OCN 120 Spring 2011 Name: Problem Set #2, Power and energy calculations Due Thursday, Feb. 10 1. a. Using Table 14.2, attached, calculate your annual energy consumption in Kilowatt‐hours (kWh) due to your personal use of computers, stereo/radio, TV, and DVD/video players. b. The HECO cost of electricity is about 27 cents per kWh. At that rate, what are your electricity costs for the year to run these devices? c. Using Table 3.3, attached, how much oil would need to be burned to supply the electricity for these devices? 2. The average human diet has an energy content of about 2000 kcal. Using the energy and power definitions in Table 3.1, attached, show through a series of unit conversions that this 2000 kcal/day is about equivalent to 100 watts. 3. Power output of engines is often rated in terms of horsepower (hp). You can also calculate power output if you know the gas mileage and the speed. Your friend’s car engine is rated at 250 hp. It gets 20 miles per gallon when driving 60 miles per hour. a. Convert the nominal engine power output of 250 hp to watts. b. Calculate the actual power output from the above data. Start by calculating the gasoline consumption rate (gal/hr) and, using Table 3.3’s energy equivalent for gasoline, convert the result to a power in watts. c. Compare the two calculations and comment on why they don’t agree. 4. The US imports about 12 million barrels of oil each day. a. Using Tables 3.1 and 3.3, convert this quantity to an equivalent power, measured in watts. b. If we wanted to replace all that imported oil with wind power, how many 5 MW wind turbines would we have to build? 2gg
CHAPTER i4
E n e r g yS: o m e B a s i c s
3.3 Quonrifying Energy
Energy unils
loule (J)
Joule equivolent*
tJ
'
kilowatt-hour (k'rX/h)
t,,^
grg"*un-y.ut
,British
:
).6 MJ
3.15PJ
calorie(cal)
4.184J
thermalunit (Btu)
1 , o 5J4
.
5l
loc.
ioF, very roughly
.r..,i.,
..'
quad (Q)
1.054EJ
exajoule
. . , . . . . ' . . . , . e . r g1 0 - 7 I
.
electron volt (eY)
I / . X 1 n - 1 9 JT
Energy gained by an electron dropping through an electrjc potential differenceof
1 volt; usedin atomic and nuclear phvsics.
1.556J
Energyunit in the Englishsysrem,equalto cheenergyinvolvedin applying a force
of I pound over a disranceof I foor.
4r.9 GJ
Energycontentof i metric tonne (1,000 kg, roughly 1 English ton) ofoil.
li::
foor-potrnd
tr
tonne oil equivalenr(toe)
'
barrel ofoil equivalent (boe) 6 . 1 2G J
Power unils
'
watt (rv)
horsepower(hp)
Btu per hour (Brulh,
or Btuh)
Bnergycontentof<lne42.gallonbaneloftlil,,|.
Wotf equlvolenf
Descripllon
,1W
Equivalent to I JA.
746W
Unit derivedoriginally lrom powersupplieclby horses;now usedprimarily to
describeenginesan.l morors.
0.293 W
.Usedprim"rily in rh9'Unite.l States,usually to describeheating an<l.ooling ,yst"-s.
+SeeTable 3.2 for Sl prefixes.
used in the Unired Statesto describethe capacityof heating and air conditioning systems is the Btu per hour (Btu/h, but often wrirren, misleadingly, as simply Btuh). As
Table 3.1 shows,1 Btu/h is just under one-third of a watt. My housel-rold
furnaceis rated
at 112,000Bru/h; Example3.1 showsthar this number is consistentwitl-rits fuel consumption rate of about 1 gallon of oil per hour. The British thermal unir is at the basis
of a unit widely used in describingenergyconsumptionof enrire counrries,namely rhe
quad (Q).One quad is 1 quadriilionBtu, or 1011Bru. The United States'rateof energy
consumptionin the early twenry-firsr cenrury,for example,is just about 100 Q per year,
a figure that accountsfor approximateiyone-fourth of humankind's total yearly energy
consumption.
54
Chopter 3
ENERGy:A Closer Look
l/lulfiplier
. ' . . .
'-1-0-?4.
,:.
Preflx
:
.
'
,
'
j
Symbol
'
:YOCto
I
1 0 - 2I
zePro
l0- r8
..:r':
' u * ,
a
femto
f
1 0 -r 5
. . .
t 0 ' . t 2 : , ,. l i
. , ,
t ' , : _
, plco
,
10-e
nano
n
10 - 6
rmlcro l
,l+
10-3
milli
m
l0olr 1)
.,,
103
kilo
k
105
rnega
M
Siga
G
l0e
IOL2
tera
l0lt
Pera
P
l0r8
exa
E
1 0 2r
lo24
Z
Y
routinely throughout this book, and you can
find them here and inside the front cover.
Note that the symbolsfor SI prefixesthat multiply
by lessthan 1 are in rowercase,
while
those that multiply by more than 1 (except for the
kilo) are capitalized,.
Back to Table 3.1, which arsolists severalunits
for power. A-ong thosein common
useis horsepower (hp), a holdover from the day
when horsessuppliedluch of the energy
coming from beyond our own bodies. one horsepower
is 746 w, or about three_
quartersofa kilowatt. So a 400-hp car engine
can,in principle, supply energyat the rare
of about 300 k\7 (most of the time the actual
rate maybe much less,and very little of
that energyends up propelling the car; more
on this in Chapter 5).
Fuels-those substancesthat store potential
energy in ihe configurationsof mole_
cules or atomic nuclei-are characterized
by their energy conrent, expressedas energy
aA//r- 3,3 A*'ff
rz*'&'/ o{ #^-lt
Typlcol energy conlent (vorles wlth fuel source)
9l units
Olher unlls
43MJtkE
abt wr,rgaton
138 kBtuigallon
glatural gas
30 k$fhl100 cubic feet
1,000 Btu/cubic foot
Hydrogen gas (H2) burned to produce H2O
Hydrogen, deuterium-deureriumnuclearfusion
Pure deuterium
'
,
Norrnalwater
: , f i ,'
\+zu1rug
)30TJtkg
12GJtks
320 Btu/cubic foot
13 MlU7h/gallon,
350 gallonsgasoline
equivalentper gallon water
containedin a given massor volume. Table 3.3 lists the energy conrentsof somecommon fuels' Some of these quantities find their way into alternative units for energy and
for energy-consumption rate, as in the tonne oil equivalent and barrel of oil equivalent
listed in Table 3.1. Related power units of millions of barrelsof oil equivalentper day
often describe the production of fossil fuels, and narional energy-consumprion rares are
sometimesgiven in millions of barrels of oil equivalent per year. Anorher handy figure
to use in considering fossil fuel energy is to approximate rhe energy conrent ofa gallon
ofpeffoleum product--oil, kerosene,gasoline-as being about 40 k'$7h (the exactamounr
varies with the fuel, and the amount ofuseful energy obtained dependson the efficiency
of the energy-conversion
process;more on this in the next chapter).Finally, Table 3.3
hints at the huge quantitative difference between chemical and nuclear fuels; just compare the energy per kilogram of petroleum with that of uranium!
You'll find Tables 3.1 through 3.3 sufficiently useful that they're printed inside the
front cover for easyreference,along with other useful energy-relatedinformation.