This lesson will require logic, estimation, and converting measures
This is a series of question that build towards answering how much it would cost to heat a swimming pool.
Setting up the problem
Start with the socratic method Ask “What variables do you think you need to figure out how much it costs to heat the pool?” Variables
- starting water temperature
- ending water temperature
- air temperature
- pool volume
- gallons from cubic feet
- [estimate average depth and ask whether the average is biased high or low you want the student to recognize that it depends on how fast the grade is from the shallow to deep end)]
- cost per mmBTU
- Definition of BTU
- Energy to raise 1 lb of water 1 degree fahrenheit (1 lb of water is about 8 gallons)
- How many BTUs do you need total to raise the temperature to 90 degrees?
- How much does it cost to heat the pool?
- For a given heater size how long does it take to heat the pool?
- Does your model of how much it costs and how long it takes match reality? If not why?
[Qualitative discussion of heat loss to environment & heater efficiency]
See the ‘Pool Heater’ tab in Moontower Math Problems For Kids