Peoples Physics Concepts

18.1. Temperature http://www.ck12.org

• More than 50% of the water rise expected from global warming is due to the thermal expansion of water


• There are 3 different temperature scales you should know-the Kelvin scale, the Celsius scale and the Fahrenheit
  scale.


• The Kelvin scale (K) is the one used in most scientific equations and has its zero value set atabsolute zero
  (the theoretical point at which all motion stops).


• The Celsius scale(◦C)is the standard SI temperature scale. It is equal to the Kelvin scale if you minus 273
  from the Celsius reading. Water has a boiling point of 100◦Cand a freezing point of 0◦C.


• The Fahrenheit scale(◦F)is the English system and the one we are familiar with.


• Newtons’ Law of Cooling:The rate of heat transfer is proportional to the difference in temperature between
  the two objects. For example, hot liquid that is put in the freezer will cool much faster than a room temperature
  liquid that is put in the same freezer.

Kinetic Theory of Gases

According to classical kinetic theory, temperature is always proportional to the average kinetic energy of molecules
in a substance. The constant of proportionality, however, is not always the same.
Consider: the only way to increase the kinetic energies of the atoms in a mono-atomic gas is to increase their
translational velocities. Accordingly, we assume that the kinetic energies of such atoms are stored equally in the
three components (x,y,andz) of their velocities.
On the other hand, other gases — called diatomic — consist of two atoms held by a bond. This bond can be
modeled as a spring, and the two atoms and bond together as a harmonic oscillator. Now, a single molecule’s
kinetic energy can be increasedeither by increasing its speed, by making it vibrate in simple harmonic motion, or
by making it rotate around its center of mass. This difference is understood in physics through the concept of
degrees of freedom: each degree of freedom for a molecule or particle corresponds to a possibility of increasing its
kinetic energy independently of the kinetic energy in other degrees.
It might seem that monatomic gases should have one degree of freedom: their velocity. They have three because
their velocity can be altered in one of three mutually perpendicular directions without changing the kinetic energy
in other two — just like a centripetal force does not change the kinetic energy of an object, since it is always
perpendicular to its velocity. These are called translational degrees of freedom.
Diatomic gas molecules, on the other hand have more: the three translational explained above still exist, but there
are now also vibrational and rotational degrees of freedom. Monatomic and diatomic degrees of freedom can be
illustrated like this:

Temperature is anaverage of kinetic energy over degrees of freedom, not a sum. Let’s try to understand why this is

in reference to our monoatomic ideal gas. In the derivation above, volume was constant; so, temperature was

essentially proportional to pressure, which in turn was proportional to the kinetic energydue to translational