The particles that make up an object can have ordered energy and disordered
energy. The kinetic energy of an object as a whole due to its motion with velocity **
v** with respect to an observer is an example of ordered energy. The
kinetic energy of individual atoms, when they are randomly vibrating about their
equilibrium position, is an example of disordered energy. **Thermal energy**** **is disordered energy. The
**temperature** is a measure of this internal,
disordered energy.

The **absolute temperature** of any substance is
proportional to the **average kinetic energy** associated with the
random motion of the atoms or molecules that make
up the substance.

In a gas, the individual atoms and molecules are moving randomly. The
**absolute temperature T **of the gas is proportional to the average
translational kinetic energy of a gas atom or molecule, ½m<v^{2}>.
In SI units, the proportional constant is (3/2)k_{B}, where k_{B
}= 1.381*10^{-23 }J/K or 1.381*10^{-23}
Pa m^{3}/K is called the **Boltzmann constant**.

½m<v^{2}> = (3/2)k_{B}T

In a solid, the atoms can move randomly about their equilibrium positions.
In addition, the solid as a whole can move with a given velocity and have
ordered kinetic energy. Only the kinetic energy associated with the random
motion of the atoms is proportional to the absolute temperature of the solid.

In ideal gases the disordered energy is all kinetic energy, in molecular
gases and solids it is a combination of kinetic and potential energy. If
we model the atoms in a solid as being held together by tiny springs, then the
random internal energy of each atom constantly switches between kinetic energy
and elastic potential energy.

In classical physics, zero absolute temperature means zero kinetic energy associated with random motion. The atoms in a substance do not move with respect to each other. (The uncertainty principle in quantum mechanics requires that there is some zero-point energy.) Room temperature is not close to absolute zero temperature. At room temperature the atoms and molecules of all substances have random motion.

In SI units the scale of absolute temperature is
**Kelvin** (K).
The Kelvin scale is identical to the **Celsius** (^{o}C) scale, except it is shifted so that 0 degree
Celsius equals 273.15 K. We have

temperature in ^{o}C = temperature in K - 273.15.

To convert to temperature in **Fahrenheit** we can use

temperature in ^{o}F = (9/5) * temperature in ^{o}C + 32.

Liquid nitrogen has a boiling point of -195.81 ^{o}C at atmospheric
pressure. Express this temperature in

(a) degrees Fahrenheit and

(b) Kelvin.

Solution:

(a) temperature in ^{o}F = (9/5) * temperature in
^{o}C + 32.

temperature in ^{o}F = [(9/5)(-195.81) + 32] ^{o}F = -320.5
^{o}F.

(b) temperature in K = (-195.81+ 273.15) K = 77.34 K.

One of the hottest temperatures ever recorded on the surface of Earth was
134 ^{o}F in Death Valley, CA.

(a) What is this temperature in ^{o}C?

(b) What is this temperature in Kelvin?

Solution:

(a) (5/9)*(temperature in
^{o}F - 32)= temperature in ^{o}C.

(5/9)*(134 - 32) ^{o}C = 56.67
^{o}C.

(b) temperature in ^{o}C + 273.15 = temperature in K.

(56.67 + 273.15) K = 329.82 K.

(a) At what temperature do the Fahrenheit and Celsius scales have the same
numerical value?

(b) At what temperature do the Fahrenheit and Kelvin scales have the same
numerical value?

Solution:

(a) temperature in ^{o}F = (9/5) * temperature in
^{o}C + 32.

X = (9/5) * X + 32, X - (9/5)X = 32, -(4/5)X = 32, X = -5*32/4 = -40.

-40 ^{o}F = -40^{ o}C.

(b) temperature in
^{o}C = (5/9)*(temperature in ^{o}F
- 32) = temperature in K - 273.15.

(5/9)*(temperature in ^{o}F - 32) + 273.15 = temperature in K.

(5/9)*(X - 32) + 273.15 = X, (X - 32) + 491.67 = (9/5)X, 459.67
= (4/5)X, X = 574.59.

574.59 ^{o}F = 574.59 K.