ENVSCI 15 Introduction to Energy
Mid Term I (150 points)
Name _______________________________________ Date ______________
.1. (5 pts) Your home uses about 350 kWh of electrical energy per month. Convert this to an average
rate of electrical energy consumption in watts.
power =
rate of energy
energy
350 kWh  mo   d   1,000 W 


 470 W
time
mo  30d   24 h   kW 
consumption
.2. (10 pts) An oil furnace consumes 0.80 gallons of oil per hour while it is operating. (a) Using the
approximate value of 40 kWh per gallon of petroleum, find the equivalent power consumption in watts.
(b) If the furnace runs only 15% of the time in the autumn, what is the furnace’s average power
consumption?
(a)
0.8 gal  40 kWh 
 32 kW
1 h  gal 
(b) 15% (32 kW) = 4.8 kW = average power consumption
.3. (10 pts) A house measures 42 feet long by 28 feet deep. It sits on a 4 inch thick concrete slab. The
ground below the slab is at 48 degrees F and the interior of the house is at 68 degrees F. (a) Find the
rate of heat loss through the slab. (b) Calculate the heat rate loss if the slab is poured on top of a 2 inch
layer of polystyrene foam.
The heat loss rate is H 
AT
, where the foundation area is
R
A  42 ft28 ft = 1,176 ft2 and the temperature difference is dT = 68F - 48F = 20F.
From Table 4.2, Rconcrete 
1.1
 0.55 ft 2  Fh/Btu and Rfoam  2  5  10 ft 2  Fh/Btu .
2
(a) With bare concrete, the heat loss rate is H concrete 
A ΔT
when we add foam insulation, because the R
R'
 10.55 ft 2  Fh/Btu .
(b) The heat loss rate will drop to H ' 
value increases to R'  Rconcrete  Rfoam
.4. (5 pts) Sources of energy include:
a. Food
b. Sun
c. Wind
d. All of the above (Food, Sun, and Wind)
.5. (5 pts) Forms of energy include:
a. Heat
1,176 ft 2  20 F 
A ΔT

 43 kBtu/h .
Rconcrete 0.55 ft 2  F  h/Btu
b. Light
c. Mechanical
d. All of the above (Heat, Light, and Mechanical)
.1. (10 pts) Assuming your computer uses 400 W and you have it on 4 hours a day, how much coal is
required per year to allow for your computing habits? How much does your computer’s electricity cost
you per year, assuming PG&E charges $ 0.139 per kW-h?
400W X (4 hrs /day) = 1.6 kW-h/day X 365 days / year = 584 kW-h/year
584 kW-h/year X $ 0.139 / kW-h = $81.77 per year
.1. (5 pts) A particular manufacturer quotes the heat output of a furnace as 35,000 BTU per hour.
Convert the heat output to Watts (Joules/second).
a. 9.7Watts
b. 33.2Watts
c. 1,026Watts
d. 10,257Watts
.1. (5 pts) A heat engine has an efficiency of 22%. During each cycle, it produces 1200 Joules of useful
work. How much thermal energy does the heat engine draw from its hot reservoir each cycle?
a. 5,455Joules.
b. 26,400Joules.
c. 264Joules.
d. Not enough information to answer.
.1. (5 pts) A person uses 2000 kilocalories in a day. What is the rate at which they use energy?
a. About 23 Watts.
b. About 97 Watts.
c. About 2,328 Watts.
d. About 83 Watts.
.1. (5 pts) A car sold in Europe gets gas mileage of 13.6 km/liter. What is the gas mileage in miles per
gallon?
a. 32 mpg.
b. 57 mpg.
c. 19.9 mpg.
d. 5.78 mpg.
.1. (10 pts) In which one of the following situations are you doing (positive) work on a bowling ball?
(A) When you lower it downward at constant velocity from a high shelf to the floor.
(B) When you hold it motionless above your head.
(C) When you slide it horizontally across the floor at constant velocity.
(D) When you carry it horizontally at constant velocity.
Why: The only case in which you do work is the one in which you exert a force on the ball and the ball
moves in the direction of that force. When the ball is motionless, as in (B) or moving at right angles to
the force you exert on it, as in (C), you do no work. When the ball moves in the direction opposite to
the direction of the force you exert on it, as in (A), you do negative work on it. But when you slide the
ball across the floor and struggle against the force of sliding friction, you push the ball in the same
direction it moves and thus do (positive) work on it.
.1. (10 pts) A construction crew is replacing the huge air conditioning unit on the roof of an office
building. They know that if they push the unit off the roof and let it fall freely, it will have 10 million
joules of kinetic energy by the time it reaches the ground. They choose instead to put the unit on a cart
and let it roll freely down a ramp. The ramp has a 10 to 1 grade, meaning that it goes down 1 meter in
height for every 10 meters you travel along its surface. By the time the air conditioning unit reaches the
ground on this ramp, it will have
(A) zero kinetic energy.
(B) 1 million joules of kinetic energy.
(C) 100 million joules of kinetic energy.
(D) 10 million joules of kinetic energy.
Why: The energy released in lowering the air conditioning unit to the ground is 10 million joules. It
doesn't matter how you lower that unit, you'll always release the same amount of energy. So long as
the energy doesn't go somewhere else (e.g. into heating something up or breaking something), it will
all be in the unit when the unit reaches the ground. After the trip down the ramp, it will be in the
unit's kinetic energy. If the crew had slowed the unit's descent, rather than letting it roll freely, they
would have taking this energy out of the unit and it wouldn't have kept all its energy. But they let it
roll freely and it ended up moving just as fast as if they had dropped it. Its kinetic energy was the
same, but its direction of travel was somewhat different.
.1. (40 pts) You are riding on a huge roller coaster with the tallest, steepest first hill in the world. To
make the roller coaster even more exciting, its designers have used high technology to eliminate air
resistance and friction, so that the coaster follows the laws of physics without producing any thermal
energy. The first hill can be divided into three parts: top, middle, and bottom. While the top portion of
the first hill slopes gradually downward, the middle portion of the hill dives almost straight down. The
bottom portion of the hill is less steeply sloped in the downward direction, becoming more and more
gradual so that it eventually levels out completely.
(A) Along which portion of the first hill does the roller coaster have its greatest speed?
Answer: Along the bottom portion.
Why: There is nothing to extract energy from the roller coaster, no friction or air resistance, so it
retains all of its energy as it plunges down the hill. It converts its gravitational potential energy into
kinetic energy as it descends and has its highest kinetic energy near the bottom of the hill. Since
kinetic energy is proportional to the square of speed, the roller coaster's speed is also highest near the
bottom of the hill.
(B) Along which portion of the first hill does the roller coaster have its greatest downward acceleration?
Answer: Along the middle portion.
Why: The downward acceleration of an object on a ramp increases as the ramp becomes steeper. The
middle portion of the track is the steepest, so it is also the portion during which the roller coaster's
downward acceleration is greatest.
(C) Along which portion of the first hill, if any, does the roller coaster have its greatest upward
acceleration?
Answer: Along the bottom portion.
Why: Along the bottom portion of the track, the roller coaster is changing its direction of travel. It is
turning upward from a downward plunge to a horizontal motion. This turning of its velocity involves
an upward acceleration. This is the only upward acceleration that occurs on the first hill--the
acceleration is downward along the top and middle portions of the track.
(D) Compare the roller coaster's total energy on the top portion of the track with its total energy on the
bottom portion of the track.
Answer: They are equal.
Why: Energy is conserved and the roller coaster has no way of transferring energy to anything. There
is no friction or air resistance, and the track doesn't move so the roller coaster can't do work on it. All
of the energy the roller coaster had near the top of the hill (mostly in the form of gravitational
potential energy) is still there near the bottom of the hill (mostly in the form of kinetic energy).
.1. (5 pts) Explain what albedo is and its role in the Earth’s radiation budget. Place the following surfaces
in order from highest albedo to lowest albedo: ocean, black road, desert, and snowfield.
Solution: Albedo is a measure of reflectivity and the Earth’s total albedo will determine how much inc
oming solar radiation is reflected back to space. In order of decreasing albedo: snowfield, desert, oce
an, black road
.1. (10 pts) In the US, we consume 18.8 million barrels/day of oil.
a) If each barrel costs $100, how much money does the US spend on oil consumed each year?
Solution: 18.8 x 106 barrels/day * $100/barrel * 365 day/ year = $686 billion per year
b) Of the 18.8 million barrels consumed per day, 8.9 million barrels are imported. How much money
does the US spend every year on imported oil? (8 points)
Solution: 8.9 x 106 barrels/day * 365 day/year * $100/barrel = $325 billion per year
.1. (10 pts) As an environmentalist, you decide to save energy by biking to work and giving up driving
your luxury sedan. You figure this means you need to wake up earlier every day. On the first day, you’re
in such a rush that you forget to turn off the lights of your house. You tell your coworker about it, who
then says you’re a hypocrite because you may have saved no energy after all. Evaluate his claim by
comparing the energy saved by not driving versus that wasted by leaving the lights on. Express the
energy savings or costs in terms of kWh. (11 points)
Useful info for this problem:
• Your sedan gives you an average of 20 mpg (miles per gallon of gasoline)
• 1 gallon of gasoline contains energy of 122 million joules.
• The round‐trip distance between your home and your workplace is 15 miles.
• You leave three 60W light bulbs on for a total of 10 hours.
Solution:
Energy saved by not driving
= 15 miles / 20 mpg * 122 MJ/gallon (energy density of gasoline)
= 91.5 MJ = 25.4 kWh
Energy wasted by leaving the lights on
=3* (60W) * (10 h) * (1 kW / 1000 W)
= 1.8 kWh