C TA = 35°C TB = 2°C τ = 12179.9 ∴t = 716.673s -> 11.94min Apparently, the answer is wrong. I even had a friend check my work and he said my work is ok. What's going on? Thanks!!