Final answer:
To keep the temperature of the swimming pool constant, the energy carried away by evaporation must be equal to the energy gained from the sun. The fraction of water that must evaporate can be calculated using the specific heat capacity of water and the energy gained from the sun. The equation can be rearranged to solve for the fraction of water that must evaporate.
Step-by-step explanation:
In order to keep the temperature of the swimming pool constant, the amount of energy carried away by evaporation must be equal to the amount of energy gained from the sun. The rise in temperature due to evaporation would be 1.50°C. To calculate the fraction of the water that must evaporate, we need to consider the specific heat capacity of water and the heat energy required to raise the temperature of water. The equation we can use is:
Energy gained from the sun = Energy carried away by evaporation
By rearranging the equation, we can solve for the fraction of water that must evaporate:
Fraction of water evaporated = (Energy carried away by evaporation) / (Energy gained from the sun)
Since the temperature rise due to evaporation is 1.50°C, we can use the specific heat capacity of water (4.18 J/g°C) to calculate the energy carried away by evaporation:
Energy carried away by evaporation = (1.50°C) x (4.18 J/g°C) x (mass of water)
The energy gained from the sun depends on the area of the swimming pool, the intensity of sunlight (given by 1.00 kW/m²), and the time period. However, since we are only interested in the fraction of water that must evaporate, we can ignore the time period. Therefore, the energy gained from the sun is given by:
Energy gained from the sun = (1.00 kW/m²) x (area of the swimming pool)
By substituting these values into the equation for the fraction of water evaporated, we can find the answer.