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An uncovered swimming pool loses water due to evaporation

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Please help with the following problem.

An uncovered swimming pool loses 1 inch of water off of its 1000ft^2 surface each week due to evaporation. The heat of vaporization for water at the pool temperature is 1050 Btu/lb. The cost of energy to heat the pool is 10.00 dollar per million BTU. A salesman claims that a 500 dollar pool cover that reduces evaporative losses by two-thirds will pay for itself in one 15 week swimming season. Is this true?

I believe the equation is change in E=m*c*change in temp, where m is going to be equal to mass/time.

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Solution Preview

The change of temperature does not play a role here, because vaporization at any temperature takes a large amount of energy (1050 Btu/lb given above). When water evaporates, it takes that heat from the remaining water, so that the remaining water needs to be heated up all the time, if the owner wants to maintain constant temperature.

So all you have to do is to calculate the ...

Solution Summary

This solution helps with a problem regarding swimming pools and evaporation.

$2.19