In the theoretical model heat engine three bodies are considered: heater, working body And fridge.
Heater - a thermal reservoir (large body), the temperature of which is constant.
In each cycle of engine operation, the working fluid receives a certain amount of heat from the heater, expands and performs mechanical work. The transfer of part of the energy received from the heater to the refrigerator is necessary to return the working fluid to its original state.
Since the model assumes that the temperature of the heater and refrigerator does not change during the operation of the heat engine, then at the end of the cycle: heating-expansion-cooling-compression of the working fluid, it is considered that the machine returns to its original state.
For each cycle, based on the first law of thermodynamics, we can write that the amount of heat Q load received from the heater, amount of heat | Q cool |, given to the refrigerator, and the work done by the working body A are related to each other by:
A = Q load – | Q cold|.
In real technical devices, which are called heat engines, the working fluid is heated by the heat released during the combustion of fuel. Yes, in steam turbine power plant heater is a furnace with hot coal. In the engine internal combustion(ICE) combustion products can be considered a heater, and excess air can be considered a working fluid. As a refrigerator, they use the air of the atmosphere or water from natural sources.
Efficiency of a heat engine (machine)
Coefficient useful action heat engine (efficiency) is the ratio of the work done by the engine to the amount of heat received from the heater:
The efficiency of any heat engine is less than one and is expressed as a percentage. The impossibility of converting the entire amount of heat received from the heater into mechanical work is the price to pay for the need to organize a cyclic process and follows from the second law of thermodynamics.
In real heat engines, the efficiency is determined by the experimental mechanical power N engine and the amount of fuel burned per unit time. So, if in time t mass fuel burned m and specific heat of combustion q, That
For Vehicle the reference characteristic is often the volume V fuel burned on the way s at mechanical engine power N and at speed. In this case, taking into account the density r of the fuel, we can write a formula for calculating the efficiency:
Second law of thermodynamics
There are several formulations second law of thermodynamics. One of them says that a heat engine is impossible, which would do work only due to a heat source, i.e. without refrigerator. The world ocean could serve for it as a practically inexhaustible source of internal energy (Wilhelm Friedrich Ostwald, 1901).
Other formulations of the second law of thermodynamics are equivalent to this one.
Clausius' formulation(1850): a process is impossible in which heat would spontaneously transfer from less heated bodies to more heated bodies.
Thomson's formulation(1851): a circular process is impossible, the only result of which would be the production of work by reducing the internal energy of the thermal reservoir.
Clausius' formulation(1865): all spontaneous processes in a closed non-equilibrium system occur in such a direction in which the entropy of the system increases; in a state of thermal equilibrium, it is maximum and constant.
Boltzmann's formulation(1877): a closed system of many particles spontaneously passes from a more ordered state to a less ordered one. The spontaneous exit of the system from the equilibrium position is impossible. Boltzmann introduced a quantitative measure of disorder in a system consisting of many bodies - entropy.
Efficiency of a heat engine with an ideal gas as a working fluid
If the model of the working fluid in the heat engine is given (for example, an ideal gas), then it is possible to calculate the change thermodynamic parameters working fluid during expansion and contraction. This allows you to calculate the efficiency of a heat engine based on the laws of thermodynamics.
The figure shows the cycles for which the efficiency can be calculated if the working fluid is an ideal gas and the parameters are set at the points of transition of one thermodynamic process to another.
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Isobaric-isochoric |
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Isochoric-adiabatic |
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Isobaric-adiabatic |
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Isobaric-isochoric-isothermal |
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Isobaric-isochoric-linear |
Carnot cycle. Efficiency of an ideal heat engine
The highest efficiency at given heater temperatures T heating and refrigerator T cold has a heat engine where the working fluid expands and contracts along Carnot cycle(Fig. 2), the graph of which consists of two isotherms (2–3 and 4–1) and two adiabats (3–4 and 1–2).
Carnot's theorem proves that the efficiency of such an engine does not depend on the working fluid used, so it can be calculated using the thermodynamic relations for an ideal gas:
Environmental consequences of heat engines
The intensive use of heat engines in transport and energy (thermal and nuclear power plants) significantly affects the Earth's biosphere. Although there are scientific disputes about the mechanisms of the influence of human activity on the Earth's climate, many scientists point out the factors due to which such an influence can occur:
- Greenhouse effect– increase in the concentration of carbon dioxide (combustion product in the heaters of thermal machines) in the atmosphere. Carbon dioxide transmits visible and ultraviolet radiation from the Sun, but absorbs infrared radiation from the Earth. This leads to an increase in the temperature of the lower layers of the atmosphere, an increase in hurricane winds and global ice melting.
- Direct influence of poisonous exhaust gases on wildlife (carcinogens, smog, acid rain from by-products combustion).
- Destruction of the ozone layer during aircraft flights and rocket launches. The ozone of the upper atmosphere protects all life on Earth from excess ultraviolet radiation from the Sun.
The way out of the emerging ecological crisis lies in increasing thermal efficiency engines (the efficiency of modern heat engines rarely exceeds 30%); use serviceable engines and neutralizers of harmful exhaust gases; use alternative sources energy ( solar panels and heaters) and alternative means of transport (bicycles, etc.).
heat engine- an engine in which the internal energy of the fuel that burns is converted into mechanical work.
Any heat engine consists of three main parts: heater, working body(gas, liquid, etc.) and refrigerator. The operation of the engine is based on a cyclic process (this is a process in which the system returns to its original state).
Carnot cycle
In heat engines, they strive to achieve the most complete conversion of thermal energy into mechanical energy. Maximum efficiency.
The figure shows the cycles used in a gasoline carburetor engine and in diesel engine. In both cases, the working fluid is a mixture of gasoline vapors or diesel fuel with air. The cycle of a carburetor internal combustion engine consists of two isochores (1–2, 3–4) and two adiabats (2–3, 4–1). A diesel internal combustion engine operates on a cycle consisting of two adiabats (1–2, 3–4), one isobar (2–3), and one isochore (4–1). The real efficiency for a carburetor engine is about 30%, for a diesel engine - about 40%.
The French physicist S. Carnot developed the work of an ideal heat engine. The working part of a Carnot engine can be thought of as a piston in a cylinder filled with gas. Since the Carnot engine - machine is purely theoretical, that is, ideal, the friction forces between the piston and the cylinder and the heat losses are assumed to be zero. mechanical work is maximum if the working fluid performs a cycle consisting of two isotherms and two adiabats. This cycle is called Carnot cycle.
section 1-2: the gas receives an amount of heat Q 1 from the heater and expands isothermally at a temperature T 1
section 2-3: the gas expands adiabatically, the temperature decreases to the refrigerator temperature T 2
section 3-4: the gas is exothermically compressed, while it gives the refrigerator the amount of heat Q 2
section 4-1: the gas is compressed adiabatically until its temperature rises to T 1 .
The work performed by the working body is the area of the resulting figure 1234.
Such an engine functions as follows:
1. First, the cylinder comes into contact with a hot reservoir, and the ideal gas expands at a constant temperature. During this phase, the gas receives some heat from the hot reservoir.
2. The cylinder is then surrounded by perfect thermal insulation, whereby the amount of heat available to the gas is conserved and the gas continues to expand until its temperature drops to that of the cold thermal reservoir.
3. In the third phase, the thermal insulation is removed, and the gas in the cylinder, being in contact with the cold reservoir, is compressed, while giving off part of the heat to the cold reservoir.
4. When the compression reaches a certain point, the cylinder is again surrounded by thermal insulation, and the gas is compressed by raising the piston until its temperature equals that of the hot reservoir. After that, the thermal insulation is removed and the cycle repeats again from the first phase.
When we talk about the reversibility of processes, it should be taken into account that this is some kind of idealization. All real processes are irreversible, and therefore the cycles they work on thermal machines, are also irreversible, and therefore nonequilibrium. However, to simplify the quantitative estimates of such cycles, it is necessary to consider them as equilibrium, that is, as if they consisted only of equilibrium processes. This is required by the well-developed apparatus of classical thermodynamics.
famous cycle ideal engine Carnot is considered to be an equilibrium inverse circular process. In real conditions, any cycle cannot be ideal, since there are losses. It takes place between two heat sources constant temperatures at the heat sink T 1 and heat receiver T 2, as well as the working fluid, which is taken as an ideal gas (Fig. 3.1).
Rice. 3.1. Heat engine cycle
We believe that T 1 > T 2 and heat removal from the heat sink and heat supply to the heat sink do not affect their temperatures, T1 And T2 remain constant. Let us denote the parameters of the gas at the left extreme position heat engine piston: pressure - R 1 volume - V 1, temperature T 1 . This is point 1 on the graph on the axes P-V. At this moment, the gas (working fluid) interacts with the heat source, the temperature of which is also T 1 . As the piston moves to the right, the gas pressure in the cylinder decreases and the volume increases. This will continue until the piston arrives at the position determined by point 2, where the parameters of the working fluid (gas) will take on the values P 2 , V 2 , T2. The temperature at this point remains unchanged, since the temperature of the gas and the heat sink is the same during the transition of the piston from point 1 to point 2 (expansion). Such a process in which T does not change is called isothermal, and curve 1–2 is called isotherm. In this process, heat is transferred from the heat source to the working fluid. Q1.
At point 2, the cylinder is completely isolated from external environment(no heat transfer) and further movement piston to the right, a decrease in pressure and an increase in volume occurs along a curve 2-3, which is called adiabatic(process without heat exchange with the environment). When the piston moves to the extreme right position (point 3), the expansion process will end and the parameters will have the values P 3 , V 3 , and the temperature will become equal to the temperature of the heat sink T 2. With this position of the piston, the insulation of the working fluid is reduced and it interacts with the heat sink. If we now increase the pressure on the piston, then it will move to the left at a constant temperature T 2(compression). Hence, this compression process will be isothermal. In this process, heat Q2 will pass from the working fluid to the heat sink. The piston, moving to the left, will come to point 4 with the parameters P4, V4 and T 2 where the working fluid is again isolated from the environment. Further compression occurs along a 4–1 adiabat with an increase in temperature. At point 1, compression ends at the parameters of the working fluid P 1 , V 1 , T 1. The piston returned to its original state. At point 1, the isolation of the working fluid from the external environment is removed and the cycle is repeated.
Efficiency of an ideal Carnot engine.
Problem 15.1.1. Figures 1, 2 and 3 show graphs of three cyclic processes that occur with an ideal gas. In which of these processes did the gas complete a cycle positive work?
Problem 15.1.3. Ideal gas, having completed some cyclic process, returned to the initial state. The total amount of heat received by the gas during the entire process (the difference between the amount of heat received from the heater and given to the refrigerator) is equal to . What is the work done by the gas during the cycle?
Problem 15.1.5. 
The figure shows a graph of the cyclic process that occurs with gas. The process parameters are shown on the graph. What work is done by the gas during this cyclic process?
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Problem 15.1.6. 
An ideal gas performs a cyclic process, the graph in coordinates is shown in the figure. It is known that process 2–3 is isochoric; in processes 1–2 and 3–1, the gas did work and, respectively. What is the work done by the gas during the cycle?
Problem 15.1.7. The efficiency of a heat engine shows
Problem 15.1.8. During the cycle, the heat engine receives an amount of heat from the heater and gives the amount of heat to the refrigerator. What is the formula for determining the efficiency of an engine?
Problem 15.1.10. Ideal efficiency a heat engine operating according to the Carnot cycle is 50%. The temperature of the heater is doubled, the temperature of the refrigerator does not change. What will be the efficiency of the resulting ideal heat engine?
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