Final answer:
The energy required to raise the temperature of the water in a swimming pool from 20.2°C to 29.9°C is approximately 4.866 x 10⁹ joules, which is calculated using the formula Q = mcΔT, where the mass of water is 120,000 kg and the change in temperature is 9.7°C.
Step-by-step explanation:
To calculate the energy required to raise the temperature of the water in the swimming pool from 20.2°C to 29.9°C, we can use the formula for heat transfer, which is Q = mcΔT, where Q is the heat energy in joules, m is the mass of water, c is the specific heat capacity of water (4.184 J/g°C), and ΔT is the change in temperature.
First, we need to find the mass of the water in the pool by multiplying its volume by the density of water (1 g/mL).
The volume of the swimming pool is 10.0 m × 4.0 m × 3.0 m, which is 120 m³ or 120,000 liters since 1 m³ = 1,000 liters.
The density of water is approximately 1 g/mL, so the mass of water is 120,000 kg (since 1 liter of water has a mass of approximately 1 kg). Now we can calculate the heat energy required:
ΔT = 29.9°C - 20.2°C = 9.7°C
Q = (120,000 kg) × (4.184 J/g°C) × (9.7°C)
Q = 4,865,856,000 J or 4.866 x 10⁹ J
Therefore, the energy required to raise the temperature of the water in the swimming pool from 20.2°C to 29.9°C is approximately 4.866 x 10⁹ joules.