# Resources

The engineering of the drinking bird – This video gives a great explanation of the drinking bird toy. While this is listed under thermodynamics, it also applies to change of phase and rotational motion.

# Video Transcript

Hello there! Welcome to lecture 18: thermodynamics!

Thermodynamics is the study of heat flow and its relationship to temperature, work, energy, and entropy. Thermodynamics has a huge relevance in our lives, as it explains the workings of and constraints of all heat engines, from power plants to internal combustion engines to refrigerators and HVAC systems.

The laws of thermodynamics play a large role in how scientists and engineers develop efficient power generators and motors. And the concept of entropy is always present in our lives, as we find that it’s easier to create disorder than order.

Each of the following concepts will be discussed in this video: absolute temperature scales, heat engines, the first law of thermodynamics, the second law of thermodynamics, Carnot efficiency, and entropy.

## Absolute temperature scales

As you hopefully recall from lecture 15, there are empirical scales and absolute scales that can be used to measure temperature. Empirical scales are useful in our daily lives, you are likely familiar with both the Fahrenheit and Celsius scales.

In thermodynamics, we are frequently interested in absolute scales. An absolute scale comes about due to a physical limit to how cold things can get. This physical limit establishes the zero end of the scale. The Kelvin scale is an absolute scale. Zero Kelvin is equal to absolute zero: the coldest possible temperature.

The Kelvin temperature scale was developed so that a change in one Kelvin is equal to a change in one degree Celsius. This makes conversion between Celsius and Kelvin a matter of simply adding and subtracting. Zero Kelvin is equal to negative 273 degrees Celsius. Therefore, to convert from Celsius to Kelvin, simply add 273. To convert from Kelvin to Celsius, subtract 273.

What evidence do we have that there is an absolute lower limit to temperature? How do we know that absolute zero exists?

Experiments establishing the relationship between the temperature of a substance and the volume of that substance were performed in the 1700s. As the temperature increased, volume increased. By extrapolating this data, it is possible to see a temperature at which the volume of the substance would be equal to zero. This establishes a physical limit to the system: it is not possible to have zero volume, and certainly not possible to have a negative volume. Experiments on other substances found a similar relationship, with the same temperature corresponding to zero volume. This temperature is known as absolute zero.

Scientists have been able to achieve extremely low temperatures, to within less than a billionth of a degree of absolute zero. To our current level of knowledge, actually achieving absolute zero is not possible.

## Heat engines

A heat engine is a machine that uses a difference in temperature to do useful work. Heat engines are used in many types of power plants: nuclear, coal and gas turbines heat water into steam to spin a coil of wire around a magnet, generating electricity. Internal combustion engines that use fossil fuels to do mechanical work, especially in automobiles, are heat engines. On a more basic level, the refrigerator in your home is a heat engine.

Let’s take a look at some examples of heat engines.

The drinking bird, which we considered in lecture 17, uses a heat difference due to the evaporation of water from the bird’s head. This causes a fluid to flow up into the bird’s head and create a torque that tips the bird. When the bird’s head tips over, fluid is released back into the base of the bird and it tips back upright again. This process will repeat until all of the fluid evaporates.

While the drinking bird is arguably not a terribly useful heat engine, and is certainly a very inefficient heat engine, it produces mechanical work from a temperature difference.

The Stirling engine uses a heat source, in this case, boiling water underneath the engine, and a cool source, in this demo, room temperature air above the engine, to expand and compress gas that causes the motion of pistons. Without a temperature difference between the hot piston and the cold piston, gas would not expand or contract, and there would be no mechanical work output.

This heat engine is known as a Hero’s engine. There is a large flask filled with water placed over an open flame. That flame causes the water to boil, creating steam. The steam releases through openings in the piping. This steam generates a torque that causes the engine to rotate. This rotation is mechanical work.

Note that this demo caused water to splatter out of the openings in the piping, demonstrating really well the concepts of centripetal force and tangential velocity, concepts we discussed in lecture eight!

## The first law of thermodynamics

The first law of thermodynamics has to do with conservation of energy in thermodynamic processes. In a closed system, the first law of thermodynamics can be stated in equation form. Delta E equals Q minus W. Delta E is the change in internal energy of the system, expressed in units of energy (Joules or calories). Q is the heat added to the system, also expressed in either Joules or calories. W is the work done by the system, also expressed in Joules or calories.

Internal energy has to do with the total energy of all of the molecules in a system. This is usually related to temperature and phase. If I increase the internal energy of a system by adding heat, and that system does no work, then the molecules in that system will heat up or change their phase, as we learned in lecture 17.

Let’s say we add heat to a reservoir of water, causing the water to heat up. The amount of heat added to the water is exactly equal to the change in internal energy of that water. If we add 100 Joules of heat, then the internal energy will increase by 100 Joules.

Now let’s say we add 100 Joules of energy to a system that then does 80 Joules of work. How much did the internal energy of that system change? According to the first law of thermodynamics, delta E equals Q minus W. In this case, 100 Joules minus 80 Joules, which is a change in internal energy of 20 Joules.

The first law of thermodynamics tells us that we cannot get energy for free. There is no such thing as a machine that can be made to do work with no energy input. It would violate conservation of energy. Simply put: “we cannot get something for nothing.”

An adiabatic process is a special type of thermodynamic process in which the heat added to or removed from a system is zero. The system is either very well insulated, or the process occurs quickly enough so that no heat is added to or removed from the system. If work is done ON the system, W will be negative, and the internal energy of the system will increase.

Let’s see an example of this. This syringe contains the head of a match. As you can see, the initial state is that the match has not been ignited. When the fire syringe is compressed very quickly with enough force, the work done on the system causes the internal energy of the match head to increase to such an extent that the match head ignites and briefly sparks a fire.

This process is used in diesel engines. Internal combustion engines require a mixture of fuel and air to be ignited to create mechanical work. In a gasoline engine, spark plugs are used to ignite that mixture. In a diesel engine, there are no spark plugs. Instead, the adiabatic compression of the piston in the engine causes the ignition of the fuel and air mixture, creating mechanical work.

## The second law of thermodynamics

Before discussing the second law of thermodynamics, let’s talk about heat flow. Heat can only spontaneously flow from hot to cold. It will never spontaneously flow from cold to hot. This is similar to gravity, which will cause a ball to roll DOWN a hill, but never up. To get something back to the top of the hill, we have to exert energy to do so. Similarly, to get heat to flow from cold to hot, such as an air conditioning unit or refrigerator does, requires external energy.

As discussed earlier, a heat engine is a device that uses a difference in temperature to do useful work. The second law of thermodynamics tells us that not all heat energy will be converted to work in this process. There will always be wasted heat energy. If the first law of thermodynamics tells us that “we can’t win”, the second law tells us “we can’t break even” either.

In this demo, I use hot and cold water to do useful work in a heat engine. Let’s consider a factory where widgets come in on one level on a conveyor belt, get raised up to a higher level, and then get moved away to another area of the factory on a second conveyor belt higher up. This heat engine raises the mass, and then lowers down so a new mass can be placed into the system. By placing the bulb of this heat engine into hot water, the gases inside the bulb warm up and expand, causing the mass to rise up to the second level. While in this demo there is no conveyor belt, much less a whole factory, I can use my hand to move the mass elsewhere.

Now the system is ready for a second mass. How do I get the system back to the lower level? I need to cool off the bulb somehow. It is currently warm, and now I must throw away that heat to reset the process. Whether I wait for the bulb to cool off in the atmosphere, or I cool the bulb by plunging the bulb into cold water, either way, that heat energy did not do any useful work. Instead, it slightly raised the temperature of the surroundings, which does not equate to any useful mechanical process.

I repeated this process several times in the demo. Every time I need to reset the system, heat energy is wasted. This is an inevitable result of physics that is formalized by the second law of thermodynamics.

When we discuss Carnot efficiency in a few minutes, we’ll learn about how the temperature of the hot source and the cold source of the heat engine can be used to determine the maximum possible efficiency of a heat engine. But the second law of thermodynamics tells us that the efficiency can never be 100%. We are always wasting some of our heat energy.

Throughout the ages, humans have been fascinated with the idea of perpetual motion machines. There have always been people who have tried to create a machine that will run forever without any input of energy. The first law of thermodynamics tells us that perpetual motion machines that create energy from nowhere are impossible. The second law of thermodynamics tells us that perpetual motion itself is impossible. For any machine to operate in a closed cyclical loop forever and ever, energy must be continually fed into the system to keep it moving.

One final way to state the second law of thermodynamics is to say that the amount of entropy in our universe always increases. We’ll talk about entropy in detail at the end of this lecture.

## Carnot efficiency

Carnot efficiency describes the maximum amount of efficiency that we can expect from any heat engine, even if it is perfectly ideal in every other way: no friction or other losses. Carnot efficiency is equal to the temperature of the hot area minus the temperature of the cold area, all divided by the temperature of the hot area. The temperature scale used in this equation must be an absolute scale. We use Kelvin in this class.

If we look at the equation, the only way the efficiency of a heat engine can be one is if the temperature of the cold area is zero: absolute zero. That isn’t possible, so the efficiency of a heat engine will never be one hundred percent. We can also see from the equation that efficiency can be maximized as much as possible by increasing the temperature difference between the hot and cold areas. If the temperature difference is small, the efficiency will be very low.

Let’s do an example. The heat engine we used to lift a mass used hot water that was at a temperature of 98 degrees Celsius. The cold water used to reset the system was 10 degrees Celsius. Let’s calculate the Carnot efficiency. The first step is to convert the temperature to Kelvin, as we must use an absolute scale for this equation to work. Add 273 to each temperature to convert from Celsius to Kelvin. 98 degrees Celsius is 371 Kelvin. 10 degrees Celsius is 283 Kelvin. Now plug into the equation. Carnot efficiency equals temperature of hot minus temperature of cold, all divided by temperature of hot. 371 Kelvin minus 283 Kelvin is 88 Kelvin, divided by 371 Kelvin is 0.24. This is an efficiency of 24 percent.

## Entropy

Entropy describes the amount of disorder in a system. When we consider a system, entropy is related to the number of different states that the system can be in. Let’s start by considering a very small system: a single coin. The coin can be either in its heads or tails configuration: two states. When I introduce a second coin into the system, there are now four different states the system can be in: both tails, both heads, and two states consisting of one heads and one tails. The more coins I introduce into my system, the more possible states there are.

We can consider disorder to be a random arrangement of heads and tails among all the coins. A highly ordered system would be one where all of the coins are the same: all heads up, or all tails up. When I have a single coin, the probability of getting all heads is 50%. When I have two coins, the odds of having all heads is 25%. The more coins in my system, the harder it is to randomly toss all of the coins in the air and have them all come up as heads. The more coins there are, the more disordered states there are compared to highly ordered states. If I have ten coins, for example, there are 1024 different states, but only one corresponds to all heads, and only one corresponds to all tails. More likely, I am going to have roughly equal numbers of heads and tails: disorder.

Most systems are much more complicated and have many, many more states than our coins. Even this relatively simple system consisting of purple and green cubes has many possible states that it can be in. Before recording this demo, I took all of the cubes out of the jar, manually sorted them, and put all of the green cubes on the bottom and all of the purple cubes on top. This is a highly ordered state.

When I shake the beaker, the cubes become random and go into one of the many possible disordered states. Theoretically, it’s possible that I could continue to shake this jar for a very long time and get back to my highly ordered arrangement of green on bottom and purple on top. But it’s extremely unlikely due to the huge number of possible states. It is easy to increase the entropy of the system, but in order to decrease the entropy, I have to manually work to organize the cubes.

Here, I have a beaker of water. There are many molecules of water in this beaker. When I place a drop of food dye into the beaker, the two different substances: water and dye, are still relatively ordered. Most of the dye is in one location, and the water is still clear. Over time, however, the dye distributes throughout the water and the entropy increases. When I stir the water, the dye distributes completely. How can I get the water to become clear again? How can I separate the dye from the water? This will not happen naturally. I would have to distill the water or filter it out, manually putting energy and effort into the process.

Now consider our surrounding environment. Think about how many molecules of air surround you, and how many different states they can be in. Most systems in our lives have many states they can take, and the highly ordered states only represent a very miniscule fraction of those possible states. Entropy is all around us.

One thing that the second law of thermodynamics tells us is that entropy increases with time. We saw that with the shaken cubes, and the food dye in the water. If I put effort into decreasing entropy somewhere, for example, by organizing the cubes, I myself create heat from my exertions and increase the entropy of my surrounding environment. A refrigerator, which acts to decrease the entropy inside the fridge and cool down my food, creates heat and actually causes an increase in entropy elsewhere. This is one of the reasons why perpetual motion is impossible. There is no way to decrease entropy in one spot without increasing it more somewhere else. We truly cannot get something for nothing!

We can consider entropy to describe the arrow of time. Some processes in physics are symmetric, that is, I could play a video of me walking around a room, and you would not necessarily be able to tell if the video were played in forward or reverse. I can walk backward just as easily as I can walk forward. However, if you were to watch THIS video, you know it is played backward. Why? Because you know that it is impossible to shake a can and obtain a more ordered state! Entropy describes the arrow of time. Entropy always increases with time.

Thanks for taking the time to learn about thermodynamics! Until next time, stay well.