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re: energy saving question
18 dec 2000
woodswun  wrote:

>gn52@accucomm.net (frank) wrote:

>>is it true that traditional energy savings techniques used for
>>electric, gas, or oil hearting such lowering the temp at night and/or,
>>depending on the situation cutting it off at night are not relevant
>>for heat pumps?

>no, that is not true.  if you turn back your thermostat at night
>(or other long periods) you will save energy.  

well, it's not always untrue. let's invent a pathological counterexample
in which the heat pump can supply all of the daily heat, with no setback,
but its electric resistance heater supplies almost all of the daily heat,
with a setback.

suppose a house cools from 70 f to 50 f over 8 hours on a 30 f day, ie
50 = 30 + (70-30)exp(-8/rc), so rc = c/g = -8/ln(20/40) = 11.54 hours.

suppose a 10 kw resistance heater takes over after a few minutes when the
heat pump can't meet the thermostat setting, and the heater takes exactly
16 hours to warm an internal house mass from 50 to 70 f while also keeping
the room air 70 f on a 30 f day. with thermal mass c btu/f and conductance
g btu/h-f, c = (34120-(70f-30f)g)16h/(70f-50f) = 27296-32(c/11.54), so
c = 7,235, eg 16 water-filled 55-gallon accent drums.

g = c/11.54 = 627 btu/h-f, so the house needs (70-30)627 = 25k btu/h
to stay 70 f all day, eg 58.8 kwh, using a 2.45 kwh heat pump with
a cop of 3.

during an 8 hour setback, the house has an average temp of about 60 f,
so it needs 8h(60-30)627 btu at night and 16h(70-30)627 during the day,
totaling 552k btu, ie 161.7k kwh with resistance heating, 2.75 times
more energy than it needed without the setback.

nick




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