A layperson's introduction to thermodynamics, part 2: Equilibrium, phase changes and steam engines

ducks
Tue, 13 Nov 2018 12:28:18 +0000

Intro

Hello everyone,

Today we cover equilibriums and phase changes. Through that we will get a basic understanding of how things like pressure, temperature, density, volume, etc. are related.

The previous chapter can be found here: https://tildes.net/~science/8ao/. I highly recommend that you read it before continuing.

A collection of all topics covered can be found here: https://tildes.net/~tildes/8al/.

Subject

Summarized

"Equilibrium" is fancy word for "balance". A system is in equilibrium when it is in balance with the surrounding systems. Any system will naturally attempt to be in equilibrim, and will adapt its physical properties to do so.

A phase change is the transition of matter from a state (solid, liquid, gas, or plasma) to a different state. This happens due to a change in internal energy, changing how a material is bonded.

Now that we have it summarised, lets dig a bit deeper.

Equilibrium

A system always tries to be in balance with its surrounding systems. We maybe don't think about this a lot, but we are all very familiar with this principle since we observe it every day.

If you have a cup of hot cocoa, it will cool down until it has reached ambient temperature. At this point, the cocoa is considered to be in "thermal equilibrium". If we fill a balloon with air, it will expand. It will do so until the air inside the balloon has the same pressure as the air outside the balloon. At this point, the balloon is considered to be in "barometric (pressure) equilibrium".

Just like when we talk about energy, there is a relationship when we talk about equilibriums. We have something we call (you may remember this from basic chemistry) an "ideal gas". An ideal gas is a good way of looking at this principle. Since the temperature, volume and pressure have a direct relationship.

Pressure-volume-temperature diagram for ideal gases.

In the diagram above we can see that if we change one of the three variables, then one (or both) of the other two variables has to change too. For instance, if we heat some air in a canister, the air will try to expand. But being unable to change in volume, it will instead increase pressure. [1]

Phase changes

Any material has a set of phases. The ones we'll discuss are the solid, liquid and gaseous phases. Unless we control the material's environment very carefully, materials will always follow this order when energy is added. Solid becomes liquid, liquid becomes gas, and vice versa. For instance water; ice (solid) becomes water (liquid), water becomes steam (gas). So each of these transformations is a phase change.

So when water is solid (ice), the molecules are in a grid. The molecules do not move around much, maybe a little bit where they stand. But they all still stand in a grid.

When the water gets heated up, the molecules will start to move. Molecules have a natural attraction to each other due to subatomic forces like the van der Waals force. So the molecules will no longer stay in a grid, but they will still keep each other close due to this attraction. So a material that sticks together but freely moves around is called a liquid.

Once the material overcomes this natural attraction, the molecules can go anywhere they want. And that's when we get a gas. Or steam, in the case of water. All of this applies even for materials we don't usually imagine would melt or evaporate, for instance steel.

Here is a visual representation of the three states.

Now comes the fun part. Ice is water that is at 0 degrees Celcius or below. Liquid water is water that is 0 degrees and above. But wait! Does that mean that water can be both solid and liquid at the same temperature? Yes, indeed. A material requires a certain amount of internal energy to become liquid. That is why internal energy and temperature is often used interchangeably, but is not exactly the same.

The water molecules in ice will use the supplied energy to get excited and start moving around. This continues until the solid-liquid water reaches a point where all molecules move around. At that point it has completely become a liquid. While water is in solid-liquid state, the amount of internal energy dictates how much is liquid and how much is solid. The exact same thing happens with water at 100 degrees. It can be steam or liquid, but not fully either until it reaches a certain amount of internal energy.

Here is a diagram of this process.

Another fun tidbit that makes water special: Water has a lower density as a solid than it has as a liquid, when both are at 0 degrees Celcius. This means that per unit of volume ice weighs less than (liquid) water. Therefore ice floats on top of water. This is the only material that behaves in this way. And thats extremely important to our existince, since it helps regulate heat in the ocean.

Steam engines (and implication)

We have learned a few new things today. But there is one really important wrinkle to all of this. A system always will try to be in balance. And this we can exploit. Pressure is a type of "pushing". So thats a type of work! And an increase in thermal energy can lead to an increase in temperature. We remember that from the ideal gas. So if we cleverly organize our system, we can create work from heat! This is the basis behind most heat engines (simplified a ton). We supply thermal energy to some gas or fluid, and extract work from this gas or fluid.

A classical example is the steam engine. We have water inside a closed system. When we heat up the water, it will turn into steam. And this steam will want to be much less dense than water. As a consequence, the pressure inside the water tank increases drastically. We release a small amount of this steam into a closed piston.

Here is an animation of this in action.

The piston suddenly gets a high pressure level. As we remember, it will want to be in equilibrium with its surroundings. Currently the pressure inside the piston is much higher than outside the piston. As we remember from the ideal gas law, a higher volume will mean a lower pressure. So the piston will be moved, as the steam expands to reach a pressure balance. The movement from the piston will drive something, like a wheel. The steam is removed from the expanded piston, and the piston will return to its closed position.[2] Then the process is repeated again and again, to have the piston continously move something.

All that from a bit of water in a tank and some supplied heat.

Whats next?

Next time we will talk about another important property. Entropy! In the previous topic I had a lot of questions regarding the quality of energy types, and what specifies heat from work on an intrinsic level. Entropy is the big answer to this. From that we will also cover the heat death of the universe, which would be a good introduction to "a laypersons introduction to nihilism" if we have any philosophers here.

Note

[1] For solid and fluid materials (as well as non-ideal gassess) this becomes a lot more complicated. If we ever do a "layperson's intro to fluid mechanics" we will cover it then.
[2] This described design is very inefficient and very simplified. Usually the piston is made so steam is supplied in turns supplied to either side of the piston. Then the work will both removed the steam that already performed work as well as move the piston. That way you can have continous movement in both directions.

See for instance this image.

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