   Chapter 11, Problem 72AP

Chapter
Section
Textbook Problem

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 1 000 W/m2 for the intensity of sun-light 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).

To determine
The amount of water lost when baked in the sun on the beach for an hour.

Explanation

Section1:

To determine : The latent heat of vaporization of water at 37°C .

Answer : The latent heat of vaporization of water at 37°C is 2.5237×106J/kg .

Explanation:

Given Info:

Formula to calculate the energy required to boil the water and vaporize it is,

Q=m(cwater(TfTi)+Lv)

• cwater is the specific heat of water,
• Ti is the initial temperature of water on the skin.
• Tf is the boiling temperature of water,
• Lv is the latent heat of vaporization of water at 100°C ,
• m is the mass of water,

Evaporation can occur at temperatures well below the boiling point of water.

Consider the water on the skin is at 37°C get evaporated.

Formula to calculate the energy required to evaporate water from the skin at 37°C is,

Q=mLv

• Lv is the latent heat of water at 37°C .

The amount of energy required to evaporate 1 kg of water at this temperature is equal to the amount of energy-required raise the temperature of water from 37°C to boil point and evaporate.

Equate both the equations and simplify.

mLv=m(cwater(TfTi)+Lv)Lv=(cwater(TfTi)+Lv)

Substitute 4186J/kg°C for cwater , 37°C for Ti , 100°C for Tf , and 2260kJ/kg for Lv to find Lv

Lv=[(4186J/kg°C)(100°C37°C)]+[(2260kJ/kg)]=2.5237×106J/kg

Thus, the latent heat of vaporization of water at 37°C is 2.5237×106J/kg .

Section2:

To determine: The energy received from the sunlight in one hour.

Answer: The energy received from the sunlight in one hour is 2.16×106J .

Explanation:

Given Info:

Consider the a person is approximately 0

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