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Energy: Home Energy AuditIntroduction
Energy Transfers and the First Law of Thermodynamics
In the 1800’s, scientists found, empirically, that rules exist that determine how energy can be transferred.
The first of these rules is called the First Law of Thermodynamics. This law is usually stated as, “Energy
can neither be created nor destroyed; it can only be transferred from one form to another.” This often
leads to the re-titling of this law as the Conservation of Energy Principle since it says that energy must be
conserved.
This statement of the First Law does not say anything about how energy can be transferred, though. It
turns out that there are only two ways. This was discovered in 1850 by the English scientist James Joule,
who found that heat and work are equivalent methods for changing the energy of an object. In his
experimental work, Joule was able to show that he could increase the thermal energy of a pot of water by
either placing it over a flame (adding heat), or by stirring it with a paddle (doing work). For this and other
important work in this area, the SI unit of energy is called a joule (1 J = 1 kg m 2 /sec2). Using this, we can
re-write the First Law mathematically as
∆E = W + Q
where ∆E is the change in the energy of an object, W is the work done on the object, and Q is the heat
added to an object. In laymen’s terms, this means that the only way to change the energy of an object is
to exchange either work or heat with it.
Energy History
The discovery of the laws of thermodynamics was extremely important, as our need to understand energy
is fueled by the overwhelming use of energy in human society. From the earliest days, humankind has
recognized the need to use energy to condition the environment around it. Wood was needed to heat
homes and to cook food. Beasts of burden were needed to plow fields and to provide transportation.
When either of these commodities became scarce, hardship prevailed, and solutions were sought. In
ancient Rome, for example, the lack of available firewood led to the passing of laws that made it illegal to
build a house or structure that would block another person’s home from getting sunlight, as this was the
primary method of heating homes without fire.
In the 20th century, fossil fuels (oil in particular)
reigned supreme as the energy of choice. Their
ubiquitous nature created historically low prices for
energy. This led to a substantial increase in the
number of mechanized tools used by the average
citizen. By the year 2000, the U.S. had a population
of about 283 million people that were driving over
200 million passenger vehicles. Almost every home
in America has a television, some type of range or
stove, and a refrigerator. About 3/4 of all
households have their own washer, dryer, and air
conditioner. Of course, this cheap price does not
come without some political and economic
consequences. Energy, and oil in particular, have
Fig. 1: U.S. Oil Consumption (Source: DOE)
played a very important role in the economy and politics throughout the last 150 years, affecting
everything from the entry of U.S. into World War II to the rampant inflation of the 1970’s to the current destabilized situation in the Middle East.
Energy Use in the U.S.
This modern dependence on many appliances of convenience requires a lot of energy. Our current
energy per capita use is over 330 million BTU’s of energy. Put another way, this means that the average
U.S. citizen would be responsible for using almost 60 barrels of crude oil each year, if all of the energy
used in America came from oil. The only other country in the Western World that was even close to this
is Canada, which has almost the same amount of usage. Most of the Western world uses 200 million
BTU’s of energy or less. Although we make up only about 5% of the world’s population, we account for
almost 25% of all of its energy consumption. In comparison, many Third World countries such as Ethiopia
use less than 1 million BTU’s per person.
The majority of this energy (82%) is supplied by fossil
fuels. Crude oil accounts for the largest share of this
(38%), followed quickly by coal (22%) and natural gas
(22%). The remaining energy comes mostly from
nuclear (8%) and renewable sources like hydroelectric,
solar, and wind (7%). Contrary to common belief, most
of this energy is produced domestically. The only
energy source that we are forced to import is crude oil,
of which we can currently supply only about 45% of our
need.
Of the energy used in the U.S., about 38% of it is used
for industrial processes (mining, milling, etc.), 36% of it
Fig. 2: U.S. Energy Consumption (DOE)
is used to power homes and offices, and 28% of it is
used for transportation. While most of us cannot directly affect the amount of energy used for industrial
processes, we can do something about our residential and transportation energy use. The figures above
mean that about 101 million Btu’s are used each year just to run our households (this does not include the
energy that was lost in producing and transporting this energy, which accounts for an additional 71 million
Btu’s). The majority of this energy use is to heat and cool our homes (55%). In this week’s lab, we are
going to begin to study ways to reduce our home energy usage, primarily through reducing our demand
for heating and cooling.
Measuring your home
In this week’s lab, we are going to prepare for the energy analysis that we are going to perform in two
weeks by measuring the surface areas of our homes that are exposed to outside temperatures. We are
also going to note what materials were used in the construction of our dwelling. This will allow us in
week three of this module to estimate the amount of energy that is being lost in our homes due to
conduction. This type of heat transfer depends upon the type of materials used for construction, the
amount of surface area through which heat is transferred, and the temperature difference across the
material. As we will see in next week’s lab, the type of material can drastically change the amount of heat
that is conducted from a hot to a cold region. Plywood, by itself, provides little resistance to the flow of
heat; plywood, combined with fiberglass and polystyrene insulation, can provide a significant barrier to
conduction and allow large temperature differences to be maintained between hot and cold regions.
While we are making these measurements of the exterior surfaces of our home, we will also be gathering
some basic information about some energy-using devices in our home, such as the refrigeration, cooking,
and water heating systems. These systems are responsible for most of the energy used in the home
outside of the heating and air-conditioning systems. These are also systems for there can be a wide
range of energy efficiency between various makes and models.
Instructions
1.
2.
3.
4.
5.
6.
7.
8.
9.
Prepare a drawing of your dwelling. This does not need to be an
intricate blueprint of your dwelling (although it helps if you already have
one), but a simple illustration of it that will allow for all external surface
measurements to be shown. Indicate north on the illustration.
On your drawing, please signify the measurements of all exterior, heatdissipating surfaces. These will be surfaces that lead from an airconditioned and heated room to either the exterior of the house or to
rooms (ex garage) that are not heated or air-conditioned. NOTE:
These measurements do not need to be made from the outside of
the home; measurements made from the inside of the house will
be sufficient)
While you are measuring the exterior components of your home, note
the materials from which they are constructed. For instance, is your
exterior door constructed of 1 1/2 inch solid wood, or is it 1 3/4 steel
with foam insulation? Enter this information on your Data Sheet
(Exterior Surface Type section) as to type of material of each exterior
surface (Interior surfaces are irrelevant for calculating heat transfer
since internal heat transfers do not affect the amount of energy lost or
gained to your home). Some homes will have more than one surface
type for each exterior surface. For instance, a house might have single
and double paned windows. If so, make sure that both types of
surfaces are entered onto the sheet.
Using the measurements from your drawing, calculate the area of each
exterior surface in your home and enter the data on the Data Sheet
provided. Round off all dimensions to the square foot and enter the
data into the appropriate slot for each surface type. If you have more
than one surface type for each component, remember to the different
areas for each type (ex. if you have 10 square feet of single paned
windows and 20 square feet of double paned windows, be sure to put
the appropriate amount in each slot). If you are unsure of how to
calculate areas of external surfaces, look at the example audit.
For each surface type, check the list of surface types and fill in the
value for the appropriate R factor (Ex. single pane window, R: .9).
From your drawing, calculate the square footage of the livable space
and write this value in the appropriate slot on your Data Sheet. If you
have not done so already, measure/estimate the average height of the
ceilings in that living space, and place the value in the slot below this.
Check the accuracy of thermostats on your heating and air
conditioning unit. While you might think that you have it set at 70
degrees, it might actually be maintaining a temperature of 72. This can
be checking by placing an accurate thermometer near the thermostat
and noting any differences between the readings. Noting any
differences, record the temperature settings for both the air conditioner
and heater during the year.
The final audit will require certain information about the appliances in
your home. You will need to know what type of heating and cooling
system your home has, as well as the types of major appliances. For
heaters and air conditioners, describe the energy source (electrical,
natural gas, wood, etc.) and tell whether the system is centralized
(ductwork takes the air to all parts of the home) or not. For the other
appliances, check the line next to the type if you have it. For electrical
stoves and dryers, we are also going to need to know the wattage of
the appliances. If you cannot find this information on the inside door of
the appliance, please note this on your data sheet.
From your utility company(ies), find out the cost per unit energy for
your energy source(s). For some companies, this information will be
printed on their bill (Ex. $.75/therm on a natural gas bill or $.08/kWhr
on an electric bill). For other companies, this information can be
Fig. 3: Sample
house drawing
extracted from the bill by dividing the total cost of the energy by the
amount of energy that was used. If this information is not on your bill,
or if you do not have a bill to check, call the companies that supply you
with energy and ask the rate that they are billing you.
Example
The floor plan at the left is of a wood-sided house built upon a cement slab. It is
two stories tall with insulated walls and twelve inches of blown fiberglass
insulation in the attic. The house is 5 years old, and has been well maintained.
The garage, while sealed with doors, is not heated or cooled. The main living
space occupies a 25’x35′ space both upstairs and downstairs (yellow and green
areas), with an additional 15’x25′ room (blue area) on the second floor that is
over the garage. Windows are as marked on the floor plan and are all 1/4″
double pane. The three exterior doors are standard 3’x7′ insulated-core steel
doors.
The Data Sheet for this house looks like the following:
Type of structure: _X_ House ______ Apartment/Duplex ______Mobile Home
Number of stories _2__
Exterior Surface Types
First Type
Second Type (if needed)
Windows
1/4″ double paned
Walls
Wood with 3 1/2″ fiberglass
and 1″ foam
Doors
1 3/4″ Pella
Sheetrock with 3 1/2″ fiberglass
Roof/Ceiling 12″ fiberglass (blown)
Ground
Floor
Concrete slab
6″ fiberglass over closed
unheated space
Exterior Surface Types Area R-factor Area R-Factor
Windows
210
1.7
Walls
1588 20
Doors
63
Roof/Ceiling
1250 43
Ground Floor
875
459
12
375
43
13
11
For instructions on how to calculate the areas in the above table, click here.
Total area of heated and air conditioned space: _2125__ sq. ft.
Average height of ceilings: _8__ ft.
o
Average indoor winter temperature ( F): _69____
Average indoor summer temperature (oF): __74____
Number of air exchanges per hour: __1___
Appliances
Heater Type: Central Natural Gas with insulated ducts___
Air Conditioning Type: __ Central Electric with insulated ducts __
Refrigerator/Freezer Combo: _1__
Gas Hot Water Heaters: _1_
Gas Stove/Oven: _1_
Electric Clothes Dryer: _1_ If yes: _2000__ Watts
Confusion About Heat and Temperature
Even though it has been over 150 years since the First Law of Thermodynamics was discovered, we still
find that heat is misunderstood. For example, the many environmental science textbooks define heat as
“the total kinetic energy of atoms or molecules in a substance not associated with bulk motion of the
substance.” THIS IS WRONG! What these books are describing is the thermal energy of a system. This
is a common misconception. While heat is energy, it is not a containable form of energy since, by its very
definition, heat is energy that is transferred. In particular, heat is the energy transferred between
objects of different temperature. The misunderstanding comes from the fact that we often talk about
heat leaving or entering an object, which gives people the idea that the object must contain heat. But this
is not the case. Once heat enters an object, it increases the internal energy of an object, which is the
same result that doing work on the object would produce. The object does not contain the heat or the
work; it merely changes its energy because of them.
This increase in internal energy can cause numerous things to occur to the object. One of the more
common things that it causes is for the temperature of the object to increase. However, it can cause
other things to occur that do not involve any change in temperature, such as a change of state (ex. water
changing into steam). The fact that one of the most common experiences is that the temperature
changes leads to another erroneous definition. Many books also define temperature as “a measure of the
speed of motion of a typical atom or molecule in a substance.” Again, this is wrong. While it may be true
for an ideal gas, it does not apply to all objects. The best definition for temperature is the property that
two objects have in common when no heat is transferred between them when placed in thermal
contact. The observant reader is going to note a certain circuitousness about these definitions for heat
and temperature. But, these are the only definitions that truly make sense. The best way to illustrate this
is to examine what happens when you measure the temperature of a glass of water with a mercury or
alcohol thermometer. Upon entering the water, the thermometer does not instantly register the correct
temperature. Instead, it takes several seconds for the liquid in the thermometer to settle to the correct
reading. During this time, heat is being exchanged between the water and the liquid in the thermometer.
As it does so, the temperature of the liquid in the thermometer changes, becoming closer to that of the
water. This change in temperature of the alcohol or mercury results in its volume changing, which is what
changes the level of the fluid in the thermometer. Once the temperature of the fluid has reached that of
the water in the glass, heat stops being transferred between them, and the volume of the fluid stops
changing.
Thus, the thermometer is not measuring the average speed of the molecules in the water. The only thing
that is being measured is the volume of the liquid in the thermometer. Somebody (or some machine)
calibrated the volume of the fluid in the thermometer to a temperature scale that is painted onto its side.
Because of this, we are able to read a value for the temperature by merely measuring the height of the
liquid in the thermometer. The temperature that we read, though, only tells us which way that heat will
flow if the object is put into thermal contact with another object.
Conduction
As we have previously stated, homeowners, on average, spend almost 50% of their energy budget for
heating and cooling. The reason for this is because heat is constantly transferring through all of the
exterior surfaces of the home. The most predominant type of heat transfer for the majority of homes is
known as conduction, which occurs when two regions of different temperature are put into direct contact,
but are not allowed to mix. As an example, the inside temperature of a home in the winter is hotter than
the exterior temperature if the home is being heated. The walls, doors, and windows are all conducting
heat to the outside since they are in direct contact with both reservoirs of air.
The rate at which heat gets transferred depends upon (1) the thickness of the material L, (2) the thermal
conductivity k (this depends on the composition of the material), (3) surface area of the material A, and 4)
the temperature difference between the reservoirs. In particular (see Fig. 2), the rate of heat transfer = A
k (TH-TC)/L. This equation shows that the thicker the material separating the two reservoirs (L larger), the
smaller the surface area that is contact (A larger), or the smaller the temperature difference, the slower
the rate of heat transfer through the substance. When it comes to heating and cooling our homes, this is
exactly what we will need to strive for in order to reduce our energy bills.
In our homes, the exterior surfaces are usually comprised of more than one type of material. For
instance, a wall can be composed of 3 1/2 inches of fiberglass insulation which is covered by 1/2 inches
of sheetrock on the inside and plywood and brick on the exterior. When two or more different materials
are between the hot and cold reservoirs, the equation on the previous page can become quite messy
since there will be various thermal conductivities and thicknesses with which to deal.
The equation is greatly simplified if we consider the R-value of objects instead of their thermal
conductivity. This is a measure of how well the material resists the flow of heat through it, and it
combines the thermal conductivity and thickness into one term (R-value = thickness/thermal conductivity
= L/k). While the common units for the R-value are ft2 hr oF/Btu, these are often not quoted. If you visit
any hardware store, you are likely to just see the R-value of a substance to just be quoted as a number,
as in “Fiberglass R-value = 13.”
From the previous page, we can see that the equation for conductive heat transfer through a single
substance is given by
rate of heat transfer = A (TH-TC ) k/L = A (TH-TC)/R
If there are multiple materials that comprise the surface (see Fig. 3), then the equation becomes
rate of heat transfer = A (TH-TC )/RT
where RT = sum of all of the individual R-values. As an example, in the wall that we proposed above, the
R-value for the fiberglass is 13, for the plywood and brick is 4, and for the sheetrock is 0.5. Therefore the
total R-value for the wall is 17.5, which is what would be placed in the denominator of the heat transfer
equation.
R-Factors for Common Materials
After you have finished making the drawing of your dwelling with the measurements of the exterior
surfaces, it is time to determine what is the R-factor of all of the exterior surfaces. The R-factor of a
surface determines how quickly heat is conducted across it. The values below are some of the more
common R-factors for surfaces found on homes in the U.S. NOTE: If your exterior surface leads into an
enclosed area that is sealed, but is not heated or air-conditioned (ex. a door that leads to a closed
garage), then multiply the R-factors below by 1.5 in order to get a better estimate of the factor. If the
enclosed area happens to be earth-sheltered (ex. a basement that is not heat or cooled), then multiply the
R-factors by 2.0.
Exterior Doors (Excluding sliding glass doors)
Calculate glass area of door as window
Roof/Ceiling
Wood Door
Material
Factor
Factor
1 1/4″ no storm door
2.4
No insulation
3.3
1 1/4″ with 1″ storm door
3.8
3 1/2″ fiberglass
13
1 1/2″ no storm door
2.7
6″ fiberglass
20
1 1/2″ with 1″ storm door
4.3
6″ cellulose
23
1 2/3″ solid core door
3.1
12″ fiberglass
43
12″ cellulose
46
14″ cellulose
54
Steel with Foam Core Door
1 3/4″ Pella
13
1 3/4″ Therma-Tru
16
Exterior Walls with Siding
Concrete block (8″)
Floor
Factor
Over unheated basement or
crawl space vented to outside
Factor
(a.) Concrete block (8″)
2.0
Un-insulated floor
4.3
with Vermiculite insulated cores
13
6″ fiberglass floor insulation
25
with foam insulated cores
20
with 4″ on un-insulated stud wall
4.3
Over sealed, unheated, completely
underground basement
with 4″ insulated stud wall
14
with 1″ air space and 1/2″ drywall
2.7
Brick (4″)
with 4″ un-insulated stud wall
with 4″ insulated stud wall
4
14
Wooden Logs
Logs (6″)
8.3
Logs (8″)
11
Wooden Frame
Un-insulated with 2″ x 4″ construction
with 1 1/2″ fiberglass
4.6
9
with 3 1/2″ fiberglass; studs 16″ o.c.
12
with 3 1/2″ fiberglass and 1″ foam
20
with 6″ fiberglass; studs 24″ o.c.
19
with 6″ fiberglass and 1″ foam
26
with 6″ cellulose
22
with 6″ cellulose and 1″ foam
28
Un-insulated floor
8
with 1″ foam on basement walls
19
with 3 1/2 fiberglass on basement walls
20
Insulated floor, 6″ fiberglass
43
Concrete Slab
No insulation
11
1″ foam perimeter insulation
46
2″ foam perimeter insulation
65
Windows and Sliding Glass Doors:
Factor
Low
Emissivity
Drapes
Quilts
Single pane
0.9
1.1
1.4
3.2
Single w/storm window
2.0
2.5
4.2
Double pane, 1/4″ air space
1.7
2.2
4.0
1/2″ air space
2.0
2.5
4.3
Triple pane, 1/4″ air space
2.6
3.0
4.8
Triple pane, 1/2″ air space
3.2
3.7
5.5
Glass
2.99
3.7
Home Audit Tips
1. Unless you live in a very unusual structure, the walls of your dwelling should be 3 1/2 inch
studded walls. The biggest question you should have is whether your walls are insulated. If you
do not know, there are a few ways to find out. If you dwelling was built since 1980, the odds are
that it is insulated with fiberglass insulation. If your home was built before this, then the answer is
not so easy. You could determine if there is insulation in the walls by cutting or smashing a hole
in the wall to see. However, this is not recommended. There are probably holes in your exterior
wall already. Remove the faceplate from either an outlet or a light switch that are on an exterior
wall. Be very careful NOT to stick anything into the socket or switch. Once the plate is off (make
sure that it does not rip the paint or paper off of the wall), you should be able to see around the
side of the outlet box to see if there is any insulation in the wall.
2. If the ceilings in your home are horizontal, then the area of the ceiling is the same as the area of
the floor. Therefore, there is no need to get on a ladder to measure the area of your ceiling. If
you have vaulted ceilings, the task of measuring the area of your ceiling is slightly more difficult.
You can try to measure the distance along the vault if your tape measurer is rigid enough to allow
this. If you cannot measure the distance this way, you will need to use a little geometry to aid
you. Measure the height (vertical distance) of the ceiling at its highest and lowest points. Then
measure the horizontal distance from the highest to the lowest points. You can now use the
Pythagorean Theorem to calculate the distance. Square the difference in the vertical distance
between the highest and lowest points. Square the horizontal distance between the two points.
Now, add the squares together and take the square root of the sum. This will give you the
distance along the vault.
3. If your ceiling is neither horizontal nor vaulted (ex. bi-level or tri-level), then you will need to
measure or estimate all horizontal and vertical surface areas and sum them together.
4. The wattage information for your electric stove, oven, or dryer should be found on tags
somewhere on the device. On these devices, this is usually on a metal tag either on the side of
the door or in the door opening. If it is not, then it is probably on the backside of the device. If it
possible to easily get to the backside of the device, please do so. If it is not easy, then write
“Could not find” on your sheet. When we get to the calculator section of the audit in two weeks,
you should just use the average values that the calculator gives you as a default.
Name:
Professor:
Structure Data
Type of structure: _____ House ______ Apartment/Duplex ______Mobile Home
Number of stories _____
Exterior Surface Types
First Type
Windows:
_____________
Walls:
_____________
Doors:
_____________
Roof/Ceiling: _____________
Ground Floor: _____________
Second Type (if needed)
_____________
_____________
_____________
_____________
_____________
Third Type (if needed)
_____________
_____________
_____________
_____________
_____________
Ext. Surface Type Area R-Factor Area R-Factor Area R-Factor
Windows
Doors
Walls
Roof/Ceiling
Ground Floor
Total area of heated and air conditioned space: __________ sq. ft.
Average height of ceilings: ___________ ft.
Average indoor winter temperature (oF): ________
Average indoor summer temperature (oF): ________
Number of air exchanges per hour: ________
Appliances
Heater Type: _________________________
Air Conditioning Type: ___________________
Refrigerators:____
Freezers:____
Refrigerator/Freezer Combo:_____
Electric Hot Water Heaters:____
Gas Hot Water Heaters:____
Electric Stove/Oven:____
If yes:______ Watts
Gas Stove/Oven:____
Electric Clothes Dryer:____ If yes:______ Watts
Gas Clothes Dryer:____
Energy Cost
Energy Source
Electricity
Natural Gas
LP gas
Wood (cord = 128 ft3)
Cost
$___/kwh
$___/therm
$___/gal
$___/cord
Energy: Synthesis and Analysis
Energy Use in the Home
Convection
The average household spends over $1,300 a year for energy to run the many devices found in the
1
home . In this week’s lab, we are going to investigate ways to save both energy and money that will not
seriously impact your current lifestyle, i.e. you can keep watching as much television as you like, but you
might want to put on a sweater to do it. In order to do this, we are going to have to use the measurements
of our homes that we made two weeks ago.
Last week, we studied how different materials affect the amount of heat flow by conduction. This was
important, since heat conduction is one of the primary ways that energy is lost in a home. Another
method by which heat is flowing into or out of our homes is convection. Convection is heat transport by
movement and mixing. When we open the doors to our homes, hot and cold air are allowed to mix, and
heat is convected. Even when doors or windows are not open, there is convection occurring through any
cracks or breaks in our windows, walls, doors, ceilings, and floors. We often notice this convection
occurring on very cold, windy days. You will often find a blast of cold air hitting you when you walk by
electrical outlets or windows on such days, a sign that your house is not airtight.
Of course, as air from the outside is coming into your home, the air inside of your home is going outside.
Over time, the total volume of air in your home will be completely replaced with air from the outside.
While this is good from the standpoint that stale, possibly toxic air is leaving your home, it is bad from an
energy standpoint since your heating/cooling system will have to come on to bring this air temperature
back to the prescribed setting. In a new, well-built home, the number of openings in your home allows
this air exchange to occur over a period of about 2 hours. In older homes that have developed more
cracks, this amount of time can be much shorter. For instance, in very old, poorly maintained homes, it
might take as little as 15 minutes for all of the air in your home to be replaced by air from the outside.
The number of air exchanges per hour, therefore, is a measure how much energy you will need to use in
order to counter the effects of heat transfer via convection.
The proper way to measure the number of air exchanges per hour in your home is somewhat involved. It
requires using air flow meter readings from various locations in your home. Since very few people have
the necessary equipment to measure it exactly, we have developed a set of guidelines for estimating this
factor. The table below gives you some idea as to the value for your home. You may need to interpolate
between the values below to get the correct estimate for your home. For instance, if you have an
average, insulated home that has been caulked and weather stripped in the last 4-5 years, you should
probably select 1.0 as your value. However, if it has been about 8-10 years since you caulked or
weatherstripped, you might want to choose something between 1.0 and 2.0 as the value.
Air exchanges per
hour
Type of home
Old, un-insulated, weatherstripping not maintained
4.0
Old, un-insulated, weatherstripping maintained
2.0
Avg. insulated house, well maintained
1.0
New, well insulated house
0.5
New, super-insulated (12″ walls)
0.2
1
The Second Law and Efficiency
Energy is also lost in our homes because of all of the energy
transformations that are taking place there. The First Law of
Thermodynamics tells us that the energy involved in any
transfer must be conserved. This would seem to mean that
we should never run out of energy and should pay no heed to
anybody talking about energy being lost. The problem is that
this is not the only law that governs energy transfers. While
the total amount of energy does not change, the Second Law
of Thermodynamics (see sidebar) puts limits on the amount
of usable energy that can be transferred. One of the
consequences of this law is that the total amount of usable
energy that comes out of any process will be less than the
total amount of energy that went into the process. The
difference between the total amount of energy input and the
usable energy output is expended as waste heat.
This brings us to the issue of efficiency, which is a measure of
the amount of usable energy that is generated during any type
of transfer. If a transfer is very efficient, then the amount of
usable energy that is generated is almost equal to the total
amount of energy that went into the transfer. This means that
very little waste energy will be produced. An inefficient
transfer, conversely, is one in which most of the energy going
into the process is converted to waste heat. For example, a
fluorescent light bulb converts about 20% of the electrical
energy that runs through it into visible light energy. While this
may not sound like a very efficient transfer, it is much better
than the 5% efficiency of an incandescent light bulb, which
most people use.
When discussing the efficiency of a process, we have to make
sure and not forget all of the transfers that might need to take
place in order to get to the one under investigation. A great
example of this occurs when comparing the efficiencies of
electric and internal combustion engine powered cars. The
efficiency of the electric motor in a car is about 90%, while the
efficiency of the internal combustion engine is only about 25%.
However, these efficiencies are not the only things that need
to be considered when comparing the two devices. How is the
electricity that charges the car created? Where does the
gasoline come from that powers the internal combustion
engine? What types of transmission systems does each car
have? There are many steps and energy transfers that take
place in getting each type of car to move, and each one of
these has its own individual efficiency. For instance, the
average electric plant is only about 30-35% efficient in
generating electricity (some newer natural gas plants are
closer to 50-60%). This fact greatly reduces the overall
efficiency of an electric car. When we consider the total
efficiency, from getting the energy from its natural source to
the car moving down the highway, we find that the electric car
is only about 20% efficient, while the internal combustion
engine automobile is about half that at 10%.
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Second Law of Thermodynamics
There are many equivalent statements of the
Second Law of Thermodynamics. Most
often, people write about the consequences
of the Second Law (Ex. “Heat will flow
spontaneously from hot to cold”, “No energy
transfer can ever be 100% efficient”, “A heat
engine and a heat pump both require a hot
and a cold reservoir”). An increasingly more
uncommon way to write it is in mathematical
terms. For example, old textbooks usually
write it something like
In a closed system, the total entropy
either increases or stays the same
The reason why most authors today are
loathe to write this is that it is not particularly
useful in this form and it requires a lot of
explanation. First, one has to define the
term “entropy”, which is a fairly non-standard
word. Entropy is actually the logarithm of the
number of states accessible to a system and
is defined by the equation
1/T = (dS/dU)N
where T is the temperature, S is the entropy,
U is the total energy of the system and
(dS/dU) N is the partial derivative of the
entropy with respect to energy while holding
particle number fixed. If your brain has not
exploded by reading this definition, and you
are still reading, then you realize why most
scientist just say “Entropy is a measure of
the chaos of a system”, which, in a way, it is
(a chaotic system usually has more states
accessible to it than a non-chaotic one).
Even if you are able to get past the entropy
difficulty, you then have to explain what a
closed system is (there are no real closed
systems in the universe, just ones that are
close) and why entropy would only increase
or stay the same in such a system. After you
have spent a great deal of time doing this,
you realize that you might have just as well
written one of the consequences of the
Second Law (which are understandable by
most people) and have called it a day.
Which is exactly what we are going to do.
Energy Use in the Home
Appliances
The efficiency of all of the appliances in our homes affects how much
money we spend and energy we use. While heating/cooling does
consume the largest single amount of the energy budget of the average
household, it does not consume the majority. Other appliances in the
home consume over 50% of all of the energy. Almost every American
home has some type of stove or range, while about 75% of them have a
washer and dryer, 50% have a dishwasher, and 33% have a separate
freezer from their refrigerator. All of these appliances, plus the
heating/cooling systems, amounted to over 101 million Btu’s of energy
being consumed in the homes of America in the last year. Considering
the inefficiencies of transporting energy to homes, the total amount of
energy that had to be consumed in order to power our houses was over
170 million Btu’s.
The amount of money consumed by an appliance depends on the type of fuel used by the appliance, the
power of the appliance, and the length of time that the appliance is allowed to run. For instance, the
average electric oven uses an average of about 2,000 watts of power to heat itself to a temperature of
o
350 F. If it is run for 1 hour, then it will use an amount of energy equal to
Energy = Power x Time = 2,000 watts x 1 hour = 2,000 watt-hour = 2 kilowatt-hour
At the current rate of about $.08 per kWhr, this corresponds to a cost of about 16 cents. The average
natural gas stove uses about 11,000 Btu/hr to maintain the same temperature. If you ran it for the same
amount of time as the electric stove, it would consume an amount of energy equal to
Energy = Power x Time = 11,000 Btu/hr x 1 hour = 11,000 Btu
The current cost of natural gas is about $.70 per therm. One therm is equivalent to 100,000 Btu. Thus,
the natural gas costs about $.000007 per Btu. This means that the cost of running the natural gas stove
for 1 hour is about 7 cents.
In the calculator that we will be using to estimate energy usage in our homes, the power usage for gas
appliances will be assumed to be the national average, while the power usage for electrical appliances
will need to be entered. This is because some gas appliances do not list a power rating or have the
information in a non-reachable place on the appliance. If you cannot find the information for your
electrical appliances, use the average values that we have provided in the calculator.
Instructions
We are now ready to use the calculator to estimate the energy usage in your home. Before we begin, we
must state a few simple facts about the calculator. The first of these is that the calculator will not include
the cost of running all of the smaller appliances in the home. The reason for this is that the list of
appliances that we would have to include would make the calculator very unwieldy to use, as you would
either have to scroll down a very lengthy list of items or to click through many different web pages. If you
wish to figure out how much these appliances will cost you to run them, simply multiply the power of the
appliance (in kilowatts) times the number of hours that you use it during the year times the cost of
electricity.
The second thing that we must state is that this estimate is only as good as the information that is entered
into the computer. If you enter incorrect data, e.g. if you enter 1 air exchange per hour when the actual
number is closer to 0.5, you might find that the estimated cost of energy for your home is radically
different than what you actually pay. Lastly, we need to point out that the calculator that we will be using
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has several assumptions built into it. As we go through the instructions below, these assumptions will be
pointed out. If these assumptions are not valid for your home, the estimates of your cost can be far from
reality. In analyzing your data, you will need to keep these assumptions in mind in order to come to valid
conclusions about the energy usage in your home
With this in mind, let us proceed to the calculator AFTER YOU HAVE READ THE INSTRUCTIONS
(http://esa21.kennesaw.edu/activities/homeanalysis/energycalculator.htm)
1. The calculator comes in two parts, both of which are on the same page. You will need to finish
the first section before proceeding to the second section. The first section concerns the
measurements of your home that you took several weeks ago. You will notice that this section is
laid out similar to the form that you filled out for each room of your home. There are two ways for
you to enter the data for this section. One way would be to enter the data for each room of your
home as it is listed on your worksheet(s). After typing this in, press the Calculate button that is on
the left side of the screen. After the program makes the calculation, click the Next Set of
Surfaces button to clear the room data. Enter the data for the next room, and proceed as above
until all rooms are finished. The second way to fill in the data can only be used if the surfaces in
your home are all the same (ex. all windows are double pane, all walls are R-factor 19 wall, all
ceilings are R-factor 30, etc.). If this is the case, then you can add up all of the area for each
component and enter it as if there were only one room.
2. After you finish entering the Conduction data, scroll down the page to the section entitled “Other
Household Data”.
3. From your drawings, you should be able to calculate the total area of all south-facing windows in
your home that are not shaded from the outside. The reason why you need to know this data is
that your south-facing windows are a source of solar energy. During the summer, each square
foot of south-facing window will allow about 37 Btu/hr of solar energy into the house, unless it is
blocked from entering the house outside of the window (curtains or shades on the inside of the
window do not count as shade since they allow the energy into the home before blocking it). In
the winter, this value is about 27 Btu/hr. Enter the area in the topmost text area of the section.
4. In the second slot, enter the total area of all east- and west-facing windows. While these windows
do not allow sunshine into the house the entire day, they do allow solar energy in for half of the
day. During the summer, this can be significant since the Sun will be further north in the sky
throughout the day.
5. The next slot asks you for the square footage of the cooled and heated floor space in your home.
You should be able to calculate this from your drawing.
6. The next slot asks for the average height of the ceilings in your home. In conjunction with the
square footage of the floors of your home, these two numbers give us an estimate of the volume
of air space in the home. This is the amount of air that must be heated and cooled as air is being
exchanged with the outside environment.
7. The next two slots ask for the thermostat settings for both winter and summer. These
temperatures will determine the rate at which heat is exchanged with the outside, and thus, how
much cooling and heating are necessary. Two assumptions go into this calculation. The first one
is that the thermostat is not being switched from this temperature setting, i.e. the thermostat is not
a programmable thermostat. If you have such a thermostat, you will need to enter an average
setting of your thermostat that will take into account the variability of the temperature in your
home. For instance, if you set your thermostat in summer at 78 during the day and 72 at night,
then you will probably want to enter 74 as your average temperature (while 75 might be the actual
average, this does not take into account that the variation in temperature during the day actually
lowers the average temperature difference between inside and outside). The second assumption
in this calculation is that we are experiencing a normal year in outside temperatures.
8. The next slot asks you to enter the number of air exchanges per hour in your home. Refer to the
first page of this module for help in estimating this number.
9. The next slot asks you to enter the number of people in the home. This number is needed, since
human bodies produce heat. In the winter, this decreases the amount of heating that you will
need; in the summer, it will increase the amount of cooling that you need.
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10. The next slot asks you what type of ductwork you have for your heating system. If you have
central heat, then you will have some type of ductwork to bring the heated air to each room. If
this ductwork is insulated, then you need to enter 1 in the slot; if it is not insulated, then you need
to enter 2. If you use a wood stove or a portable kerosene heater in your home, you have no
ductwork, and should enter 0 in the slot.
11. The next slot asks you what type of heater that you have. This is important, since it will
determine what type of fuel that you use and how efficient each type of heater is. We are
assuming that a natural gas and propane heaters are 80% efficient, a resistive electric heater is
100% efficient, a heat pump is 250% efficient (remember our discussion about heat pumps in
week three of this module), and a wood stove is 60% efficient. If your true efficiencies differ from
this, it will cause some error in the estimates. In order to select the appropriate stove, please
enter the corresponding number in the slot
12. The next slot asks for the type of air conditioner that you have. We have assumed that all air
conditioners have a seasonal performance factor of 2.5. If you have no air conditioner, enter a 0
in the slot; for window units, enter 1; for a central air conditioning system, enter 2.
13. The next several slots deal with some of the major appliances in your home. Enter the
appropriate data in each slot, including the number of hours each appliance is used in a typical
week. We have assumed that all refrigerators and hot water heaters are always operating.
14. The last bit of data that you need to enter is the price of each fuel that you use. This data should
be available from the energy supplier that you use. If it is not, we have provided an estimated
average of current costs.
15. After completing all of this data, press the Calculate Summary button at the bottom of the page.
The program should return the cost of energy in your home for the year. If you find that you wish
to change any of the Other Household data (the second section), you may do so without having
to go back and enter the Conduction data again. Merely change the data that you want, and then
press the Calculate Summary button again. It will recalculate your costs with the new changes.
If you wish to change something about the Conduction data, you will need to press the New
Energy Analysis button, which will clear the entire calculator and allow you to begin over again.
Assignment
Your assignment for this exercise is to run the energy calculator for your residence, complete the
questions listed on the activity sheet, and attach printouts of your runs of the energy calculator.
References
1 “A Look At Residential Energy Consumption in 1997”, U.S. Department of Energy, November 1999.
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ESA 21: Environmental Science Activities
Activity Sheet
Energy: Synthesis &
Analysis
Name:
Lecture Professor:
Attach copies of your runs of the energy calculator to this sheet.
Analysis:
Are the yearly electricity and natural gas costs reasonable for your home based on your
experience? If not, can you think of any reasons to explain this discrepancy?
Calculating the effects of lifestyle changes:
Make the changes below in the calculator and see how they affect annual energy costs.
(a.) Lower the thermostat setting in the winter a few degrees below your current setting and
elevate the summer setting by the same amount.
Initial setting
New setting
Winter
Summer
Annual Energy Savings ($):
Would you make this change? Why or why not?
(b.) Reduce the number of hours you use your oven or dryer by a reasonable amount.
Initial no. of hours
New no. of hours
Oven
Dryer
Annual Energy Savings ($):
Would you make this change? Why or why not?
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