Our body's primary defense against high temperatures is through sweating (perspiration)

Our body's primary defense against high temperatures is through sweating (perspiration). Consider a 185 lb (84 kg) male farmer in the Central Valley of California on a July day when the air temperature is 110°F (43°C). On this day, the humidity is low enough such that all the sweat evaporates from the farmer's skin, enabling him to maintain a body temperature of 100°F (38°C). The farmer sweats 1 liter (1000 g of water) per hour and 60% of the latent heat needed to evaporate this sweat is provided by farmer's body (the other 40% is provided by the air). If the farmer suddenly dehydrates and stops sweating, how long will it take for his body temperature to rise to a near-fatal 110°F (43°C)? Please show all of your work.


Assumptions:
1.     It takes 4200 Joules of energy to warm each kilogram (kg) of his body 1°C (1.8°F).
2.     The latent heat of vaporization is 2,400,000 J/kg. This value means that it takes 2,400,000 Joules of energy to convert one kilogram of sweat (a liquid) into a gas.


Hint: First calculate how much energy it takes to raise his body from 38°C to 43°C. Then calculate how much energy his body was giving away when he was sweating at a rate of 1-liter/hr (1 kg/hr). Use the ratio of these two numbers to find the time!