Page 249 - Schaum's Outline of Theory and Problems of Applied Physics

234 KINETIC THEORY OF MATTER [CHAP. 20

SOLIDS AND LIQUIDS
The molecules of a solid are close enough together to exert forces on one another that hold the entire assembly
to a definite size and shape. As in the case of a gas, the molecules are in constant motion, but they vibrate about
fixed locations instead of moving randomly. The molecules of a liquid continually move around past one another
more or less freely, which enables the liquid to flow, but their spacing does not change, and so the volume of a
given liquid sample does not vary.
When a solid melts, the original ordered arrangement of its molecules changes to the random arrangement
of molecules in a liquid. To accomplish the change, the molecules must be pulled apart against the forces holding
them in place, which requires energy. The heat of fusion of a solid represents this energy. When a liquid boils,
the heat of vaporization represents the energy needed to pull its molecules entirely free of one another so that a
gas is formed.

SOLVED PROBLEM 20.1

Gas molecules have velocities comparable with those of rifle bullets, yet we all know that a gas with a
strong odor, such as ammonia, takes several seconds to diffuse through a room. Why?
Gas molecules collide frequently with one another, which means that a particular molecule follows a long, very
complicated path in going from one place to another.

SOLVED PROBLEM 20.2

Explain the evaporation of a liquid at a temperature below its boiling point on the basis of the kinetic
theory of matter.
At any moment in a liquid, some molecules are moving faster and others are moving slower than the average.
The fastest ones are able to escape from the liquid surface despite the attractive forces exerted by the other molecules;
this constitutes evaporation. The warmer the liquid, the greater the number of very fast molecules, and the more
rapidly evaporation takes place. Since the molecules that remain behind are the slower ones, the liquid has a lower
temperature than before (unless heat has been added to it from an outside source during the process).

SOLVED PROBLEM 20.3
◦
What is the average kinetic energy of the molecules of any gas at 100 C?
The absolute temperature corresponding to 100 Cis
◦

T K = T C + 273 = 373 K

The average kinetic energy at this temperature is

3
3
KE av = kT = ( )(1.38 × 10 −23 J/K)(373 K) = 7.72 × 10 −21 J
2 2
SOLVED PROBLEM 20.4
◦
What is the average velocity of the molecules in a sample of oxygen at 100 C? The mass of an oxygen
molecule is 5.3 × 10 −26 kg.
2
1
3
Since KE av = mv = kT ,
2 av 2

3kT
v av =
m