HEATING A HOUSE
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Keeping a home warm can be a major cost of owning or renting a home.
Understanding the physics of heating processes can help one to think of ways to
lower costs in homes that were not designed for maximum thermal efficiency.
HOT: A substance, solid, fluid, or gas, is
“hot” if molecules are in a state of agitation.
The more vigorous is this motion, the hotter
is the material with the result that molecules
tend to be further apart. Most heated liquids
expand to cause a column of fluid to rise in a
tube as a measure of temperature. A coil of
steel expands when heated.
Heat flow from one body to another
results when the more active molecules in
the hotter substance add mechanical energy
to the molecules of the cooler one and
become less active process. If the wall of a
house has one temperature on the inside and
a lower one on the outside, heat will flow
through the wall. A wall has a resistance to
heat flow called the “R” value.
Heat is removed on the outside surface of
the house in three ways. Cold air can be
warmed by the exterior surface. A cold wind
can increase the rate of heat flow—the “chill
factor.” Rapid fluctuations of molecules can
cause radiation analogous to what a radio
transmitting antenna does. The radiation
factor is largest for dark exterior surfaces.
The measure of heat in the English
system of units is the “British Thermal Unit”
or Btu.
One Btu increases the temperature of a
pint of water by one degree Fahrenheit.
On earth (but not elsewhere) one pint of
water weighs 16 ounces (one pound) and
fills two standard 8-ounce drinking glasses.
There are 8 pints in a gallon weighing 8
pounds.
Important: Weight is not the same as
mass. A pint of water on the moon has the
same mass as one on the earth but weighs
much less. It is not proper to refer to the
weight of an object to define mass. This
“error” can be tolerated as long as
calculations refer to the earth.
Heat transfer formula:
Btu/hour = (Temp diff)*(Total area)/R
EXAMPLE: Assume a house measures
40 by 50 feet giving an area of 2,000 square
feet. Ceiling height is 8 feet. Assume that
the walls, floor, and ceiling all have the
same R value of 10 and that the temperature
difference for all surfaces is 30 degrees
Fahrenheit. The sum of floor and ceiling
areas is 2000*2=4000 square feet. The area
of perimeter walls is 180*8=1440 square
feet. The total surface area is 5440 square
feet. At a temperature difference of 30
degrees in the winter:
Btu/hour=5440*30/R=5440*30/10=16,320.
Assume that the winter temperature
difference lasts all day and all night. The
thermostat can be turned down at night to
maintain a constant difference of 30 degrees.
Multiply the heat loss per hour by 720
(hours per month) to get 11,750,400 Btu per
month, assuming calm exterior air and no
radiation.
The gas company charges by the
“therm.” One therm=100,000 Btu. You
will be charged for 117.5 therms if your
furnace is 100% efficient. If your furnace
efficiency is 80%, you will require more
therms than calculated above. Divide the
first value by 0.8 to get 146.88 therms per
month. (Natural gas produces 1005 Btu per
cubic foot at atmospheric pressure.)
A typical gas bill will ask for perhaps
$1.40 per therm, perhaps a little more. Your
monthly winter heating bill comes to
$205.63. This cost might increase somewhat
because you must change air in order to not
build up too much carbon dioxide as people
breath. The cost might be reduced due to
heat from electric lights and other electric
utilities. A 100 watt light bulb puts out about
340 Btu per hour. Drape over windows in
order to reduce radiation. Have plants and
other objects near the outside of the house in
order to reduce the chill factor when wind is
present. People in the house produce about
300 Btu per hour awake or asleep. You act
like a light bulb! People in the old days
huddled together in tents or igloos in order
to stay warm. Most couples still sleep in the
same bed so as to keep warm when the
furnace is turned down. Heating costs are
saved but is sleep then hampered?
But the best thing you can do in order to
reduce your heating bill is to remove
unintentional
leaks,
increase
heater
efficiency by improving insulation of ducts,
and most of all, by increasing R values.
EXAMPLE R VALUES:
Ordinary window. R=0.8
Double glazed window. R=2
Plaster board. R=0.36
Fir sheathing. R=1.17
PER INCH THICKNESS:
Corkboard. R=4
Styrofoam board. R=4.9
Polyurethane. R=7
(For a web search, use “R value.”)
A layered arrangement of different
materials yields a net R value that is the sum
of individual values. Three inches of
Polyurethane gives R=3*7=21. An air gap
between inner and outer wall surfaces may
give an R value of about 1, up to about 6
with reflective materials.
Different parts of a house can have
different R values. But some things are
difficult to control or too expensive to
correct. Pity the poor person living in an
older house where R values may not be
larger than 1. Some elderly and poor
individuals freeze to death in the winter (or
die of heat prostration in summer).
HEATING WATER: If you heat water
with gas, calculate how much water you use
in a shower or for a washing machine or for
dishes. Calculate the number of Btu’s
needed. A gas water heater might not be
very efficient with heat lost when not in use.
HEATING AIR: Upon returning from
vacation, you want to increase the inside air
temperature by 30 degrees Fahrenheit. Your
home has an area of 2,000 square feet with
an 8 foot ceiling. The volume of air in the
house is 16,000 cubic feet. Air weighs about
0.075 pounds per cubic foot in a normal
atmosphere. Raise the temperature of one
cubic foot of air by one degree F with 0.24
Btu. Raise the air temperature in the house
by 30 degrees with
16,000*0.24*30 = 115,200 Btu
The inside walls, ceiling, and floor will
also be 30 degrees cooler than desired. They
need warming as well.
Air in a home should be changed on a
continuing basis. In winter we need 115,200
Btu per day to heat exchanged air by 30
degrees F. In a month, this is
30*115200=3,456,000 Btu or 34.56 therms.
Add about $48 to your monthly bill.
The simple way to bring outside air into
the house is with leaks or a partly open
window. For maximum efficiency, outgoing
air can pass through special ducts that
surround pipes that bring air in. The
incoming air gains some heat.
HEATING WITH ELECTRICITY:
An electric heater produces heat:
One watt-hour=3.413 Btu.
Heating with electricity can be almost
100% efficient. The house example required
11,750,000 Btu per month. This amount of
heat is provided in watt-hours as 3,442,719
watt-hours. The power company charges by
the kilowatt-hour. Divide watt-hours by
1000 to get 3443 Kw-hrs. At 7.65 cents per
Kw-hr your monthly winter bill is $263.39.
NOTE ON HEAT MEASURE: In most
of the world, the gram-calorie is used. This
is the amount of heat required to raise the
temperature of one gram of water by one
degree Celsius. The large calorie (which is
used for food energy) refers to heating one
kilogram (one liter) of water by one degree
C. There are 9 degrees F in 5 degrees C. One
liter of water weighs 1 Kg = 2.205 pounds.
1 Kg-Cal = 2.205*9/5=3.969 Btu.
HUMAN BODY: R-values also apply to
your own body and your clothing with wind
chill being an important factor. What is the
equivalent R value and surface area of the
human body? Can you stroll in cool air or
snorkel in Hawaii to lose weight?
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