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November 24, 2014

November 24, 2014

Posted by **Samuel** on Friday, April 26, 2013 at 6:48pm.

- math/physics -
**Count Iblis**, Friday, April 26, 2013 at 7:04pmThe amount of heat per unit time that leaks out of the house is approximately proportionate to difference between the inside and outside temperature. The thermostat will make sure that as much heat is produced by the heating as is leaking away, so that thee temperature stays constant on average.

So, if the thermostat is left at 68 F all day, the total amount of heat used per day will be some constant c times (68-15), while if it is set at 50 F for half a day and 68 for the other half, you'll use

1/2 c (50-15) + 1/2 c (68-15)

per day.

c (68 - 15) = 53 c

1/2 c (50-15) + 1/2 c (68-15) =

44 c

44c/(53 c) = 0.83

So, you save 17%

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