The evaporation of perspiration is the primary mechanism for cooling the human b

Question

The evaporation of perspiration is the primary mechanism for cooling the human body. Estimate the amount of water you will lose when you bake in the sun on the beach for an hour. Use a value of 1,081 W/m2 for the intensity of sunlight and note that the energy required to evaporate a liquid at a particular temperature is approximately equal to the sum of the energy required to raise its temperature to the boiling point and the latent heat of vaporization (determined at the boiling point). (Assume that the area of your body exposed to the sun is 0.62 m2 and that your skin temperature is 37°C.)

____ kg

Explanation / Answer

given

a rea A = 0.62 m2   

I = 1,081 W/m2

t = 1 hour = 3600 sec

t1 = 37°C ( initial temp )

t2 = 100oC ( final temp )

dt = t2 - t1

dt = 63oC

C = 4186 J/Kg/oC

L = 2.26 X 106 J/Kg ( water )

rate of energy is P = I X A

P = 1,081 X 0.62

P = 670.22 W

energy is E = P t

E = 670.22 X 3600

E = 2412792 J

using equation

E = m C dt + m L

2412792 = m X 4186 X 63 + m X 2.26 X 106

2412792 = m ( 2523718 )

m = 0.956 kg

the amount of water you will lose when you bake in the sun on the beach for an hour is m = 0.956 kg

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