Physics 111 - Energy On This World and Elsewhere - Fall 2013
Problem Set #2
When doing unit conversions, for full credit, you must explicitly show how units cancel.
Also, you may need to look up certain equivalence relations on the internet. Show your
work!
Useful information
1 gallon of gasoline = 1.3 × 108 J
1, 054 J = 1 BTU
1. With regard to finding and producing the necessary energy, why does the transportation sector (as opposed to other sectors) present a particular challenge to our society?
2. A truck weighing 2000 kg is climbing a hill with a height of 8 meters.
h = 8m
a. What is the change in the gravitational potential energy of the truck as it goes
from the bottom of the hill to the top of the hill? Express your answer in both
Joules and BTU’s.
b. Assuming that the truck’s engine is 100% efficient in converting gasoline into the
mechanical work that it takes to drive up the hill, how much gasoline is needed
(in gallons) to climb the hill? In other words, what is the “gasoline equivalent”
of your answer to part “a” in gallons of gasoline?
c. Assuming that the truck takes 2.5 seconds to climb the hill, what is the power
output of the engine? Give your answer both in Watts and in horsepower.
3. A household furnace has an output of 100,000 Btu/hour. What size electrical heating
unit (in kW) would be needed to replace it? Use the “substitution method” described
in the class notes, and find an appropriate unit to substitute for both “Btu’s” and
“hour”. You might find it most convenient to first convert to Watts (joules/sec), and
then to kW.
4. A particular household draws an average of 2.5 kilowatts of electrical power from the
electrical grid. How many joules does the house use in one day?
5. Why is the United States particularly well situated to take advantage of renewable
energy sources? (Hint: this issue is specifically discussed in one of the readings.)
6. What is the relationship betweeen brownian motion and the internal energy of gases.
7. When the price of oil went up significantly in the early 1970’s, power companies were
able to shift away from generating electricity using oil relatively rapidly. What were
some of the factors that contributed to their ability to respond in a timely manner?
Physics 1110 - Energy On This World and Elsewhere - Fall 2013
Problem Set #2 – continued
8. Convert the following quantities into the indicated units. In all cases show your work,
being certain to show explicitly that your units cancel in the conversion to give the
desired final units.
a. What is the equivalent of 570 kW − hrs in BTUs?
b. What is 50 m/s in miles per hour?
c. How much gasoline is the equivalent of 15 kW-hrs?
Hot reservoir, TH
9. Consider the diagram at right illustrating a heat
engine. Assume that the efficiency of the engine
20%, and that it performs 500 J of useful work during each cycle.
a. How much heat energy does the engine consume while doing the work?
b. How much heat, QC , is expelled during each
cycle.
c. If TH = 700 K and TC = 300 K, what is the
maximum efficiency allowed by the 2nd law of
thermodynamics? How does this engine’s efficiency compare with its theoretical maximum?
QH
work
QC
Cold reservoir, TC
10. Consider the seesaw below, which you can assume is in a balanced condition. Assume
the person sitting on the left (Mbig ) has a mass of 80 kg, and is sitting 1.0 meters
from the pivot, and the person sitting on the right (Msmall ) is sitting 2.5 m from the
pivot.
lshort
mbig
llong
msmall
a. What is the mass of the the person on the right (msmall )?
b. If the seesaw tips by some angle so that the larger person is closer to the ground,
what can you say about their change in gravitational potential energy with respect
to the change in gravitational potential energy of the smaller person.
11. What are the two laws or physics principles that lead to the Carnot’s maximum
efficiency for a heat engine.
12. You and a friend take a drive in the Blue Ridge Mountains. When you return, you
park in the same space from which you initially left. What happened to the energy
in the gasoline you used? Be specific. For example, don’t just say “heat”.