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1 June, 09:35

An uncovered swimming pool loses 1.0 inch of water off its 1,000 ft^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 per million btu. A salesman claims that a S500 pool cover that reduces evaporation losses by two-thirds will pay for itself in one 15-week swimming season. Can it be true?

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  1. 1 June, 12:48
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    The affirmation is true, the cover will be worth buying

    Explanation:

    The equation necessary to use is

    E = m*cv,

    Where

    cv: the heat of vaporization.

    Finding the rate at which the water evaporates (m^3/week).

    The swimming pool loses water at 1 inch/week off its 1,000 ft^2

    Than,

    1000 ft² * 1 in/wk * 1 ft/12 in = 83.33 ft³/week

    To obtains the rate of mass loss it is necessary to multiply it for the density of water

    83.33 ft³/week * 62.4 lb/ft³ = 5200 lb/week

    Knowing the vaporization heat it is possible to find the rate of heat which is leaving the swimming pool

    5200 lb/week * 1050 BTU/lb = 5460000 btu/week

    Over a 15-week period, the pool loses 81.9 million BTU.

    Knowing the cost of energy to heat the pool is $10.00 per million btu

    The price = $819

    This way, the affirmation is true, the cover will be worth buying
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