What is the Carnot Cycle?

The Carnot cycle is a simple cycle with only two heat sources (a high temperature heat source temperature T1 and a low temperature heat source temperature T2). Since the working substance can only exchange heat with two heat sources, the reversible Carnot cycle consists of two isothermal processes and two adiabatic processes. ^[1]

The Carnot cycle was proposed by the French engineer Nicolas Leonard Sadie Carnot in 1824 to analyze the working process of the heat engine. The Carnot cycle includes four steps: isothermal absorption, adiabatic expansion, isothermal Exothermic, adiabatic compression. That is, the ideal gas absorbs heat isothermally from state 1 (P1, V1, T1) to state 2 (P2, V2, T2), and then adiabatically expands from state 2 to state 3 (P3, V3, T3). Thereafter, it is isothermal from state 3 Heat release to state 4 (P4, V4, T4), and finally adiabatic compression from state 4 back to state 1. This cycle consisting of two isothermal processes and two adiabatic processes is called a Carnot cycle.

Chinese name: Kano cycle
Foreign name: Carnot cycle
Presenter: French engineer Nicolas Leonard Sardy Kano

Presentation time: 1824
Applied discipline: Engineering Thermodynamics
Scope of application: Thermodynamics

Kano Cycle Introduction

The Carnot cycle includes four steps: isothermal heat absorption, in which the system absorbs heat from a high-temperature heat source; adiabatic expansion, where

Kano cycle ts diagram During this process, the system performs work on the environment and the temperature decreases; during isothermal exotherm, the system releases heat to the environment and compresses the volume; during adiabatic compression, the system recovers to its original state. Negative work. The Carnot cycle can be imagined as a quasi-static process working between two constant temperature heat sources. The temperature of the high temperature heat source is T1 and the temperature of the low temperature heat source is T2. This concept was put forward by NLS Carnot in 1824 during a theoretical study of the maximum possible efficiency of a heat engine. Carnot assumes that the working substance only exchanges heat with two constant-temperature heat sources, and there is no loss of heat dissipation, air leakage, and friction. In order to make the process quasi-static, the heat absorption of the working substance from the high temperature heat source should be an isothermal expansion process without temperature difference. Similarly, the heat release to the low temperature heat source should be an isothermal compression process. Due to the limitation of exchanging heat with only two heat sources, it can only be an adiabatic process after leaving the heat sources. The heat engine that makes Carnot cycle is called Carnot heat engine.

Carnot cycle principle

Kano cycle efficiency

According to the theorem of thermodynamics, we can get that the efficiency of Carnot cycle c = 1-T2 / T1.

Kano cycle The efficiency of the Carnot cycle is only related to the thermodynamic temperature of the two heat sources. If the temperature T1 of the high-temperature heat source is higher and the temperature T2 of the low-temperature heat source is lower, the efficiency of the Carnot cycle is higher. Because T1 high-temperature heat source or T2 = 0K (-273 ° C) low-temperature heat source cannot be obtained, the efficiency of the Carnot cycle must be less than 1.

Kano cycle Kano cycle efficiency is consistent

It can be proved that the efficiency of the Carnot cycle is the same with any working substance; it can also be proved that the efficiency of all actual cycles is lower than the efficiency of the Carnot cycle under the same conditions. After determining the efficiency of the Carnot cycle is the highest efficiency limit of all heat engines working between them. Therefore, to improve the efficiency of the heat engine, efforts should be made to increase the temperature of the high-temperature heat source and reduce the temperature of the low-temperature heat source. The low-temperature heat source is usually the surrounding environment. It is difficult and costly to reduce the temperature of the environment. Modern thermal power plants try to raise the temperature of water vapor as much as possible, and use superheated steam to propel the steam turbine, which is based on this principle.

Carnot cycle direction to improve heat engine efficiency

Carnot's theorem clarifies the limitation of the efficiency of the heat engine, and points out the direction of improving the efficiency of the heat engine (increasing T1, reducing T2, reducing irreversible losses such as heat dissipation, air leakage, friction, and making the cycle as close as possible to the Carnot cycle). Becomes the theoretical basis of the heat engine research, the limitation of the heat engine efficiency. The study of the irreversibility of actual thermodynamic processes and the relationship between them led to the establishment of the second law of thermodynamics. Based on Kano's theorem

Kano cycle The absolute thermodynamic temperature scale, which has nothing to do with the temperature measurement substance and temperature measurement attributes, makes the temperature measurement based on an objective basis. In addition, the Carnot cycle and Carnot theorem can be used to study the relationship between surface tension, saturated vapor pressure and temperature, and the electromotive force of reversible batteries. It should also be emphasized that Carnot's abstract and universal theoretical research, aside from specific devices and specific working materials, has been throughout the entire thermodynamic research.

Carnot cycle related formula

A reversible thermodynamic cycle consisting of two constant temperature processes and two adiabatic processes (see Thermodynamic Processes). The Carnot cycle was named after French engineer S. Carnot in the 19th century. The Carnot cycle is divided into positive and negative. In the pressure-capacity ( p - V ) diagram and the temperature-entropy ( T - S ) diagram (see figure), - b - c - d - is a positive Carnot cycle, and - b is a reversible constant-temperature endothermic process. The working medium absorbs heat Q 1 from a high-temperature heat source at the same temperature at temperature T 1; b - c is a reversible adiabatic process, and the working medium temperature is reduced from T 1 to T 2; c - d is a reversible constant-temperature exothermic process. At the temperature T 2, the heat Q 2 is discharged to a low-temperature heat source of the same temperature; d - is a reversible adiabatic process. The temperature of the working medium is raised from T 2 to T 1 to complete a reversible cycle, and net work W is performed externally. The reverse Carnot cycle is opposite to the above-mentioned forward cycle, in the direction of - d - c - b - , so Q 2 is the heat absorbed by the working medium from the low-temperature heat source (commonly referred to as cooling capacity), and Q 1 is the working medium discharged to high temperature. The heat of the heat source, W is the net work of the external input required to complete the reverse cycle.

The thermal economic index of the positive Carnot cycle is expressed by the Carnot cycle thermal efficiency t,

Kano cycle

The thermal economic index of the inverse Carnot cycle is expressed by Carnot refrigeration coefficient or Carnot heating coefficient

Kano cycle

According to the second law of thermodynamics, in all the cycles that work between the same high and low temperature heat source temperatures T 1 and T 2, the thermal efficiency of the Carnot cycle is the highest, which is called Carnot's theorem. Carnot cycle has extremely important theoretical and practical significance. Although it is difficult to achieve a device that works completely in accordance with the Carnot cycle, the Carnot cycle indicates the direction and gives the limit value for improving the thermal efficiency of various cycles.

Kano loop to create background

At the beginning of the 19th century, the role of steam engines in industry and transportation became more and more important, but the theory of various factors that control steam engines to convert heat into mechanical motion has not yet formed. French military engineer S. Carnot (1796-1832) published the book "Thinking about the Power of Fire" in 1824, summarizing his early research results. Carnot took the cause of the imperfection of the heat engine as the starting point of research, and clarified that the conditions for obtaining power from the heat engine can improve the efficiency of the heat engine. Carnot analyzed the basic structure and working process of the steam engine

Kano cycle Aside from all the secondary factors, starting from the ideal cycle, in the form of a universal theory, make a conclusion about the mechanical work by consuming heat. He pointed out that the heat engine must work between a high-temperature heat source and a low-temperature heat source, "wherever there is a temperature difference, power can be generated; conversely, where the force can be consumed to form a temperature difference, it may disrupt the balance of heat and mass. "He constructed an ideal cycle between the heater and the condenser: the cylinder is connected to the heater, the working substance water and saturated steam in the cylinder are the same temperature as the heater, and the steam in the cylinder is expanding so slowly, So that steam and water are in thermal equilibrium throughout the process. The cylinder is then isolated from the heater and the steam adiabatically expands until the temperature drops to the same temperature as the condenser. Then the piston slowly compresses the steam. After a period of time, the cylinder is detached from the condenser and subjected to adiabatic compression until it returns to its original state. This is a cycle consisting of two isothermal processes and two adiabatic processes, which are later called "Kano cycles".

Carnot further proved that the efficiency of all actual heat engines working between the same high temperature heat source and the same low temperature heat source will not be greater than the same heat source based on the principle of conservation of thermal mass and the principle that the perpetual motion machine cannot be made. Efficiency of a reversible Carnot heat engine working between. Carnot concluded from this: The efficiency of an ideal reversible Carnot heat engine has a maximum value, which is determined only by the temperature of the heater and the condenser. All the actual heat engine efficiency is lower than this extreme value.

Kano cycle Kano meaning

Carnot's research has many implications. His work has pointed out the direction for improving the efficiency of thermo-mechanics; his conclusion already contains the basic idea of the second law of thermodynamics, but it is only a hindrance to the concept of thermal mass. Because of Kano's early death, his work was soon forgotten. Later, Carnot's theory was noticed by the French engineer Clappeyron (1799-1864), who re-researched and developed in 1834. Clapeyron expressed the Carnot cycle on a pressure (force) -capacity (product) diagram and proved that the work done by the Carnot heat engine in one cycle is exactly equal to the area enclosed by the cycle curve . Clapeyron's work created conditions for the further development of Kano's theory.