Thermodynamics:
Entropy

Thermodynamics Gateway Page
In this module:
Introduction
Disorder in Atoms
Disorder in Energy
Measuring Entropy
Entropy of Phase Changes
Patterns in the Entropies of Substances
Entropy in Thermochemical Equations
The Second Law of Thermodynamics
The Effect of Temperature
Predicting How Reactions will Go
Two Examples

Disorder in Energy

Entropy measures the amount of disorder in energy as well as the amount of disorder in atoms. To see how, read on.

Consider two atoms, A and B, and two pieces of energy, symbolized by *. There are three possible arrangements of the energy on the atoms: A could have both pieces of energy (A**), B could have both (B**), or A and B could each have one (A*B*).

Now, if A and B are allowed to interact with three more atoms, C, D, and E, many more arrangements of energy over the atoms is possible.

Click on atoms A-E below to add energy to them. Click on Enter to register an arrangement. Continue until you have determined all the possible arrangements of energy on the five atoms.

A**

A*B*

A*C*

A*D*

A*E*

B**

B*C*

B*D*

B*E*

C**

Correct!
You are not done yet!

C*D*

C*E*

D**

D*E*

E**

As you can see, there are 15 possible arrangements (5 + 4 + 3 + 2 + 1) of the two pieces of energy on the 5 atoms. Out of these, three of them (3/15 or 1/5) still have both pieces of energy on A and B, while in the other 12 (12/15 or 4/5) at least one piece of energy has been transferred to either C, D, or E.

If A and B are brought into contact with 100 other atoms, there are 5050 possible arrangements (100 + 99 + 98 + ... + 3 + 2 + 1). Only three of these (3/5050 or 0.06%) still have both pieces of energy on A and B, while in the rest (5047/5050 or 99.94%) at least one piece of energy has been transferred to another atom. If A and B come into contact with a mole of other atoms, there are over 1047 possible arrangements. The probability that both pieces of energy will stay on A and B is so small that it is certain that energy will be transferred to the other atoms.

What this means is that energy, such as heat, electrical, or chemical energy, will always flow from places where it is plentiful to places where it is absent. Arrangements where energy is spread over many atoms are more disordered than (have more entropy than) arrangements where it is more concentrated. Energy may be transiently concentrated on a few atoms, but it will never spontaneously group up so that it is all on a few atoms in a system.

Disorder in Energy