The problem of heat engine! ! !

A heat engine does not just convert energy into mechanical energy. Heat engine refers to a machine that absorbs heat from a high-temperature heat source and releases heat to a low-temperature heat source after doing external work. The efficiency calculation of heat engine is not as simple as what is said upstairs. Carnot cycle is the most efficient of all heat engines. Therefore, even without friction and heat loss, the efficiency of the heat engine cannot be higher than that of the Carnot cycle under the same conditions. See below for the principle of Carnot cycle.

Carnot cycle was put forward by French engineer Nicolas Leonard sadi carnot in 1824 to analyze the working process of heat engines. Carnot cycle includes four steps: isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression. That is, the ideal gas expands isothermally from state 1(P 1, V 1, T 1) to state 2(P2, V2, T2), then adiabatically expands from state 2 to state 3(P3, V3, T3), and then compresses isothermally from state 3 to state 4. This cycle consisting of two isothermal processes and two adiabatic processes is called Carnot cycle. brief introduction

Carnot cycle includes four steps: isothermal expansion, in which the system absorbs heat from the environment; Adiabatic expansion, here

Carnot cycle

In this process, the system does work for the environment; Isothermal compression, where the system releases heat to the environment; Adiabatic compression, the system returns to its original state, and the system does negative work to the environment. Carnot cycle can be imagined as a quasi-static process between work and two constant temperature heat sources. The temperature of the high-temperature heat source is T 1, and the temperature of the low-temperature heat source is T2. This concept was put forward by N.L.S Cano in 1824 when he made a theoretical study on the maximum energy efficiency of heat engines. Carnot assumes that the working medium only exchanges heat with two constant temperature heat sources, and there is no loss such as heat dissipation, air leakage and friction. In order to make the process quasi-static, the heat absorption of high-temperature heat source should be an isothermal expansion process without temperature difference, and the heat release of low-temperature heat source should be an isothermal compression process. Because it is only limited to exchange heat with two heat sources, it can only be an adiabatic process after leaving the heat source. Carnot cycle heat engine is called Carnot heat engine [1].

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principle

Efficiency of Carnot cycle

The efficiency η c = 1-T2/t 1 of Carnot cycle can be obtained through the relevant theorems of thermodynamics, from which it can be seen that

Carnot cycle

The efficiency of Carnot cycle is only related to the thermodynamic temperatures of two heat sources. If the temperature of high-temperature heat source T 1 is higher and the temperature of low-temperature heat source T2 is lower, the efficiency of Carnot cycle will be higher. Because there is no high-temperature heat source of T 1→∞ or low-temperature heat source of T2=0K(-273℃), the efficiency of Carnot cycle is necessarily less than 1.

Carnot cycle of any working medium has the same efficiency.

It can be proved that the efficiency of Carnot cycle is consistent with that of any working medium; It can also be proved that the efficiency of all practical cycles is lower than that of Carnot cycle under the same conditions, that is, if the temperatures of high-temperature heat source and low-temperature heat source are determined, the efficiency of Carnot cycle is the highest efficiency limit of all heat engines working between them. Therefore, in order to improve the efficiency of the heat engine, we should try our best to raise the temperature of the high-temperature heat source and lower the temperature of the low-temperature heat source, which is usually the surrounding environment. It is difficult and costly to reduce the ambient temperature, which is not a good way. It is for this reason that modern thermal power plants try to raise the temperature of steam and use superheated steam to drive steam turbines.

The direction of improving the efficiency of heat engine

Carnot theorem defines the limit of heat engine efficiency and points out the direction of improving heat engine efficiency (increasing T 1, reducing T3, reducing irreversible losses such as heat dissipation, air leakage and friction, and making the cycle as close as possible to Carnot cycle). It becomes the theoretical basis of heat engine research and the limit of heat engine efficiency. The research on the irreversibility of actual thermodynamic process and its relationship leads to the establishment of the second law of thermodynamics. Based on Carnot theorem.

Carnot cycle

The absolute thermodynamic temperature scale, which has nothing to do with the temperature measuring materials and properties, makes the temperature measurement based on an objective basis. In addition, the relationship between surface tension, saturated vapor pressure and temperature, as well as the electromotive force of reversible batteries can be studied by applying Carnot cycle and Carnot theorem. It should also be emphasized that Carnot's abstract and universal theoretical research, which puts aside specific devices and specific working fluids, runs through the whole study of thermodynamics.

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Create background

/kloc-At the beginning of the 9th century, steam engines played an increasingly important role in industry and transportation, but the theory that steam engines converted heat into mechanical motion to control various factors was not formed. French military engineer saadi? S. Carnot (1796— 1832) published the book Thinking about the Power of Fire in 1824, summarizing his early research results. Carnot's starting point is to find out the reasons for the imperfection of the heat engine, and to clarify the conditions for obtaining power from the heat engine can improve the efficiency of the heat engine. Cano analyzed the basic structure and working process of the steam engine.

Carnot cycle

Putting aside all secondary factors, starting from the ideal cycle, in the form of general theory, a conclusion about consuming heat and getting mechanical work is drawn. He pointed out that the heat engine must work between high temperature heat source and low temperature heat source. "Where there is a temperature difference, power can be generated; On the contrary, where this force can be consumed, a temperature difference can be formed, which may destroy the balance between heat and mass. " He constructed an ideal cycle between the heater and the condenser: the cylinder is connected with the heater, and the working fluid water and saturated steam in the cylinder are at the same temperature as the heater. The steam in the cylinder expands so slowly that the steam and water are in thermal balance during the whole process. Then the cylinder is isolated from the heater, and the steam expands adiabatically until the temperature drops to the same as that of the condenser. Then the piston slowly compresses the steam, and after a period of time, the cylinder is separated from the condenser for adiabatic compression until it returns to its original state. This is a cycle consisting of two isothermal processes and two adiabatic processes, which was later called "Carnot cycle".

According to the idea of conservation of heat and mass and the principle that perpetual motion machines cannot be manufactured, Carnot further proves that the efficiency of all practical heat engines working between high-temperature heat sources and low-temperature heat sources at the same temperature will not be greater than that of reversible Carnot heat engines working between the same heat sources. Carnot deduced that the efficiency of the ideal reversible Carnot heat engine has a maximum value, which is only determined by the temperature of the heater and condenser, and the efficiency of all practical heat engines is lower than this maximum value.

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Kano's meaning

Cano's research has many meanings. His work pointed out the direction for improving the efficiency of heat engine; His conclusion already contains the basic idea of the second law of thermodynamics, but he failed to fully explore the final answer to the question because of the concept of heat and mass. Because of Kano's untimely death, his works were soon forgotten. Later, due to the re-study and development of French engineer Claperon (B.P.E.Clapeyron, 1799- 1864) in 1834, Kano's theory was noticed by people. Clapper used "pressure (force)-volume (product) diagram" to represent Carnot cycle, and proved that the work done by Carnot heat engine in a cycle is exactly equal to the area enclosed by the cycle curve. Claperon's work created conditions for the further development of Carnot's theory.