Shulou(Shulou.com)11/24 Report--

Carnot cycle is an unavoidable hurdle when learning the second law of thermodynamics. I'm sure you can count the efficiency of this cycle clean! But you must have wondered why Cano found this ideal cycle in a flash, and it was the most efficient cycle.

Without laying the groundwork for the background of Cano's time, it will be difficult to understand why Cano has such a magical idea in mind.

That is the period when the thermal mass hypothesis is dominant. To put it simply, the thermal mass is considered to be a special component of the object, and the amount of heat contained in the object is reflected in the difference between the hot and cold of the object. In fact, it is not difficult to understand the idea that what you contain will reveal the nature of your appearance.

In addition, heat and mass will flow between objects at different temperatures and have the characteristics of conservation in the process of flow. After all, people's obsession with conserved quantities has never stopped since ancient times. With regard to the theory of heat and mass, you can know the above two core ideas.

Another background is that all kinds of machines have been widely used because of the industrial revolution. How to improve the efficiency of machines is a very realistic problem.

Machines are not just steam engines, but water-driven turbines also count. Cano's father is very knowledgeable about improving the efficiency of hydraulic turbines. He believes that the design of an ideal turbine should not have the slightest loss (such as not causing a splash or whirlpool, etc.). The current must be allowed to push the device smoothly. If the water rushes down like a waterfall to push the turbine, it looks quite spectacular, but the turbine is not very efficient.

The water should flow smoothly in the water wheel. 02 Carnot's ideal heat engine tiger father has no dog son. If there is anything remarkable about Carnot's solution, it is that he looks for the universal law behind the phenomenon, which is to see the essence through the phenomenon.

Carnot first made clear the working principle of the heat engine-whether the heat engine works or not does not depend on how much heat is contained in the working medium, but on the flow of heat and mass in the working medium!

It's not surprising to have this idea, because it's a complete analogy to how a turbine works-even if it gives you water in the Pacific, can it drive the turbine if it doesn't flow? So running water is the key, and it is not surprising to transfer to the heat engine and require the flow of heat and mass.

As for how to make the heat and mass flow, can't you just get two objects with different temperatures? Because when objects with different temperatures come into contact with each other, heat will flow from high-temperature objects to low-temperature objects. You see, this is so similar to the flow of water from high to low.

As the flow of heat and mass in the working medium will be accompanied by the change of the volume of the working medium, the common phenomenon of thermal expansion and cold contraction is popular. It is the change of the working medium volume that can promote the movement of the piston in the heat engine, thus making the heat engine work.

While the phenomenon of thermal expansion and cold contraction is not an exclusive phenomenon of gas, it will occur in both liquids and solids, so Carnot is acutely aware that whether the heat engine works has nothing to do with the selected working medium, it is not picky!

As for the efficiency of the heat engine, Cano believes that the ideal heat engine should not be lost, which is deeply influenced by his father's design concept of the ideal machine. For the heat engine, in addition to all kinds of mechanical friction, its loss comes from the temperature change of the working medium, which is not caused by the volume change of the working medium.

It's a little tongue-twisting, isn't it? In fact, it is easy to understand, because a change in temperature means that heat and mass will flow, which makes it possible for the heat engine to work; on the other hand, if the temperature changes, but the heat engine does not work, then the change process is a loss for the heat engine!

Cano points out that there are two ways to change the temperature of a working medium-changing its volume and coming into contact with objects at different temperatures (he rigorously points out that temperature changes caused by chemical reactions are not taken into account). Among them, only the volume change will make the heat engine work, and the latter way belongs to the loss in Cano's eyes! So Cano's ideal heat engine does not allow objects with different temperatures to come into contact.

Therefore, after figuring out the nature of the heat engine, in order to pursue the maximum efficiency, Carnot abstracted the ideal heat engine into such a simplified model: the gas (working medium) is enclosed in a cylinder. There is a piston that can move back and forth without friction in the cylinder, and there is a constant temperature high temperature heat source and a constant temperature low temperature heat source outside the cylinder.

Why the heat engine model 03 thinks of the Carnot cycle is easy to understand, which is to make the working medium change back and forth between high temperature and low temperature, so that the heat engine can work continuously. As for how to complete the cycle, Cano has proposed the most efficient standard-to avoid contact with objects at different temperatures!

1. You have to contact the cylinder with excellent thermal conductivity with the high temperature heat source A so that the gas in it reaches the same temperature as the high temperature heat source A. this is the starting point of the cycle, assuming that the piston is now in the cd position.

2. Then, on the premise of keeping the cylinder in contact with the high temperature heat source A, move the piston to increase the volume of the gas, because this enables the gas to absorb the heat and mass from the high temperature heat source A. Assume that at the end of this process, the piston is in the ef position. Obviously, the heat and mass flow produced here is accomplished by a change in the volume of the gas, so there is no loss as Carnot said.

Now that the gas in the column has absorbed the heat and mass from the high temperature heat source A, it needs to be transferred to the low temperature heat source B. But now that the temperature of the gas is in a state of high temperature, it should not be in direct contact with the low temperature heat source B, otherwise it will produce what Carnot called the loss, thus making the efficiency of the heat engine lower. If it were you, what plan would you come up with?

Or the gas temperature in the column can only be changed by changing the volume! At this point, the gas temperature needs to be lowered, so the cylinder can no longer be in contact with high temperature heat source A. At the same time, in order to avoid the flow of heat and mass to other objects (such as the air outside the column), the cylinder needs to be wrapped so that it does not have heat transfer, that is, the gas inside the column is adiabatic.

In this case, if you continue to increase the volume of the gas, the temperature of the gas will decrease. When its temperature drops to the same time as the temperature of the low temperature heat source B stops expanding, it is assumed that the piston has reached the gh position.

4. Then you can bring the unwrapped cylinder into contact with low temperature heat source B. Because the temperature of the gas inside the cylinder is the same as that of the low temperature heat source B, the heat mass previously absorbed from the high temperature heat source A can be transferred to the low temperature heat source B only by compressing the volume of the gas. When the piston returns to the cd position, all the previously absorbed heat and mass is transferred to the low temperature heat source.

5. The last step is easy to understand. In order for the heat engine to work continuously, the gas must return to the high temperature state to start the next cycle. Without loss, be sure to disconnect the cylinder from low temperature heat source B and wrap it so that the gas inside it is adiabatic; then continue to compress the gas to heat it up until the temperature of the gas is equal to that of high temperature heat source A, assuming that the piston is in the ik position.

6. Then the next cycle begins. The unwrapped cylinder is contacted with the high temperature heat source A, and the piston is moved from the position ik to the position ef. The heat and mass in the high temperature heat source is absorbed by increasing the volume of the gas. Then follow 3-4-5-6-3-4-5-6. This order goes on and on.

These are the four steps of the Carnot cycle-isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression.

04 reversible is the key to the ideal heat engine envisioned by Carnot, which must be able to run in the opposite direction accurately. Because the ideal heat engine does not have all kinds of losses, it means that the heat engine absorbs a certain amount of heat mass Q from the high temperature heat source An and transfers it to the low temperature heat source B and outputs a certain amount of work W; in turn, the outside world inputs the same work W to the heat engine. The heat engine can transfer how much heat mass Q from the low temperature heat source B to the high temperature heat source A.

An ideal heat engine with forward operation VS an ideal heat engine with reverse operation you can make an analogy that a heat engine with forward operation is a hydraulic turbine, which uses the potential energy of water to do external work. The heat engine running in the opposite direction is the water pump, and the outside world can pump water from the low to the high by doing work on it. Without considering any loss, if all the output work of the hydraulic turbine is applied to the pump, the pump will be able to pump so much water from the bottom to the high place intact.

This reversibility is the logical support necessary to demonstrate that the ideal heat engine has the highest efficiency in all heat engines working between two fixed heat sources. Although Cano had envisioned an ideal heat engine, which must be the most efficient, he still had to demonstrate it logically.

Suppose there is any other heat engine that is better than this ideal heat engine, that is, the device can use the same heat mass to generate more work, that is, there is a relationship in the following figure.

Non-ideal heat engine VS ideal heat engine if this heat engine is combined with Carnot's ideal heat engine, then part of the output work of the heat engine can be used in the reverse operation of the ideal heat engine, thus returning the same amount of heat mass from the low temperature heat source to the high temperature heat source. At the same time, the rest of the output work is, this result is greater than zero!

The output work of the combined heat engine is greater than zero, but there is no need for heat and mass flow, which means that in a cycle, we have output work out of nothing! If the cycle continues, this combination of machines can continuously output more work without using the flowing heat and mass, isn't it a perpetual motion machine? Therefore, it is not assumed that among all the heat engines working between two fixed heat sources, no heat engine is more efficient than the ideal heat engine.

In the same way, you can use another ideal heat engine to talk about things. If there are two ideal heat engines working between two fixed heat sources, you first use the A heat engine to drive the reverse operation of the B heat engine, it is inevitable that the efficiency of An is not higher than that of B. On the other hand, you can still use the second heat engine to drive the reverse operation of the A heat engine? Then you will come to the conclusion that the efficiency of B is not higher than that of A.

Taken together, you will come to the conclusion that all ideal heat engines operating between two fixed heat sources must have the same efficiency! This also confirms Carnot's point of view: the efficiency of the ideal heat engine has nothing to do with the working medium!

This is the first expression of the famous Carnot theorem. However, we also regret to point out that although this conclusion is correct, there is something wrong with Carnot's proof basis, and the thermal mass hypothesis must come out and take the blame! It was not until more than 20 years later that Joule put forward the idea of thermal work transformation, and the Carnot theorem was proved correctly by Clausius.

How to achieve reversibility since reversibility is so important to Carnot's ideal heat engine, does it mean that as long as all kinds of friction are ignored in the cycle of the heat engine, then the cycle process is reversible?

In fact, it is not. After all, the heat engine absorbs heat mass from the high temperature heat source and transfers it to the low temperature heat source and does work, which means that there is an obvious difference in temperature between the high temperature heat source and the low temperature heat source, which cannot make a reversible operation without changing any conditions.

So Cano put forward this approach: you can imagine that there are a series of heat sources B, C, D between high-temperature heat source An and low-temperature heat source Z, so that A to B, B to C, C to D. The temperature differences between them are infinitely small. Heat and mass from high temperature heat source A through B, C, D. It is gradually transferred to the low-temperature heat source Z, and the heat engine works with maximum efficiency in each small process. Since the reverse operation can be done in each small process, it can be reversed for the whole loop.

Yo, the reversible process that Carnot envisioned is an ideal limit case!

This article comes from the official account of Wechat: ID:gh_8bb6a1229347.

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