A swimming pool, 10.0 m by 4.0 m, is filled with water to a depth of 3.0 m at a temperature of 20.2°C.
How much energy is required to raise the temperature of the water to 24.0°C?
To find the energy required to raise the temperature of the water, we can use the equation:
Q = m * c * ΔT
Where:
Q is the heat energy required (in Joules),
m is the mass of the water (in kg),
c is the specific heat capacity of water (4.18 J/g·°C), and
ΔT is the change in temperature (in °C).
To solve the problem, we need to find the mass of the water first. The formula to calculate the mass of the water is:
mass = density * volume
The density of water is approximately 1000 kg/m³. The volume of the pool is given as length × width × height, which is 10.0 m × 4.0 m × 3.0 m = 120 m³.
Therefore, the mass of the water is:
mass = 1000 kg/m³ × 120 m³ = 120,000 kg
Now we can substitute the values into the equation:
Q = 120,000 kg * 4.18 J/g·°C * (24.0°C - 20.2°C)
After performing the calculations, we can find the amount of energy required to raise the temperature of the water from 20.2°C to 24.0°C.