- In Solution Box 6.1, the site energy and primary energy using a gas furnace versus a straight
electric resistance heater were compared for a home.
a. Compare the carbon emissions for these two houses assuming natural gas emits 5 kg CO2 per
therm (100,000 Btu) and a coal-fired power plant that emits 1 kg CO2 per kWh that it
delivers.
b. Now, consider replacing the ordinary resistance heater with an efficient heat-pump heater
that delivers 12,000 Btu of heat per kWh of input electric power (e.g. Section 6.12). Now
compare the CO2 emissions for gas heater with a new heat-pump space heater.
c. Now, reconsider the source of electricity for the heat pump space heater. Replacing the old
coal-fired power plant with a new combined-cycle, natural-gas-fired power plant (e.g.
Section 9.5.4), carbon emissions drop to around 0.4 kg CO2/kWh. Now compare the carbon
emissions for the gas furnace versus the heat-pump space heater.
- In Solution Box 6.5, the R-value of a conventional 2×4 wall with a 15% framing factor and R-11
fiberglass insulation between the studs was determined to be 11.4. Suppose that wall did
not have any insulation between the studs resulting in an air gap that itself has an R-value of
1.0. Find the overall R-value of this un-insulated wall. - Suppose a blower door test on a 2000 ft2 house with 8-ft ceilings required 2400 cfm of airflow
to create a 50 Pa pressure difference.
a. Estimate the average annual infiltration rate n(ach) using the rule-of-thumb given in Eq.
6.17.
b. Estimate the equivalent (UA)-value (Btu/hroF) for the infiltration rate.
c. What is the annual Btu/yr that must be supplied by the heating system if this house is in a
region characterized by HDD65 = 4000 degree days.
d. With a 75% efficient heating system and natural gas costing $1.30/therm, what is the annual
cost of fuel to heat this house due to this infiltration?
Chapter 7 - Consider the decision about whether to purchase a fiberglass insulating jacket to put around
your home water heater. When you touch the metal on the outside of the water heater it
seems pretty cool, so you are not convinced that it needs more insulation.
Suppose the exterior metal surface of the water heater is 75oF while the room that it is in is
70oF. The water inside the tank is 130oF. Using a convective resistance from outer-metaljacket-to-air of 0.68 hr-ft2
oF/Btu:
a. Estimate the overall R-value (from water to room air) of this water heater. Equation 6.7
will help.
b. Under the above conditions, how long would it take (in days) before a 22-ft2
, $10 water
heater insulating blanket would pay for itself if it adds R-7 to the tank. Assume it is a 70%
efficient gas water heater, with gas costing $1.30/therm (1 therm = 100,000 Btu).
- Those very handy sun-path diagrams, such as the one shown below, can be downloaded
from the University of Oregon’s website:
http://solardat.uoregon.edu/PolarSunChartProgram.html.
a. For the above sun-path diagram, use your knowledge of solar angles at noon to figure out
the latitude for which it has been drawn.
b. Download the sun path diagram for the equator… pretty strange, eh?
c. Can you imagine what the sun path diagram looks like at the north pole? Download it and
see whether you figured it out correctly.
- Create the following spreadsheet for a “Suntempered” house. Notice that the south-facing
windows have been treated as if they are not even there (thermally neutral). The annual
fuel bill is estimated to be $897/yr.
After replicating the spreadsheet, suppose a neighbor builds a new structure that
completely shades those south-facing windows. What would your spreadsheet predict as
the new annual fuel bill for heating? How much has that shading cost the original “suntempered” homeowner ($/yr)?
- Suppose you have enough space on your roof to fit 50 m2of 19%-efficient
photovoltaics. Your PVs are “premium” 19%-efficient modules, which face due south with a
tilt angle of 25o
.
a. How many kW (rated under Standard Test Conditions) of PV modules can you fit onto that
roof area?
b. Suppose your house is in Reno, Nevada. Using PVWatts, how many kWh/yr would you
expect this array to produce? (be sure to select “premium” (19% eff) for your modules).
c. Suppose you will be using some of that PV electricity to supply a modest 60 gallons/day of
water heated from 60oF to 120oF using a heat pump with a 3.25 efficiency-factor (Table 7.4).
How much of your PV area would be needed to meet that need?
d. What would be the rated power (kW) of the PVs needed for that hot water?
Chapter 8 - Update progress of LED performance and cost compared to DOE goals described in
Figure 8.7. - A “Home Energy Analysis” spreadsheet is given below.
a. Construct your own spreadsheet.
b. Run the spreadsheet with the following cases, providing answers for total
gasoline, natural gas, and electricity use and costs, total energy cost and total CO2
emissions in the log sheet. Please highlight the changes in results in bold or by
highlighting or circling on spreadsheet.
i. Default values, current prices: $1.10/therm; $0.12/kWh; $2.75/gal gasoline
ii. High efficiency case with current prices: House with thermal index of 3.5,
automobiles @ 50 mpg and 11000 miles, and the following efficiency measures:
high efficiency gas furnace (96%)
high efficiency water heater (0.75)
efficient refrigerator (400 kwh/yr), efficient dishwasher (200 kWh/yr),
washing machine (250 kWh/yr), and related clothes drying efficiency (900
kWh/yr)
LED lamps (replace indoor 2 100W with 2 12W and 5 60W with 5 9W, all
on 5 hours/da; replace outdoor 3 75W with 3 11W, all on 6 hours/da),
efficient room air conditioner (300 kWh/yr)
add ceiling fan: (50 w, 4 hr/da),
iii. High energy price case: Original situation but with a gas price of $1.75 per
therm, electricity price of 16 cents per kWh, and gasoline price of $3.75 per
gallon.
iv. High efficiency case (ii) with high energy prices (iii)
HOME ENERGY ANALYSIS (Entries with * are calculated)
(everything else is data entry)
HOME HEATING:
Floor Area: 2000 square feet
Thermal Index 8 Btu/ft2-degree-day (24 x UAtot / floor area)
Degree Days: 5000 degree-days/yr
Furnace Efficiency: 0.65
Natrl Gas price: 1.25 $/therm (1 therm = 100,000 Btu)
Heating Energy Use: * 1231 therms/yr (area x thermal index x DegDays/furn eff)
Heating Energy Cost: * 1538 $/yr
CO2 coefficient – NG 11.7 lb/therm
COOKING:
Gas Stove 8 therm/mo
Cooking Energy cost: * 120 $/yr
WATER HEATING:
Hot Water use: 80 gal/day (at 20gal/person/da and 4 person)
Heater efficiency: 0.6
HW Energy to heat: * 23.352 therms/mo (assume 30da/mo, 70oF temp rise)
energy = (gal/d x 30d/mo x 8.34lb/g x 1Btu/lbF x 70F)/(eff x 100000Btu/th)
HW Energy Cost: * 350.28 $/yr
ELECTRICITY: Watts Hrs/day: kWh/mo * $/mo *
Refrigerator: 500 120 12.00
Color TV: 250 5 38 3.75
Stereo: 60 6 11 1.08
Computer: 120 5 18 1.80
Lights: indoors 500 5 75 7.50
Lights: outdoors 225 12 81 8.10
Washing machine: 500 1 15 1.50
Clothes Dryer 2000 120 12.00
Room air cond.: 1400 2 84 8.40
Furnace fan: 280 4 34 3.36
Clocks, nite lites: 40 24 29 2.88
Dishwasher: 1300 1.5 59 5.85
Microwave oven: 1500 0.5 23 2.25
Toaster: 1200 0.2 7 0.72
Vacuum cleaner: 600 0.2 4 0.36
TOTAL* 715.5 71.55 (assume 30 days/mo)
Electricity price: 10 cents/kWh
CO2 coefficient – Elect 2 lb/kWh AEP rate
AUTOMOBILES 18000 miles, @ 20 mpg, and 2.5 $/gal
TOTAL GASOLINE * 900 gallons 2250 $/yr 17640 lb CO2
CO2 coefficient – gasoline 19.6 lb/gal
TOTAL NATL GAS * 1607 therms/yr 2009 $/yr 18802 lb CO2
TOTAL ELECTRIC * 8586 kWh/yr 859 $/yr 17172 lb CO2
TOTAL ENERGY * 5117 $/yr 53614 lb CO2
Sample Solution
