Physics 140: Greenhouse Effect
Homework #1 solutions
due Wednesday, February 6, 2008
Problem 1 (4 points)
The gas tank in your car holds 13.2 gallons of gas. Show your work!
(a) If you get 30 miles per gallon, how far can you go on one tank of
gas?
Answer: 13.2 gal x 30 miles/gal = 396 miles
(b) If you were to improve your gas mileage by 10%, how far could you
go?
Answer: 30 miles/gal x 1.10 = 33 miles/gal
13.2 gal x 33 miles/gal = 436 miles
Problem 2 (8 points)
Your house has an oil-fired heating system. Show your work!
(a) If you burn 5 gallons of heating oil per day in January, how much CO2
do you emit that month? Use 26 lbs of CO2 emitted per gallon
of
heating oil.
Answer: 5 gal/day x 31 days x 26 lbs of CO2/gal
= 4,000 lbs (rounded to two sig figs)
If you burn 5 gallons of heating oil per day in January, how much carbon
do you emit that month? Use 7.1 lbs of carbon emitted per gallon of
heating oil.
Answer: 5 gal/day x 31 days x 7.1 lbs of carbon/gal = 1,100 lbs (rounded to two sig figs)
Answer: $60/ton x 1 ton/2000 lbs x 26 lbs of CO2/gal =$0.78 per gallon
(c) How much would the tax in (b) add to your heating oil bill for
January?
Answer: 5 gal/day x 31 days x $0.78/gal = $120.90
(d) Search on the Internet for a news report that gives the amount of a
carbon
tax proposed or in effect by some national,
regional or local government. How much is the tax per ton of CO2?
(attach
a printout of the page and be careful--the tax might be just counting
the
carbon atoms, that is, it would be per ton of carbon rather than per
ton of CO2).
How much would the tax you found add to the price of a gallon of
heating oil?
If the tax is per metric ton of CO2, you need to use the conversion 1 metric ton = 2200 lbs (that is, 1000 kg) when you redo 2(b).
If the tax is per ton of carbon, you need to use 7.1 lbs of carbon/gal instead of 26 lbs of CO2/gal when you redo 2(b).
Problem 3 (8 points) Show your work!
(a) If you use heating oil as fuel at $3.80 per gallon, how much do
you pay
for 1 Btu?
Answer: $3.80/gal x 1 gal/139,000 Btu = $0.000273/Btu
(b) How many Btus does it take to bring 25 gallons of water from room
temperature (72 F) to boiling point (212 F)? (1 gallon of water weighs
8.34
lbs.)
Answer: 25 gal x 8.34 lbs/gal x (212 deg F – 72 deg F) x 1 Btu/(lb deg F) = 29,190 Btu (29,000 Btu, rounded to two sig figs).
(c) If you use heating oil as the fuel, how much does it cost?
Answer: 29,190 Btu x $3.80/139,000 Btu = $0.80
(d) If instead you use natural gas as the fuel at $13.50 per thousand
cubic
feet, how much does it cost to heat the water in (b)?
Answer: 29,190 Btu x 1 cf/1026 Btu x $13.50/(1000 cf) = $0.38
Which is cheaper?
Answer: Natural gas (of course this
depends on the prices
given!)
Energy content of various fuels
1 barrel (42 gallons) of crude oil = 5,800,000 Btu
1 gallon of gasoline = 124,000 Btu
1 gallon of heating oil = 139,000 Btu
1 gallon of diesel fuel = 139,000 Btu
1 barrel of residual fuel oil = 6,287,000 Btu
1 cubic foot of natural gas = 1,026 Btu
1 gallon of propane = 91,000 Btu
1 pound of coal = 10,000 Btu
1 kilowatthour of electricity = 3,412 Btu