j/Discussion questions A-C.
that the following six forms are proposed for the “... ” in dE 1 /dt=k(...).- T 1
- T 2
- T 1 −T 2
- T 2 −T 1
- T 1 /T 2
- T 2 /T 1
Give physical reasons why five of these are not possible.
B How should the rate of heat conduction in j/2 compare with the rate
in j/1?
C The example in j/3 is different from the preceding ones because
when we add the third object in the middle, we don’t necessarily know the
intermediate temperature. We could in fact set up this third object with
any desired initial temperature. Suppose, however, that the flow of heat
issteady. For example, the 36◦object could be a human body, the 0◦
object could be the air on a cold day, and the object in between could be
a simplified physical model of the insulation provided by clothing or body
fat. Under this assumption, what is the intermediate temperature? How
does the rate of heat conduction compare in the two cases?
D Based on the conclusions of questions A-C, how should the rate
of heat conduction through an object depend on its length and cross-
sectional area? If all the linear dimensions of the object are doubled,
what happens to the rate of heat conduction through it? How would this
apply if we compare an elephant to a shrew?5.2 Microscopic description of an ideal gas
5.2.1 Evidence for the kinetic theory
Why does matter have the thermal properties it does? The ba-
sic answer must come from the fact that matter is made of atoms.
How, then, do the atoms give rise to the bulk properties we observe?
Gases, whose thermal properties are simple, offer the best opportu-
nity for us to construct a simple connection between the microscopic
and macroscopic worlds.
A crucial observation is that although solids and liquids are
nearly incompressible, gases can be compressed, as when we in-
crease the amount of air in a car’s tire while hardly increasing its
volume at all. This makes us suspect that the atoms in a solid are
packed shoulder to shoulder, while a gas is mostly vacuum, with
large spaces between molecules. Most liquids and solids have den-
sities about 1000 times greater than most gases, so evidently each
molecule in a gas is separated from its nearest neighbors by a space
something like 10 times the size of the molecules themselves.
If gas molecules have nothing but empty space between them,
why don’t the molecules in the room around you just fall to the316 Chapter 5 Thermodynamics