If the price of electrical energy is $0.10 per kilowatt*hour, what is the cost of using electrical energy to heat the water in a swimming pool (12.0m*9.00m*1.5m) from 15 to 27 degrees Celcius?
$230
To calculate the cost of using electrical energy to heat the water in a swimming pool, we need to determine the amount of energy needed to heat the water and then multiply it by the cost per kilowatt-hour.
Step 1: Calculate the volume of the water in the pool.
Volume = length * width * height
Volume = 12.0m * 9.00m * 1.5m = 162 cubic meters
Step 2: Convert the volume from cubic meters to liters.
1 cubic meter = 1000 liters
Volume = 162 cubic meters * 1000 = 162,000 liters
Step 3: Calculate the mass of the water.
The density of water is approximately 1 gram per milliliter.
Mass = volume * density
Mass = 162,000 liters * 1000 grams/liter = 162,000,000 grams
Step 4: Calculate the energy required to heat the water.
The specific heat capacity of water is approximately 4.18 joules per gram per degree Celsius.
Energy = mass * specific heat capacity * temperature change
Temperature change = final temperature - initial temperature = 27°C - 15°C = 12°C
Energy = 162,000,000 grams * 4.18 J/g°C * 12°C = 80,076,960,000 joules
Step 5: Convert the energy from joules to kilowatt-hours.
1 kilowatt-hour (kWh) = 3,600,000 joules
Energy (kWh) = 80,076,960,000 joules / 3,600,000 joules/kWh = 22,244 kWh
Step 6: Calculate the cost of using electrical energy.
Cost = energy (kWh) * cost per kilowatt-hour
Cost = 22,244 kWh * $0.10/kWh = $2,224.40
Therefore, the cost of using electrical energy to heat the water in a swimming pool from 15°C to 27°C is approximately $2,224.40.
To calculate the cost of using electrical energy to heat the water in a swimming pool, you need to determine the energy required to raise the temperature of the water and then multiply it by the cost per kilowatt-hour.
First, calculate the volume of the water in the pool:
Volume = length * width * depth
Volume = 12.0m * 9.00m * 1.5m
Volume = 162 cubic meters
Next, calculate the mass of the water based on its volume and density:
Density of water = 1000 kg/m^3
Mass = Volume * Density
Mass = 162 m^3 * 1000 kg/m^3
Mass = 162,000 kg
To find the energy required to heat the water, you can use the specific heat capacity of water, which is 4186 J/kg°C.
Energy = Mass * Specific Heat Capacity * Temperature Change
Temperature Change = Final Temperature - Initial Temperature
Temperature Change = 27°C - 15°C
Temperature Change = 12°C
Energy = 162,000 kg * 4186 J/kg°C * 12°C
Energy = 81,787,776,000 J
Now, convert the energy from joules to kilowatt-hours:
1 kilowatt-hour = 3,600,000 joules
Energy in kilowatt-hours = Energy in joules / 3,600,000
Energy in kilowatt-hours = 81,787,776,000 J / 3,600,000
Energy in kilowatt-hours ≈ 22,719.94 kWh
Finally, calculate the cost:
Cost = Energy in kilowatt-hours * Cost per kilowatt-hour
Cost = 22,719.94 kWh * $0.10/kWh
Cost ≈ $2271.99.
Therefore, the cost of using electrical energy to heat the water in the swimming pool from 15 to 27 degrees Celsius is approximately $2271.99.