The hot bar is heated up, and the air inside the chamber starts to expand.This causes the piston to move, which in turn spins the flywheel.Then, the cold bar is cooled down, and the air inside the chamber starts to contract.This causes the flywheel to spin in the opposite direction, and the process repeats.
Sadi Carnot realized that this ideal heat engine could convert up to 100% of the thermal energy into useful mechanical work.This was a major breakthrough, and it would later become known as the Carnot Cycle.But the real breakthrough was the realization that this cycle could be used to explain the energy transfer between the earth and the sun.
Sadi Carnot had discovered the secret of the Earth’s energy transfer from the sun: the Carnot Cycle.This cycle explains how the sun’s energy is converted into useful mechanical work on Earth, such as powering ships, mining ore, and excavating ports.It also explains why the Earth radiates back a certain amount of energy into space relative to the amount it receives from the sun.This is one of the most important, yet least understood concepts in all of physics, governing everything from molecular collisions to humongous storms.It may, in fact, determine the direction of time and even be the reason that life exists. But today, with modern materials, we can reach temperatures much higher than that, and this allows us to make more efficient engines.
The air inside the chamber starts off at a temperature just below that of the hot bar. This hot bar is brought into contact with the chamber, causing the air to expand and heat to flow into it to maintain its temperature. This in turn pushes the piston up, turning the flywheel. The hot bar is then removed, and the air continues to expand, but without heat entering, the temperature decreases until it is the same as the cold bar. The cold bar is brought into contact with the chamber, and the flywheel pushes the piston down, compressing the air and transferring heat into the cold bar. The cold bar is then removed, and the flywheel compresses the gas further, increasing its temperature until it is just below that of the hot bar. The hot bar is reconnected, and the cycle repeats. Through this process, heat from the hot bar is converted into the energy of the flywheel.
It is interesting to note that Carnot’s ideal engine is completely reversible. If the engine were to be run in reverse, the air would expand, lowering the temperature, and then the chamber would be brought into contact with the cold bar, the air expanding more and drawing in heat from the cold bar. The air is then compressed, increasing its temperature, and the chamber is placed on top of the hot bar, using the energy of the flywheel to return the heat back into the hot bar.
The efficiency of this engine is not 100%, even though it is fully reversible. Each cycle, the energy of the flywheel increases by the amount of heat flowing into the chamber from the hot bar, minus the heat flowing out of the chamber at the cold bar. To increase the efficiency of the engine, the temperature of the hot side or the temperature of the cold side can be increased, or both.
Lord Kelvin learns of Carnot’s ideal heat engine and realizes it could form the basis for an absolute temperature scale. If the gas is allowed to expand an extreme amount, cooling to the point where all the gas particles effectively stop moving, it would take no work to compress it on the cold side, so no heat would be lost, forming the basis for absolute zero.
Using the Kelvin scale, the efficiency can be expressed as a ratio of the work done by the gas on the piston on the hot side and the work done by the piston on the gas on the cold side. To reach 100% efficiency, infinite temperature would be needed on the hot side or absolute zero on the cold side, both of which are impossible in practice. Even with no friction or losses to the environment, it is impossible to make a heat engine 100% efficient.
Today, with modern materials, temperatures much higher than 160 degrees Celsius can be reached, allowing for more efficient engines. Now, the chance of the left bar having more energy packets than it started is 0.000001%.So, even though it’s still possible, it’s so improbable that it’s almost impossible to observe.
Their theoretical maximum efficiency was 32%, but their real efficiency was more like 3%. This is because real engines experience friction, dissipate heat to the environment, and do not transfer heat at constant temperatures, so less energy ends up in the flywheel. The rest of the energy spreads out over the walls of the cylinder, the axle of the flywheel, and is radiated out into the environment. This process is irreversible, meaning the total amount of energy does not change, but it becomes less usable.
In 1865, German physicist Rudolf Clausius studied Carnot’s engine and came up with a way to measure how spread out the energy is. He called this quantity entropy. When all the energy is concentrated in the hot bar, that is low entropy, but as the energy spreads to the surroundings, entropy increases. This means the same amount of energy is present but in a more dispersed form, making it less available to do work.
Clausius summarizes the first two laws of thermodynamics as such: first, the energy of the universe is constant, and second, the entropy of the universe tends to a maximum. In other words, energy spreads out over time. This second law is core to many phenomena in the world, such as why hot things cool down and cool things heat up, why gas expands to fill a container, and why perpetual motion machines are impossible.
Ludwig Boltzmann made an important insight that heat flowing from cold to hot is not impossible, it’s just improbable. The chance of this happening increases as the number of atoms and energy packets increases, but even with a large number of atoms and energy packets, the chance is still so small it is almost impossible to observe. There is now only a 0.05% chance that the left solid ends up hotter than it started, and this trend continues as we keep scaling up the system. In everyday solids, there are around 100 trillion, trillion atoms and even more energy packets, so heat flowing from cold to hot is just so unlikely that it never happens. It’s like a Rubik’s cube: with each random turn, it moves further and further from being solved, as there is only one way for it to be solved and quintillions of ways for it to be almost entirely random.
Without thought and effort, the natural tendency of energy is to spread out and get messier. This is why air conditioning is possible, where the cold interior of a house gets cooler and the hot exterior gets hotter: the decrease in entropy at the house is more than paid for by an increase in entropy required to make that happen.
The increase in entropy can be seen in the relative number of photons arriving at and leaving the earth. For each photon received from the sun, 20 photons are emitted, and all the activities on earth such as plants growing, trees falling, herds stampeding, hurricanes and tornadoes, people eating, sleeping, and breathing are part of the process of converting fewer, higher energy photons into 20 times as many lower energy photons. Without a source of concentrated energy and a way to discard the spread out energy, life on earth would not be possible. It has even been suggested that life itself may be a consequence of the second law of thermodynamics, as life is spectacularly good at converting low entropy into high entropy. The surface layer of seawater produces between 30 to 680% more entropy when cyanobacteria and other organic matter is present than when it’s not. Jeremy England takes this one step further, proposing that if there is a constant stream of clumped up energy, this could favor structures that dissipate that energy, eventually resulting in life. He states that, “You start with a random clump of atoms, and if you shine light on it for long enough, it should not be so surprising that you get a plant.”
The sun is the source of low entropy for life on Earth, but where did the sun get its low entropy? The answer is the universe. It is known that the total entropy of the universe is increasing with time, meaning that it was lower entropy yesterday and even lower entropy the day before that, all the way back to the Big Bang. Right after the Big Bang, entropy was at its lowest. This is known as the past hypothesis.
The early universe was hot, dense, and almost completely uniform, with everything mixed and the temperature being the same everywhere, varying by at most 0.001%. However, this state was actually an extremely unlikely one due to gravity, which tends to clump matter together.
As the universe expanded and cooled, matter started to clump together in more dense regions, turning potential energy into kinetic energy. This energy could be used like how water flowing downhill can power a turbine, but as bits of matter started hitting each other, some of their kinetic energy was converted into heat, decreasing the amount of useful energy and thus increasing entropy.
Over time, the useful energy was used to form stars, planets, galaxies, and life, increasing entropy all along. Jacob Bekenstein proposed another source of entropy, black holes, suggesting that the entropy of a black hole should be proportional to its surface area. Stephen Hawking was able to refine Bekenstein’s proposal and determine just how much entropy they have. All black holes together account for almost all the entropy of the universe. It is clear that the entropy of the universe was low in the early days, making it possible for planetary systems to form, galaxies to merge, asteroids to crash, stars to die, and life to flourish. This is because the entropy of the universe has been increasing in one direction, and we never observe the opposite. This is why there is an arrow of time, as we are going from unlikely to more likely states. Eventually, this process will lead to the heat death of the universe, where nothing interesting will ever happen again. This is due to the fact that entropy will reach its highest level, and the universe will be in its most probable state. At this point, the arrow of time will disappear, and it will be impossible to tell the difference between the past and the future.
However, just because maximum entropy has low complexity, this does not mean that low entropy has maximum complexity. It is in the middle where complex structures appear and thrive. Therefore, we should make use of the low entropy we have while we can. With the right tools, we can understand and explore anything, from a cup of tea cooling down to the evolution of the entire universe. To gain access to powerful tools to help us reach our goals, we should check out Brilliant.org. Through this link, the first 200 of you to sign up will get 20% off Brilliant’s annual premium subscription.