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It has been determined that the body can generate 5500 kJ of energy during one hour of strenuous exercise. Perspiration is the body's mechanism for eliminating this heat. How many liters of water would have to be evaporated through perspiration to rid the body of the heat generated during two hours of exercise? (The heat of vaporization of water is 40.6 kJ/mol. Assume the density of water is 1.000 g/mL)
M0leswater*40.6kJ=5500kJ/hr*2hr
solve for moles water.
now, solve for liters water
moleswater*18gwater/mole*1liter/1000g=...liters of water.
To determine how many liters of water would need to be evaporated through perspiration to rid the body of the heat generated during two hours of exercise, we need to calculate the heat generated and then convert it to the amount of water that needs to be evaporated.
First, let's calculate the heat generated during two hours of strenuous exercise. We are given that the body can generate 5500 kJ of energy during one hour of exercise. So, for two hours, the total heat generated would be:
Total heat generated = 5500 kJ/hour * 2 hours
Total heat generated = 11000 kJ
Now, let's convert the heat generated to the amount of water that needs to be evaporated. We'll use the heat of vaporization of water and the density of water to do this.
The heat of vaporization of water is given as 40.6 kJ/mol. However, we need to convert it to kJ/g since we'll be working with grams of water. One mole of water has a molar mass of approximately 18.015 g/mol.
Heat of vaporization (kJ/g) = Heat of vaporization (kJ/mol) / Molar mass of water (g/mol)
Heat of vaporization (kJ/g) = 40.6 kJ/mol / 18.015 g/mol
Heat of vaporization (kJ/g) ≈ 2.25 kJ/g
Now, we can calculate the amount of water that needs to be evaporated by dividing the total heat generated by the heat of vaporization:
Amount of water evaporated (g) = Total heat generated (kJ) / Heat of vaporization (kJ/g)
Amount of water evaporated (g) = 11000 kJ / 2.25 kJ/g
Amount of water evaporated (g) ≈ 4888.89 g
Since we are asked for the amount of water evaporated in liters, we need to convert the grams of water to liters using the density of water.
The density of water is given as 1.000 g/mL.
Amount of water evaporated (L) = Amount of water evaporated (g) / Density of water (g/mL)
Amount of water evaporated (L) = 4888.89 g / 1.000 g/mL
Amount of water evaporated (L) ≈ 4888.89 mL
Finally, we can convert the milliliters (mL) to liters (L) by dividing by 1000:
Amount of water evaporated (L) = 4888.89 mL / 1000
Amount of water evaporated (L) ≈ 4.889 L
Therefore, approximately 4.889 liters of water would have to be evaporated through perspiration to rid the body of the heat generated during two hours of exercise.