How much heat, expressed in Kwh, is required to raise the temperature of water in a 20,000 gallon pool by 10 degrees C. ? This is a real world question, I'm 18 years old and I service my neighbors pool.
To calculate the amount of heat required to raise the temperature of water in a pool, you need to know the specific heat capacity of water and the mass of the water.
1. Specific heat capacity of water:
The specific heat capacity of water is approximately 4.186 joules per gram per degree Celsius (or 1 kilocalorie per kilogram per degree Celsius).
2. Convert the volume to mass:
First, convert the volume of water in the pool from gallons to liters. Then, convert the liters to kilograms by multiplying by the density of water, which is approximately 1 kilogram per liter.
3. Calculate the heat required:
Using the formula: Q = m * c * ΔT
where Q is the heat energy required, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.
Let's work through the calculations:
1. Specific heat capacity of water: 4.186 kJ/kg°C (or 1 kcal/kg°C)
2. Convert volume to mass:
Assuming the density of water is 1 kg/L
20,000 gallons ≈ 75,708 liters
75,708 liters ≈ 75,708 kg
3. Calculate heat required:
Q = m * c * ΔT
Q = 75,708 kg * 4.186 kJ/kg°C * 10 °C
Q ≈ 3,158,688 kJ (or 3,158.688 kWh)
Therefore, approximately 3,158.688 kilowatt-hours (kWh) of heat energy is required to raise the temperature of the water in a 20,000-gallon pool by 10 degrees Celsius.