The contradiction between the Carnot cycle and the second law of thermodynamics

No problem, it doesn't violate the second law of thermodynamics.

As you say in your narrative "a kind of cyclic action of the heat engine", your process is not cyclical. Clausius of the second law of thermodynamics states that heat cannot be transferred spontaneously and without cost from a cold object to a hot object.

And your doubts are mainly due to a lack of understanding of the isothermal expansion process. In this process you've designed, the real driving isothermal expansion process is that while it appears to be driven by heat, it keeps increasing entropy.

When the working fluid runs out, it cannot be continued, which is also a price. The increase in entropy itself illustrates the second law of thermodynamics. If you still can't figure it out, you can think about it in terms of state parameters. Isothermal expansion before and after the gas although the temperature is equal, if do the ideal gas.

Considering , the internal energy and enthalpy are single-valued functions of temperature, but the entropy is absolutely different, and the increase in entropy is the cost of expansion and heat transfer. In terms of energy grade, mechanical energy.

Higher than thermal energy. Ideal isothermal expansion seems to convert one unit of thermal energy into one unit of mechanical energy, but its entropy increase cannot be ignored.

Personally, I understand it this way, first of all, the four processes of the Carnot cycle I think are actually two processes, namely, isothermal (high temperature) expansion and isothermal (contraction at low temperature) compression. It's just that the two of them are separated into two processes. And for this isothermal compression, you have to meet the temperature of the gas that is higher than the low-temperature heat source (rather a cold source), otherwise how can it be compressed naturally?

Finally, it becomes the same temperature as the low-temperature heat source. There is a problem with the circulation of Nakano, the heat is not completely converted into mechanical energy, and some of it is released to a low-temperature heat source to help it compress itself (e.g. high-temperature water vapor relative to natural air). If it is completely converted into mechanical energy, then after isothermal expansion, the temperature will be equal to the temperature of the low temperature heat source, that is, the work done by the water vapor will become mechanical energy and finally equal to the natural temperature, then the water vapor will become the same level as the water vapor (humidity) in the air.

This raises the question, if the same level how to achieve Carnot's isothermal (low-temperature) compression, air compression itself? In this case, all the heat energy is done, but the volume is the same as that of natural air (this is the effect, because without the effect, the water vapor would become a smaller water vapor). To have this "effect", then you have to compress it with an external force.

The Carnot cycle is thermally efficient, i.e., it is not completely successful. That is, "G......9 "That's it, you're in a cyclical process, not a 100 percent thermal cycle.

Because Carnot's theorem is based on the second law of thermodynamics.

In 1824, the French engineer Sadie Carnot proposed Carnot's theorem. The German Rudolph Clausius and the Englishman Lord Kelvin re-examined Carnot's theorem after the establishment of the first law of thermodynamics, realizing that Carnot's theorem had to be based on a new theorem, the second law of thermodynamics. They came up with the Clausius formulation and the Kelvin formulation in 1850 and 1851, respectively.

On the other hand, isn't the second law explaining the Carnot heat engine?

The description of the second law of thermodynamics is described in a negative sentence, so the more feasible solution is to use the counterproof method (assuming that Carnot's theorem is not true, then the second law of thermodynamics is not true either).

Suppose there is a Carnot heat engine with an efficiency of 40%, it absorbs heat from a high-temperature heat source for 100 J, releases heat from a low-temperature heat source for 60 J, and does work for 40 J in one cycle.

The Carnot cycle is a reversible cycle, and there must be a Carnot refrigerator (called A), which releases 100J of heat to a high-temperature heat source in a cycle, and absorbs 60J of heat from a low-temperature heat source, and requires 40J of work from the outside world.

If Carnot's theorem is not true, there is a heat engine (called B) with an efficiency of 41%, which absorbs 100 J of heat from a high-temperature heat source, releases 59 J of heat from a low-temperature heat source, and does 41 J of work externally in one cycle.

Now put A and B together to work together for a cycle, the result of which is to absorb heat from a low heat source for 1J and do work for 1J externally, without causing other changes. This result violates the second law of thermodynamics.

You can also use a similar method to prove that if the second law of thermodynamics is not true, then Carnot's theorem is not true either.

Because this conclusion is drawn from the second law of thermodynamics.

The first law of thermodynamics mainly objects to thermal processes, whereas the second law of thermodynamics mainly objects to thermal processes or cycles.

The thermal efficiency of the Carnot cycle is satisfactory derived from the second law of thermodynamics.

Of course, it is not violated, and all processes involving thermal phenomena (as is often said in thermal or thermodynamics textbooks, in fact, all macroscopic processes) are irreversible processes, referring to processes that actually occur, not processes that occur under ideal conditions (but cannot actually happen). The ideal Carnot cycle is a reversible process (such a process must take an infinite amount of time for it to occur), but it does not actually exist.

The law of heat is generally true for finite macroscopic processes and can certainly be used to prove Carnot's theorem. Carnot's theorem is a corollary of the first and second laws. The reversible machine does not actually exist, but it can exist theoretically, and the hot law says that all actual macroscopic processes must be irreversible, and does not deny that the ideal process can be a reversible process, and the above expression of the hot law can also be equivalent to the macroscopic reversible process must be an ideal process (which does not actually exist).

The second law of thermodynamics only tells us the law of the actual situation, but does not tell us the law of the ideal situation" The situation you said makes sense at first glance, but you still haven't figured out the logic of the process of proving Carnot's theorem. The behavior of an ideal reversible machine (the law it obeys) is determined by the definition of the reversible process and has nothing to do with the second law itself, which does not deny the existence of a theoretically reversible machine. That being the case, we can assume that there are two reversible machines operating between the same T1 and the same T2 heat source, and this is not a matter of the second law, which is proved to be equal in efficiency before using the Kelvin formulation of the second law.

In addition, I would like to remind the landlord that the expression of the second law can be varied, and the expression "all actual macro processes are irreversible processes" only reflects one aspect of the second law, not the whole picture. For example, "the entropy of adiabatic reversible processes does not change, and the entropy of adiabatic irreversible processes increases" is also a formulation of the second law.

In the process of proving Carnot's theorem, it can only be expressed in Kelvin, and not directly in the expression "all actual macroscopic processes are irreversible", because the object of discussion is not the actual process.

If you still have any questions, please ask questions.

Of course, no, my brother LB said, that is the highest and highest efficiency, which is an ideal situation.

In practice, the efficiency is less than the Carnot efficiency.