numbers. With a purely numerical approach, we wouldn’t even
have known what value ofmto pick, or if we’d guessed a value
like 1 kg, we wouldn’t have known whether our answer depended
on that guess.
Solving for∆T, and writingvinstead ofvifor simplicity, we find∆T=
v^2
2 c
≈ 40 ◦C.
The passengers would be boiled alive if not for the refrigeration.
The first stage of cooling happens via heat exchangers in the
engine struts, but a second stage, using a refrigerator under the
floor of the cabin, is also necessary. Running this refrigerator
uses up energy, cutting into the fuel efficiency of the airplane,
which is why typically only 50% of the cabin’s air is replaced in
each pumping cycle of 2-3 minutes. Although the airlines prefer
to emphasize that this is a much faster recirculation rate than in
the ventilation systems of most buildings, people are packed more
tightly in an airplane.2.1.4 Power
Power, P, is defined as the rate of change of energy, dE/dt.
Power thus has units of joules per second, which are usually abbre-
viated as watts, 1 W=1 J/s. Since energy is conserved, we would
have dE/dt= 0 ifEwas the total energy of a closed system, and
that’s not very interesting. What’s usually more interesting to dis-
cuss is either the power flowing in or out of an open system, or the
rate at which energy is being transformed from one form into an-
other. The following is an example of energy flowing into an open
system.
Heating by a lightbulb example 4
.The electric company bills you for energy in units of kilowatt-
hours (kilowatts multiplied by hours) rather than in SI units of
joules. How many joules is a kilowatt-hour?
.1 kilowatt-hour = (1 kW)(1 hour) = (1000 J/s)(3600 s) = 3.6 MJ.
Now here’s an example of energy being transformed from one
form into another.
Human wattage example 5
.Food contains chemical energy (discussed in more detail in sec-
tion 2.4), and for historical reasons, food energy is normally given
in non-SI units of Calories. One Calorie with a capital “C” equals
1000 calories, and 1 calorie is defined as 4.18 J. A typical person
consumes 2000 Calories of food in a day, and converts nearly all
of that directly to body heat. Compare the person’s heat produc-
tion to the rate of energy consumption of a 100-watt lightbulb.
.Strictly speaking, we can’t really compute the derivative dE/dt,80 Chapter 2 Conservation of Energy