bra symbols.
1 J = 1
kg·m^2
s^2
= 1
kg·m^2
s^2
×
1000 g
1 kg
×
(
100 cm
1 m
) 2
= 10^7
g·cm^2
s^2
= 10^7 erg
Cabin air in a jet airplane example 3
.A jet airplane typically cruises at a velocity of 270 m/s. Outside
air is continuously pumped into the cabin, but must be cooled off
first, both because (1) it heats up due to friction as it enters the en-
gines, and (2) it is heated as a side-effect of being compressed to
cabin pressure. Calculate the increase in temperature due to the
first effect. The specific heat of dry air is about 1.0× 103 J/kg·◦C.
.This is easiest to understand in the frame of reference of the
plane, in which the air rushing into the engine is stopped, and its
kinetic energy converted into heat.^6 Conservation of energy tells
us
0 =∆E
=∆K+∆Eheat.
In the plane’s frame of reference, the air’s initial velocity isvi=270
m/s, and its final velocity is zero, so the change in its kinetic en-
ergy is negative,
∆K=Kf−Ki
= 0−(1/2)mvi^2
=−(1/2)mvi^2.
Assuming that the specific heat of air is roughly independent of
temperature (which is why the number was stated with the word
“about”), we can substitute into 0 =∆K+∆Eheat, giving
0 =−
1
2
mvi^2 +mc∆T
1
2
vi^2 =c∆T.
Note how the mass cancels out. This is a big advantage of solving
problems algebraically first, and waiting until the end to plug in
(^6) It’s not at all obvious that the solution would work out in the earth’s frame of
reference, although Galilean relativity states that it doesn’t matter which frame
we use. Chapter 3 discusses the relationship between conservation of energy and
Galilean relativity.
Section 2.1 Energy 79