Explaining Entropy (like Feynman teaching a layman)

Question

I'm currently a high school student learning about thermodynamics. I (think) I understand the preliminaries to entropy (i.e. microscopic definition of heat, etc.). I've read/watched multiple high-school-level sources but still don't have a decent understanding of entropy.

I can handle college-level text as long as mathematics (especially statistics and integral calculus) is kept to a minimum.

Are there any good explanations and/or sources that explain entropy, preferably with little advanced math?

I'm beginning to read "Entropy Demystified" by Ariel Ben-Naim. Any opinions regarding this book?

Answer 1

Entropy is a measure of a number of options a system has.

What do I mean by options?

Let me clear it with an example of coins. Let's take 3 coins and give them name coin A, coin B, coin C. If I tell you, two of the three coins showing heads and one showing tail, then there are three possibilities (options)

1) Coin A and Coin B showing heads, coin C showing tail

2)Coin B and coin C showing heads, coin A showing tail

3)coin C and coin A showing heads, coin B showing the tail.

So there are three possibilities (options).

Now if I tell you all of them showing heads, there is just one possibility (option), that is,

Coin A is showing head, coin B showing head, coin C showing head. Similarly, if I tell you, of the three coins, only one is showing head, there are three possibilities(think about it yourself).

The more the possibilities(options), the more the entropy, in the 2nd case entropy is minimum (only one possibility).

Now let me connect this idea with actual physical systems, let's take the famous example, gas molecules in a box. A system of gas molecules in a box in equilibrium is going to have some definite entropy.

Here in this example by possibilities or options, we mean possible position and momentum the molecules of gas can have. What will happen if we double the volume of the box, entropy increase or decrease?

When we double the volume the possible positions that the molecules in the gas can take the increase, the molecules now can explore a larger volume of space. Possibilities increase so thus entropy. Similarly, if we heat the gas keeping volume constant, the molecules going to vibrate and move faster, so the entropy increases, possible momentums the molecules can have increased.

Think about entropy, as a measure of possibilities or options the system has, the more the options the more the entropy.

Answer 2

There are many different--mostly equivalent--definitions of entropy. But the one I see as being at the heart of it all has to do with information theory. Entropy measures a particular kind of information--the tricky part is understanding exactly what kind of information.

In order to define entropy, you have to make a distinction between the information contained in the full microscopic details of the state of a physical system and the amount of information contained in the approximate description of that system given by a small set of thermodynamic variables (like volume, temperature, pressure, etc.). The entropy is just the difference between the two. It's the amount of information you are missing if you only know the thermodynamic state as opposed to the full microscopic details.

In SI units, entropy is measured in Joules per Kelvin, but a more natural unit for entropy (in light of its modern foundation in information theory) is bits, the same way information is measured in computer science. When measured in bits, 1 J/K of entropy is equal to 13 Zettabytes (13-billion Terabytes).

Intuitively, you can think of the 2nd law as saying that as any ergodic system evolves in time from a particular set of initial conditions, it will tend to progress into states where you can infer less and less about the specific microscopic details from looking at the macroscopic state. In other words, if the system starts out in a macroscopic state that is special in any way, the specialness will go away little by little, until eventually you have the most generic (non-special) state possible. At that point, knowing the macroscopic state will tell you almost nothing about the exact state of the system. Nearly all of the information about which initial state was chosen has become scrambled and is hidden in subtle microscopic correlations which could not be used to reconstruct the original state without precisely tracking all of the individual components of the system (atoms, molecules, etc.)

Answer 3

The universe is lazy and always tend to do the easiest, most probable things.

Any state of disorder is simply the state that is most probable. For example consider a large number of dices, and throw them all at once. If you take a sufficiently large number you will notice that 1/6 of them read 1, 1/6 read 2 and so on.

Explaining this is quite easy, this happens as its the most probable outcome. Now consider disorder in this system; its obviously the most disorderly arrangement of dices and hence most entropic! Hence the dices dont assume a low entropy state like all dices reading 1 simply because its less likely to happen.

Thus entropy is tendency of system to go toward mote likely state.

Answer 4

Have you considered Encyclopaedia Britannica? Here is the start of the article on entropy (physics):

the measure of a system's thermal energy per unit temperature that is unavailable for doing useful work. Because work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorder, or randomness, of a system. The concept of entropy provides deep insight into the direction of spontaneous change for many everyday phenomena. Its introduction by the German physicist Rudolf Clausius in 1850 is a highlight of 19th-century physics.

Compare that clarity of writing to this deranged babbling from Wikipedia, which is the place Google sends you if you type the word "entropy":

Entropy is a measure of the energy of a system that is unavailable for doing useful work. In statistical thermodynamics, entropy (usual symbol S) is a measure of the number of microscopic configurations Ω that correspond to a thermodynamic system in a state specified by certain macroscopic variables. Specifically, assuming that each of the microscopic configurations is equally probable, the entropy of the system is the natural logarithm of that number of configurations, multiplied by the Boltzmann constant kB (which provides consistency with the original thermodynamic concept of entropy discussed below, and gives entropy the dimension of energy divided by temperature)

For simple explanations with not too much maths, Encyclopaedia Britannica is not bad.

Answer 5

Entropy is a way to measure the usefulness of energy in a system. If a system has low entropy, work can be performed when it changes from low to high entropy.

For example, gas confined in a cylinder has relatively lower entropy than gas dispersed throughout space. There are fewer microstates for each molecule in the cylinder than there are for each molecule occupying a greater volume of space. If gas is released from the cylinder into space, its entropy rises significantly and useful work can be extracted due to the rise in entropy. But the entropy of gas dispersed throughout space can not easily be raised. It has high entropy and little useful energy.

Answer 6

(1) Don't allow yourself to fall into the belief system that entropy is a measure of disorder ... it's not. Order can increase while entropy decreases; there's no problem there.

(2) Understanding the concept of Entropy is very, very accessible to the average high school student if the mathematics are omitted. Statistical Mechanics is not very simple, and that's generally what's required to get a good feel for what exactly thermodynamics is.

(3) Check out the Entropy videos on YouTube by the channel SixtySymbols. Also, check out "Where does Complexity Come From?" by minutephysics, also on YouTube.