a) How much energy is required to evaporate all the water in a swimming pool of area 158 m2 and depth 4.1 m
(b) The intensity of sunlight is about 1080 W/m2. If all of this energy is absorbed by the water in the pool, how long will it take for take the water to evaporate?
(a) To calculate the energy required to evaporate all the water in the swimming pool, you need to know the specific heat of water and the latent heat of vaporization.
The specific heat of water is the amount of energy required to raise the temperature of water by 1 degree Celsius. For water, it is approximately 4.18 joules/gram °C.
First, let's calculate the volume of water in the swimming pool:
Volume = area * depth = 158 m2 * 4.1 m = 647.8 m3
Next, we need to convert the volume of water to mass. The density of water is approximately 1000 kg/m3.
Mass = volume * density = 647.8 m3 * 1000 kg/m3 = 647,800 kg
Now, we can calculate the energy required to heat the water from its initial temperature to its boiling point. Let's assume the initial temperature is 25°C and the boiling point is 100°C.
Energy = mass * specific heat * temperature difference
= 647,800 kg * 4.18 J/g°C * (100°C - 25°C)
Note that we need to convert the specific heat from joules/gram °C to joules/kilogram °C. Since 1 kg = 1000 g, the specific heat in joules/kilogram °C is 4.18 J/kg°C.
Energy = 647,800 kg * 4.18 J/kg°C * 75°C
Finally, to calculate the energy required to evaporate the water, we need to consider the latent heat of vaporization. The latent heat of vaporization for water is approximately 2.26×10^6 J/kg.
Energy = mass * latent heat of vaporization
= 647,800 kg * 2.26×10^6 J/kg
Add the two energy values together to get the total energy required to evaporate all the water in the swimming pool.
(b) To determine how long it will take for the water to evaporate using the given intensity of sunlight, you need to consider the rate of energy absorption and the total energy required.
Given that the intensity of sunlight is approximately 1080 W/m2 and assuming that all of this energy is absorbed by the water:
Energy absorption rate = intensity of sunlight * area
= 1080 W/m2 * 158 m2
To find the time required to evaporate the water, divide the total energy required (calculated in part a) by the energy absorption rate:
Time = Total energy required / Energy absorption rate
Now, substitute the values and calculate the time.