# What has more entropy out of steam, water and ice?

1. Jun 14, 2012

### CraigH

I'm trying to understand entropy, because I have no clue what it is. Iv seen questions like this posted in other places on the web, but there seems to be a disagreement over the answer. Some people say it is the randomness and chaos of a system, and other people say it is how close it is to equilibrium.

So in a closed system, all with the same mass, all under the same conditions, ie (the same pressure and temperature). Witch would have the most entropy, steam, ice, or water?

What about in an open system, such as outside in a field?

A metal cube at 300 kelvin is touching a cube at 400 kelvin. This is the closed system, no heat can leave these cubes, they only can transfer heat to each other.

In a separate system There is a 300 and 500 kelvin block. Which out of these two systems has the highest entropy.

As a separate question, within the systems, which block has the highest entropy?

Thanks!

2. Jun 15, 2012

### CraigH

By the way, this isn't a homework question, so i do not need specific answers to the example questions i wrote, Im just after a general idea of what will have the most entropy.

3. Jun 15, 2012

### J Hill

Well, there are a lot of ways to conceptualize entropy, based on how the math works out, but when it comes right down to it there is one strict definition of entropy, S:

$S = k_B \log \Omega$, where kB is Boltzmann's constant (~1.38×10−23 J K−1) and Ω is what is called the multiplicity-- what that represents the number of possible states the system can occupy. I'll refer to this for a concise example. Suppose you are rolling a die-- the multiplicity corresponds to the number you roll, so there are six possible states. Now suppose you roll two dice and consider the sum of the sides-- now there are twelve states available to the system. If you keep doing this with n dice, you see there are going to 6×n states.
Now, this is where entropy gets mixed in with order. Let's consider the ice/water/steam issue. Ice is a crystalline solid, and that means that it is very well ordered (like a snow flake). If you look at the motion of the molecules in the ice, you'll notice that it is constrained by the crystalline structure of the ice itself, so there are a limited number of states that these molecules can occupy. If we heat the ice up, it becomes water-- the molecules begin moving around with a faster average temperature, and are no longer constricted by the crystalline bonds, but at the same time, the liquid is still confined to the volume of the water itself, so while there are more states to occupy, it is still limited. Finally, we can boil the water and turn it into steam. Now the molecules are moving with a pretty high average speed, and are no longer constrained to a fixed volume (remember a gas fills the chamber it is in), so now the number of available states has grown, yet again. So after this long explanation, do you think you have a clear idea as to which one has the highest entropy and why?

Now as for your question regarding the questions regarding the cubes, this is where things get interesting. The second law of thermodynamics states that the entropy of a closed system tends toward a maximum as time progresses. Now, if you do some mathematical work with these concepts you'll find

$d S = \frac{d Q}{T}$, where dQ is a change in heat and T is temperature (see this for some information). At any rate, if you use this, you will clearly find that the 300-500 block system will have a greater change in entropy-- however, I can't speak to the absolute entropy.
However, your question about which block has the highest entropy brings up a possibly more interesting question: Do any of the blocks have a negative change in entropy? You see, while the entropy of the system will increase as time passes, objects within the closed system can have negative entropy change. I suggest you try reading some of these resources, and trying your hand at the computation yourself, but I hope this information helps.

Also, if you are interested, this paper may be of some interest to you.

4. Jun 16, 2012

### CraigH

Thankyou!

5. Jun 16, 2012

### Studiot

Well Craig, hopefully things will go well for you in the exam.

What is entropy -simply.

Well originally it was introduced so as to pair with temperature to be able to calculate energy in a diagram such as I have included. This sort of diagram is called an indicator diagram and the area under a section of the diagram indicates the energy of that process.
This is the same for pressure and volume the area under a p-v indicator diagram indicates the energy to gtet from point a to point B on the diagram.

With that in mind let us look at my sketch.

I have taken the liberty of changing your example slightly to perform better. So instead of water I am using propane and instead of 3 'cubes' - a cube of gas is difficult to maintain - I am starting at absolute zero with a 1 mole block of propane crystal in an open vessel.

This is picture 1 at the top left.
The temperature is 0°K and the entropy is zero.

If I slowly warm the block I am adding heat energy. The amount is given by CpΔT since the block is in an open beaker at constant pressure.
This is line OA on the diagram. OA is not necessarily a straight line.

Warming to 114°K will increase the entropy to 68J/mole°K
At this point the block melts and become liquid
No further temperature rise takes place but the entropy continues to increase as the latent heat of fusion is taken up.
This is line AB on the diagram. Note the latent heat represents a greater rise per mole than the specific heat. This is common. Note AB is vertical.

Further warming again results in heat addition due to specific heat and temperature rise to 261°K as a liquid.
This is line BC, which is again not necessarily a straight line, and the entropy increases to 201 J/mole°K

This time the vertical line CD shows the takeup of the latent heat of vapourisation as the propane turns to a gas. This is where the choice of substance helps because propane is denser than air so stays in the vessel. The heat added will also appear as pv work, as shown in picture 5 where the gas has expanded relative to the liquid.

Note that the energy for any given part of the process will be given by the area in that part of the diagram for example ABFE shown hatched on the sketch represents the energy due to latent heat of fusion and since AB is vertical can be calculated simply as the rectangle q = ΔTΔS.

Going down the statistical route is difficult because not all arrangements of things are associated with energy and therefore they are not associated with thermodynamic entropy, although they may be used in an information sense.

For example if I take some blocks from a bag of blue and red blocks and make a stack there are no energy implications as to whether the blocks are blue or red.
However the fact that I have two colours means that the stack can store information in the possible arrangements of blue and red blocks.
Information states may be about things other than energy. However when they are about energy states they obey the same rules of probability.

go well

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Last edited: Jun 16, 2012