Modern realities involve the widespread use of heat engines. Numerous attempts to replace them with electric motors have so far failed. The problems associated with the accumulation of electricity in autonomous systems are solved with great difficulty.
Still relevant are the problems of technology for the manufacture of electric batteries, taking into account their long-term use. The speed characteristics of electric vehicles are far from those of cars with internal combustion engines.
The first steps in creating hybrid engines can significantly reduce harmful emissions in megacities, solving environmental problems.
A bit of history
The possibility of converting steam energy into energy of motion was known in antiquity. 130 BC: Philosopher Heron of Alexandria presented to the audience a steam toy - eolipil. A sphere filled with steam came into rotation under the influence of jets emanating from it. This prototype of modern steam turbines in those days did not find application.
For many years and centuries the development of the philosopher was considered only a fun toy. In 1629, the Italian D. Branca created an active turbine. The steam set in motion a disk equipped with blades.
From this moment began the rapid development of steam engines.
Thermal machine
The conversion of the internal energy of fuel into the energy of movement of parts of machines and mechanisms is used in thermal machines.
The main parts of the machines: a heater (a system for generating energy from outside), a working fluid (performs a useful action), and a refrigerator.
The heater is designed so that the working fluid has accumulated a sufficient supply of internal energy to perform useful work. The refrigerator removes excess energy.
The main characteristic of efficiency is called the efficiency of thermal machines. This value shows how much of the energy spent on heating is spent on useful work. The higher the efficiency, the more profitable the operation of the machine, but this value cannot exceed 100%.
Calculation of efficiency
Let the heater acquire energy from outside equal to Q 1 . The working fluid did the work A, while the energy given to the refrigerator was Q 2 .
Based on the definition, we calculate the value of the efficiency:
η = A / Q 1 . We take into account that A = Q 1 - Q 2.
Hence, the efficiency of the heat engine, the formula of which is of the form η = (Q 1 - Q 2 ) / Q 1 = 1 - Q 2 / Q 1, allows us to draw the following conclusions:
- Efficiency cannot exceed 1 (or 100%);
- to maximize this value, you must either increase the energy received from the heater, or reduce the energy given to the refrigerator;
- increase in heater energy is achieved by changing the quality of the fuel;
- reducing the energy given to the refrigerator allows you to achieve design features of the engines.
The perfect heat engine
Is it possible to create such an engine, the efficiency of which would be maximum (ideally - equal to 100%)? The French theoretical physicist and talented engineer Sadie Carnot tried to find the answer to this question. In 1824, his theoretical calculations about the processes occurring in gases were published.
The main idea embedded in an ideal machine can be considered as conducting reversible processes with an ideal gas. We start with the expansion of the gas isothermally at a temperature T 1 . The amount of heat required for this is Q 1. After gas without heat transfer expands (adiabatic process). Having reached temperature T 2 , the gas is isothermally compressed, transferring energy Q 2 to the refrigerator. The return of gas to its initial state is adiabatic.
The efficiency of an ideal Carnot heat engine in accurate calculation is equal to the ratio of the temperature difference between the heating and cooling devices to the temperature that the heater has. It looks like this: η = (T 1 - T 2 ) / T 1.
Possible efficiency of a heat engine, the formula of which is of the form: η = 1 - T 2 / T 1 , depends only on the temperature values of the heater and cooler and cannot be more than 100%.
Moreover, this ratio allows us to prove that the efficiency of heat engines can be equal to unity only when the refrigerator reaches absolute zero temperatures. As you know, this value is unattainable.
Carnot's theoretical calculations allow us to determine the maximum efficiency of a heat engine of any design.
The Carnot theorem proved is as follows. An arbitrary heat engine is under no circumstances capable of having a coefficient of performance greater than the same efficiency value of an ideal heat engine.
Problem Solving Example
Example 1. What is the efficiency of an ideal heat engine if the temperature of the heater is 800 ° C and the temperature of the refrigerator is 500 ° C lower?
T 1 = 800 = 1073 , ΔT = 500 = 500 , η -?
Decision:
By definition: η = (T 1 - T 2 ) / T 1.
We are not given the temperature of the refrigerator, but ∆T = (T 1 - T 2 ), hence:
η = ΔT / T 1 = 500 K / 1073 K = 0.46.
Answer: Efficiency = 46%.
Example 2. Determine the efficiency of an ideal heat engine if the useful work of 650 J is achieved due to the energy gained from one kilojoule of heater. What is the temperature of the heater of the heat engine if the temperature of the cooler is 400 K?
Q 1 = 1 kJ = 1000 J, A = 650 J, T 2 = 400 K, η -?, T 1 =?
Decision:
In this problem we are talking about a thermal installation, the efficiency of which can be calculated by the formula:
η = A / Q 1.
To determine the temperature of the heater, we use the efficiency formula of an ideal heat engine:
η = (T 1 - T 2 ) / T 1 = 1 - T 2 / T 1.
Having completed the mathematical transformations, we get:
T 1 = T 2 / (1- η).
T 1 = T 2 / (1- A / Q 1 ).
We calculate:
η = 650 J / 1000 J = 0.65.
T 1 = 400 K / (1 - 650 J / 1000 J) = 1142.8 K.
Answer: η = 65%, T 1 = 1142.8 K.
Real conditions
The ideal heat engine designed with ideal processes in mind. Work is done only in isothermal processes, its value is defined as the area limited by the schedule of the Carnot cycle.
In fact, it is impossible to create conditions for the process of changing the state of the gas without the accompanying temperature changes. There are no materials that would preclude heat exchange with surrounding objects. The adiabatic process becomes impossible. In the case of heat transfer, the gas temperature must necessarily change.
The efficiency of heat engines created in real conditions is significantly different from the efficiency of ideal engines. Note that the processes in real engines are so fast that the variation of the internal thermal energy of the working substance in the process of changing its volume cannot be compensated by the influx of heat from the heater and the return to the refrigerator.
Other heat engines
Real engines run on different cycles:
- Otto cycle: the process with an unchanged volume changes adiabatic, creating a closed cycle;
- Diesel cycle: isobar, adiabat, isochore, adiabat;
- gas turbine: the process that occurs at constant pressure changes to adiabatic, closes the cycle.
It is not possible to create equilibrium processes in real engines (to bring them closer to ideal) in modern technology. The efficiency of thermal machines is much lower, even taking into account the same temperature conditions as in an ideal thermal installation.
But you should not reduce the role of the calculated formula for the efficiency of the Carnot cycle, since it is it that becomes the reference point in the process of working to increase the efficiency of real engines.
Ways to change efficiency
Comparing the ideal and real heat engines, it is worth noting that the temperature of the refrigerator of the latter cannot be any. Typically, the atmosphere is considered a refrigerator. To take the temperature of the atmosphere is possible only in approximate calculations. Experience shows that the temperature of the cooler is equal to the temperature of the exhaust gases in engines of gases, as is the case in internal combustion engines (abbreviated as ICE).
ICE is the most common heat engine in our world. The efficiency of the heat engine in this case depends on the temperature created by the burning fuel. A significant difference between ICE and steam engines is the fusion of the functions of the heater and the working fluid of the device in the air-fuel mixture. By burning, the mixture creates pressure on the moving parts of the engine.
The temperature rise of the working gases is achieved, significantly changing the properties of the fuel. Unfortunately, it is impossible to do this unlimitedly. Any material of which the engine’s combustion chamber is made has its own melting point. The heat resistance of such materials is the main characteristic of the engine, as well as the ability to significantly affect the efficiency.
Engine Efficiency Values
If we consider a steam turbine, the temperature of the working steam at the inlet of which is 800 K, and the exhaust gas is 300 K, then the efficiency of this machine is 62%. In reality, this value does not exceed 40%. This decrease occurs due to heat loss during heating of the turbine housing.
The highest value of the efficiency of internal combustion engines does not exceed 44%. Raising this value is a matter of the near future. Changing the properties of materials, fuel is a problem that the best minds of mankind are working on.