re: air conditioning
17 may 1997
junaid omar wrote:
>9. cooling an empty room is probably more costly than a room filled
>with big solid objects.
air-conditioning an empty room is less costly than air-conditioning one filled
with big solid objects, if the room temperature goes up and down daily, since
it takes energy to lower the temperature of the big solid objects. if the room
temp is constant, empty or full makes little difference. however, a room full
of big solid objects will stay cooler than an empty one, if ventilated at
night with cooler outdoor air, with no ventilation during the day.
some examples: suppose a 16x16x16' superinsulated house in phoenix, arizona,
with 1,500 ft^2 of average r20 walls and ceilings has an inherent thermal mass
of 750 btu/f (1/2" drywall) and a thermal conductance of 1,500/20 = 75 btu/h-f.
the 24-hour average july temperature in phoenix is 93.5 f, with average daily
min and max of 81 and 105.9. keeping the house at 70 f all day requires
24h(93.5-70)75 = 42k btu, about 4 kwh of electrical energy using an ac with a
cop of 3, ie one that moves 3 kwh of heat per kwh of electrical energy input.
if every day were 105.9 and every night 81 f, cooling the house to 70 f for
12 night hours would require 12h(81-70)75 = 9900 btu or about 1 kwh/day of
ac energy, if the house had no thermal mass. but the house has an inherent
rc time constant of 750/75 = 10 hours, so if it were 70 f at dawn, it would
warm up to 105.9-(105.9-70)exp(-12/10) = 95 f at dusk. cooling its thermal
mass back to 70 f requires an additional (95-70)750 = 19k btu, making the
total cooling required about 29k btu/day, a total of 2.8 kwh of ac energy.
now let's add lots of thermal mass to the house, say 300 55 gallon drums full
of water (accent drums, each 3' high x 2' in diameter :-), an extra 300x55x8
= 132k btu/f, which raises rc to 133k/75 = 1770 hours or 74 days. if the house
were 70 f at dawn, by dusk it would be 105.9-(105.9-70)exp(-12/1770) = 70.24 f,
so it's pointless to turn the ac off during the day, since the house temp
won't rise much at all, in this case, so there will be hardly any energy
savings. this house requires almost the same ac energy as the house in the
first example, even though the ac only runs at night. (the ac may be more
efficient at night, cooled by cooler outside air.)
if we open the windows at night and close them during the day, or use a whole
house fan, this house can be close to 81 f all day, which might be comfortable
in phoenix, with an average relative humidity of 32% in july, average humidity
ratio of 0.0105 #water/#dry air, with a dew point of about 59 f, average 7.6
mph windspeed, elevation of 1112 feet and average air pressure of 14.1 psia,
vs 14.7 psia at sea level.
instead of opening windows at night, we might move water down into the house
from a shallow roof pond to a water-air heat exchanger, something like an
automobile radiator with a fan or a passive plumbing arrangement like a cool
cell (a real product made by zomeworks.) a 16x16 = 256ft^2 70 f pond with a
still air film conductance of 1.5 btu/h-f-ft^2 might gain 12h(81f-70f)x256x1.5
= 51k btu of heat per night by convection, which doesn't help, but...
the ratio of evaporative to convective pond heatflow is 1000(pp-pa)/(tp-ta)),
independent of windspeed, where pp and pa are vapor pressures of water in the
pond and air in inches of mercury, and tp and ta are farenheit pond and air
temps. the vapor pressure of 70 f water is 0.74 "hg (clausius-clapeyron:
ln(pw) = 17.863-9621/tabs), and air with a 0.0105 humidity ratio, w, has
pa = 29.92/(1+0.62198/w) = 0.5 "hg. phoenix elevation increases this ratio by
a factor of 14.7/14.1, so the pond might lose 1000(0.74-0.5)/(81-70)x14.7/14.1
= 23 times more heat by evaporation than it gains by convection (assuming this
formula works with opposite heatflows), on an average july night. a total of
about a million btu/day, about 25 times more cooling than needed. night sky
radiation helps too...
this would also make a good solar house. the average jan temperature in phoenix
is 53.6 f, with an average daily max of 65.9 and average 1550 btu/ft^2/day of
sun falling on south walls. keeping this house at 70 f over an average day
requires 24h(70-53.6)75 = 29.5k btu. a square foot of thin low-thermal-mass
sunspace at 80 f during the day with r1 clear plastic single glazing that
transmits 90% of the sun would gain about 1400 btu and lose about 6h(80-65.9)
= 85 btu over a 6 hour winter day, for a net gain of about 1300 btu, so this
house might be 100% solar heated in winter using 29.5k/1300 = 24 ft^2 of
glazing, something like a 4x6' clear plastic picture frame air heater over a
dark-colored insulated, low-thermal-mass wall with holes in the wall at top
and bottom to let warm air circulate through the house during the day.
having lots of insulation, few air leaks, and lots of thermal mass inside the
house makes for a large rc time constant, which makes it possible to use these
monthly weather averages, vs detailed daily or hourly temperatures.
ps to doug (for whom $0.0021 = 0.0021 cents and 1/0.0021 = 5? :-) and theresa:
i hope the first paragraph of this posting makes sense, at least. this part
of the universe is more easily explored with numbers than plain english words
like "warmer" or "cooler."