Simple Nature - Light and Matter

absolute zero, the temperature at which all random molecular motion ceases, and equals 273 K

at the freezing point of water. We can get away with using the Celsius scale as long as we are

only interested in temperature differences; a difference of 1 degree C is the same as a difference

of 1 degree K.

It is an observed fact that ideal gases obey theideal gas law,

PV=nkT,

and this equation can be explained by the kinetic theory of heat, which states that the gas

experts pressure on its container because its molecules are constantly in motion. In the kinetic

theory of heat, the temperature of a gas is proportional to the average energy per molecule.

Not all the heat energy in an object can be extracted to do mechanical work. We therefore

describe heat as a lower grade of energy than other forms of energy. Entropy is a measure of

how much of a system’s energy is inaccessible to being extracted, even by the most efficient heat

engine; a high entropy corresponds to a low grade of energy. The change in a system’s entropy

when heatQis deposited into it is

∆S=

Q

T

.

The efficiency of any heat engine is defined as

efficiency =

energy we get in useful form

energy we pay for

,

and the efficiency of a Carnot engine, the most efficient of all, is

efficiency = 1−

TL

TH

.

These results are all closely related. For instance, example 11 on page 323 uses ∆S=Q/Tand

efficiency = 1−TL/THto show that a Carnot engine doesn’t change the entropy of the universe.

Fundamentally, entropy is defined as the being proportional to the natural logarithm of

the number of states available to a system, and the above equation then serves as a definition

of temperature. The entropy of a closed system always increases; this is the second law of

thermodynamics.

Chapter 6, Waves, page 353

Wave motiondiffers in three important ways from the motion of material objects:

Waves obey the principle of superposition. When two waves collide, they simply add

together.

The medium is not transported along with the wave. The motion of any given point in

the medium is a vibration about its equilibrium location, not a steady forward motion.

The velocity of a wave depends on the medium, not on the amount of energy in the wave.

(For some types of waves, notably water waves, the velocity may also depend on the shape

of the wave.)

1078 Chapter Appendix 5: Summary