Modern realities involve the widespread operation of heat engines. Numerous attempts to replace them with electric motors have so far failed. 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 power accumulators, taking into account their long-term use. Speed characteristics electric vehicles are far from those of cars on engines internal combustion.
First steps to create hybrid engines can significantly reduce harmful emissions in megacities, solving environmental problems.
A bit of history
The possibility of converting steam energy into motion energy was known in antiquity. 130 BC: Philosopher Heron of Alexandria presented to the audience a steam toy - aeolipil. A sphere filled with steam began to rotate under the action of jets emanating from it. This prototype of modern steam turbines at that time 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. Branchi created an active turbine. Steam set in motion a disk equipped with blades.
From that moment began the rapid development steam engines.
heat engine
The conversion of fuel into energy for the movement of parts of machines and mechanisms is used in heat engines.
The main parts of machines: a heater (a system for obtaining energy from outside), a working fluid (performs a useful action), a refrigerator.
The heater is designed to ensure 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 heat engines. This value shows what part of the energy spent on heating is spent on doing useful work. The higher the efficiency, the more profitable job machine, but this value cannot exceed 100%.
Efficiency calculation
Let the heater acquire from outside the energy equal to Q 1 . working body did work A, while the energy given to the refrigerator was Q 2 .
Based on the definition, we calculate the efficiency:
η= A / Q 1 . We take into account that A \u003d Q 1 - Q 2.
From here thermal efficiency machine, the formula of which is η \u003d (Q 1 - Q 2) / Q 1 \u003d 1 - Q 2 / Q 1, allows us to draw the following conclusions:
- Efficiency cannot exceed 1 (or 100%);
- to maximize this value, either an increase in the energy received from the heater or a decrease in the energy given to the refrigerator is necessary;
- an increase in the energy of the heater is achieved by changing the quality of the fuel;
- reducing the energy given to the refrigerator, allow you to achieve design features engines.
Ideal heat engine
Is it possible to create such an engine, coefficient useful action which would be the maximum (ideally - equal to 100%)? The French theoretical physicist and talented engineer Sadi Carnot tried to find the answer to this question. In 1824, his theoretical calculations about the processes occurring in gases were made public.
The main idea behind perfect car, we can consider carrying out 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 the gas expands without heat exchange. Having reached the temperature T 2, the gas is compressed isothermally, transferring the energy Q 2 to the refrigerator. The return of the gas to its original state is adiabatic.
Ideal efficiency heat engine Carnot, when accurately calculated, 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.
The possible efficiency of a heat engine, the formula of which is: η= 1 - T 2 / T 1 , depends only on the temperature 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 temperatures. As you know, this value is unattainable.
Carnot's theoretical calculations make it possible to determine the maximum efficiency of a heat engine of any design.
The theorem proved by Carnot is as follows. Free heat engine under no circumstances is it capable of having a coefficient of efficiency greater than the similar value of the efficiency of an ideal heat engine.
Example of problem solving
Example 1 What is the efficiency of an ideal heat engine if the heater temperature is 800°C and the refrigerator temperature is 500°C lower?
T 1 \u003d 800 o C \u003d 1073 K, ∆T \u003d 500 o C \u003d 500 K, η -?
By definition: η=(T 1 - T 2)/ T 1.
We are not given the temperature of the refrigerator, but ∆T = (T 1 - T 2), from here:
η \u003d ∆T / T 1 \u003d 500 K / 1073 K \u003d 0.46.
Answer: efficiency = 46%.
Example 2 Determine the efficiency of an ideal heat engine if 650 J of useful work is performed due to the acquired one kilojoule of heater energy. What is the temperature of the heat engine heater if the coolant temperature is 400 K?
Q 1 \u003d 1 kJ \u003d 1000 J, A \u003d 650 J, T 2 \u003d 400 K, η -?, T 1 \u003d?
In this problem, we are talking about a thermal installation, the efficiency of which can be calculated by the formula:
To determine the temperature of the heater, we use the formula for the efficiency of an ideal heat engine:
η \u003d (T 1 - T 2) / T 1 \u003d 1 - T 2 / T 1.
After performing mathematical transformations, we get:
T 1 \u003d T 2 / (1- η).
T 1 \u003d T 2 / (1- A / Q 1).
Let's calculate:
η= 650 J / 1000 J = 0.65.
T 1 \u003d 400 K / (1- 650 J / 1000 J) \u003d 1142.8 K.
Answer: η \u003d 65%, T 1 \u003d 1142.8 K.
Real conditions
The ideal heat engine is designed with ideal processes in mind. Work is done only in isothermal processes, its value is defined as the area bounded by the Carnot cycle graph.
In fact, it is impossible to create conditions for the process of changing the state of a gas without accompanying changes in temperature. There are no materials that would exclude heat exchange with surrounding objects. The adiabatic process is no longer possible. In the case of heat transfer, the temperature of the gas must necessarily change.
The efficiency of heat engines created in real conditions differ significantly from the efficiency ideal engines. Note that the processes in real engines occurs so rapidly that the variation in 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 return to the cooler.
Other heat engines
Real engines operate on different cycles:
- Otto cycle: the process at a constant volume changes adiabatically, creating a closed cycle;
- Diesel cycle: isobar, adiabat, isochor, adiabat;
- the process occurring at constant pressure is replaced by an adiabatic one, closing the cycle.
Create equilibrium processes in real engines (to bring them closer to ideal ones) under conditions modern technology does not seem possible. The efficiency of heat engines 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 efficiency calculation formula, since it is it that becomes the starting point in the process of working to increase the efficiency of real engines.
Ways to change efficiency
When comparing ideal and real heat engines, it is worth noting that the temperature of the refrigerator of the latter cannot be any. Usually the atmosphere is considered to be a refrigerator. The temperature of the atmosphere can be taken only in approximate calculations. Experience shows that the temperature of the coolant is equal to the temperature of the exhaust gases in the engines, as is the case in internal combustion engines (abbreviated internal combustion engines).
ICE is the most common heat engine in our world. The efficiency of a heat engine in this case depends on the temperature created by the burning fuel. A significant difference between an internal combustion engine and steam engines is the merging of the functions of the heater and the working fluid of the device into air-fuel mixture. Burning, the mixture creates pressure on the moving parts of the engine.
An increase in the temperature of the working gases is achieved by significantly changing the properties of the fuel. Unfortunately, it is not possible to do this indefinitely. Any material from which the combustion chamber of an engine 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.
Motor efficiency values
If we consider 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%. Such a decrease occurs due to heat losses during heating of the turbine housing.
The highest value of internal combustion does not exceed 44%. Increasing this value is a matter of the near future. Changing the properties of materials, fuels is a problem that is being worked on the best minds humanity.
In reality, the work done with the help of any device is always more useful work, since part of the work is done against the friction forces that act inside the mechanism and when moving its individual parts. So, applying movable block, commit extra work, lifting the block itself and the rope and, overcoming the friction forces in the block.
Let us introduce the following notation: useful work denote $A_p$, full work- $A_(full)$. In doing so, we have:
Definition
Coefficient of performance (COP) called the ratio of useful work to full. We denote the efficiency by the letter $\eta $, then:
\[\eta =\frac(A_p)(A_(poln))\ \left(2\right).\]
Most often, the efficiency is expressed as a percentage, then its definition is the formula:
\[\eta =\frac(A_p)(A_(poln))\cdot 100\%\ \left(2\right).\]
When creating mechanisms, they try to increase their efficiency, but mechanisms with an efficiency equal to one (and even more than one) do not exist.
And so, the efficiency factor is a physical quantity that shows the share that useful work is from all the work done. With the help of efficiency, the efficiency of a device (mechanism, system) that converts or transmits energy that performs work is evaluated.
To increase the efficiency of mechanisms, you can try to reduce the friction in their axes, their mass. If friction can be neglected, the mass of the mechanism is significantly less than the mass, for example, of the load that the mechanism lifts, then the efficiency is slightly less than unity. Then the work done is approximately equal to the useful work:
The golden rule of mechanics
It must be remembered that a gain in work cannot be achieved using a simple mechanism.
Let us express each of the works in formula (3) as the product of the corresponding force by the path traveled under the influence of this force, then we transform formula (3) into the form:
Expression (4) shows that using a simple mechanism, we gain in strength as much as we lose on the way. This law called the "golden rule" of mechanics. This rule was formulated in ancient Greece by Heron of Alexandria.
This rule does not take into account the work to overcome friction forces, therefore it is approximate.
Efficiency in power transmission
The efficiency factor can be defined as the ratio of useful work to the energy expended on its implementation ($Q$):
\[\eta =\frac(A_p)(Q)\cdot 100\%\ \left(5\right).\]
To calculate the efficiency of a heat engine, the following formula is used:
\[\eta =\frac(Q_n-Q_(ch))(Q_n)\left(6\right),\]
where $Q_n$ is the amount of heat received from the heater; $Q_(ch)$ - the amount of heat transferred to the refrigerator.
The efficiency of an ideal heat engine that operates according to the Carnot cycle is:
\[\eta =\frac(T_n-T_(ch))(T_n)\left(7\right),\]
where $T_n$ - heater temperature; $T_(ch)$ - refrigerator temperature.
Examples of tasks for efficiency
Example 1
Exercise. The crane engine has a power of $N$. For a time interval equal to $\Delta t$, he lifted a load of mass $m$ to a height $h$. What is the efficiency of the crane?\textit()
Solution. Useful work in the problem under consideration is equal to the work of lifting the body to a height $h$ of a load of mass $m$, this is the work of overcoming the force of gravity. It is equal to:
The total work that is done when lifting a load can be found using the definition of power:
Let's use the definition of the efficiency factor to find it:
\[\eta =\frac(A_p)(A_(poln))\cdot 100\%\left(1.3\right).\]
We transform formula (1.3) using expressions (1.1) and (1.2):
\[\eta =\frac(mgh)(N\Delta t)\cdot 100\%.\]
Answer.$\eta =\frac(mgh)(N\Delta t)\cdot 100\%$
Example 2
Exercise. An ideal gas performs a Carnot cycle, while the efficiency of the cycle is equal to $\eta $. What is the work in the gas compression cycle at constant temperature? The work done by the gas during expansion is $A_0$
Solution. The efficiency of the cycle is defined as:
\[\eta =\frac(A_p)(Q)\left(2.1\right).\]
Consider the Carnot cycle, determine in which processes heat is supplied (it will be $Q$).
Since the Carnot cycle consists of two isotherms and two adiabats, we can immediately say that there is no heat transfer in adiabatic processes (processes 2-3 and 4-1). In isothermal process 1-2 heat is supplied (Fig.1 $Q_1$), in isothermal process 3-4 heat is removed ($Q_2$). It turns out that in expression (2.1) $Q=Q_1$. We know that the amount of heat (the first law of thermodynamics) supplied to the system during an isothermal process goes completely to perform work by the gas, which means:
The gas performs useful work, which is equal to:
The amount of heat that is removed in the isothermal process 3-4 is equal to the work of compression (the work is negative) (since T=const, then $Q_2=-A_(34)$). As a result, we have:
We transform the formula (2.1) taking into account the results (2.2) - (2.4):
\[\eta =\frac(A_(12)+A_(34))(A_(12))\to A_(12)\eta =A_(12)+A_(34)\to A_(34)=( \eta -1)A_(12)\left(2.4\right).\]
Since by condition $A_(12)=A_0,\ $finally we get:
Answer.$A_(34)=\left(\eta -1\right)A_0$
Example. The average traction force of the engine is 882 N. It consumes 7 kg of gasoline per 100 km. Determine the efficiency of its engine. Find a useful job first. It is equal to the product of the force F by the distance S, overcome by the body under its influence Ап=F∙S. Determine the amount of heat that will be released when burning 7 kg of gasoline, this will be the work expended Az = Q = q∙m, where q is specific fuel, for gasoline it is equal to 42∙10^6 J/kg, and m is the mass of this fuel. Engine efficiency will be equal to efficiency=(F∙S)/(q∙m)∙100%= (882∙100000)/(42∙10^6∙7)∙100%=30%.
IN general case to find the efficiency of any heat engine (internal combustion engine, steam engine, etc.), where the work is done by the gas, has a coefficient useful actions equal to the difference in the heat given off by the heater Q1 and received by the refrigerator Q2, find the difference in the heat of the heater and the refrigerator, and divide by the heat of the heater Efficiency = (Q1-Q2)/Q1. Here the efficiency is in submultiples from 0 to 1, to translate the result, multiply it by 100.
To obtain the efficiency of an ideal heat engine (Carnot engine), find the ratio of the temperature difference between the heater T1 and cooler T2 to the temperature of the heater COP=(T1-T2)/T1. This is the maximum possible efficiency for a specific type of heat engine with given temperatures of the heater and refrigerator.
Define a common . This kind of information can be obtained by referring to the population census data. To determine the total birth, death, marriage and divorce rates, you need to find the product of the total population and the estimated period. Write the resulting number in the denominator.
Put on the numerator an indicator corresponding to the desired relative. For example, if you are faced with determining the total fertility rate, then in place of the numerator there should be a number reflecting the total number of births for the period you are interested in. If your goal is the death rate or marriage rate, then put the number of deaths in the place of the numerator. billing period or the number of people married, respectively.
Multiply the resulting number by 1000. This will be the overall coefficient you are looking for. If you are faced with the task of finding the total growth rate, then subtract the death rate from the birth rate.
Related videos
Sources:
- General Vital Rates
The word "work" refers primarily to activities that give a person a livelihood. In other words, he receives a financial reward for it. Nevertheless, people are ready in their free time either free of charge or for a purely symbolic fee to also participate in socially useful work aimed at helping those in need, landscaping yards and streets, planting trees and shrubs, etc. The number of such volunteers would certainly be even greater, but they often do not know where their services may be needed.
The humidity coefficient is a special indicator developed by meteorologists to assess the degree of climate humidity in a particular region. At the same time, it was taken into account that the climate is a long-term characteristic weather conditions in this locality. Therefore, it was also decided to consider the humidification coefficient in a long time frame: as a rule, this coefficient is calculated on the basis of data collected during the year.
Thus, the humidity coefficient shows how much precipitation falls during this period in the region under consideration. This, in turn, is one of the main factors determining the predominant type of vegetation in the area.
Moisture coefficient calculation
The formula for calculating the moisture coefficient is as follows: K = R / E. In the indicated formula, the symbol K denotes the moisture coefficient itself, and the symbol R denotes the amount of precipitation that fell in a given area during the year, expressed in millimeters. Finally, the symbol E denotes the amount of precipitation, which is from the surface of the earth, for the same period of time.The indicated amount of precipitation, which is also expressed in millimeters, depends on , the temperature in a given region at a particular time period and other factors. Therefore, despite the apparent simplicity of the above formula, the calculation of the moisture coefficient requires a large number preliminary measurements with the help of precise instruments and can only be carried out by a fairly large team of meteorologists.
In turn, the value of the moisture coefficient in a particular area, taking into account all these indicators, as a rule, allows a high degree reliability to determine which type of vegetation is predominant in this region. So, if the moisture coefficient exceeds 1, this indicates high level humidity in this area, which entails the predominance of such types of vegetation as taiga, tundra or forest-tundra.
A sufficient level of humidity corresponds to a moisture coefficient equal to 1, and, as a rule, is characterized by a predominance of mixed or. Moisture coefficient ranging from 0.6 to 1 is typical for forest-steppe massifs, from 0.3 to 0.6 - for steppes, from 0.1 to 0.3 - for semi-desert territories, and from 0 to 0.1 - for deserts .
Sources:
- Humidification, humidification coefficients
The work done by the engine is:
This process was first considered by the French engineer and scientist N. L. S. Carnot in 1824 in the book Reflections on the driving force of fire and on machines capable of developing this force.
The purpose of Carnot's research was to find out the reasons for the imperfection of heat engines of that time (they had an efficiency of ≤ 5%) and to find ways to improve them.
The Carnot cycle is the most efficient of all. Its efficiency is maximum.
The figure shows the thermodynamic processes of the cycle. In the process of isothermal expansion (1-2) at a temperature T 1 , the work is done by changing the internal energy of the heater, i.e., by supplying the amount of heat to the gas Q:
A 12 = Q 1 ,
Cooling of the gas before compression (3-4) occurs during adiabatic expansion (2-3). Change in internal energy ΔU 23 in an adiabatic process ( Q=0) is completely converted into mechanical work:
A 23 = -ΔU 23 ,
The temperature of the gas as a result of adiabatic expansion (2-3) decreases to the temperature of the refrigerator T 2 < T 1 . In the process (3-4), the gas is isothermally compressed, transferring the amount of heat to the refrigerator Q2:
A 34 = Q 2,
The cycle is completed by the process of adiabatic compression (4-1), in which the gas is heated to a temperature T 1.
Maximum efficiency value heat engines running on ideal gas, according to the Carnot cycle:
.
The essence of the formula is expressed in the proven WITH. Carnot theorem that the efficiency of any heat engine cannot exceed the efficiency of the Carnot cycle carried out at the same temperature of the heater and refrigerator.
The coefficient of performance (COP) of a boiler unit is defined as the ratio of useful heat used to generate steam (or hot water), to the available heat (the heat supplied to the boiler unit). In practice, not all useful heat selected by the boiler unit is sent to consumers. Part of the heat is spent on own needs. Depending on this, the efficiency of the unit is distinguished by the heat released to the consumer (net efficiency).
The difference between the generated and released heat is the consumption for the boiler house's own needs. Own needs consume not only heat, but also electrical energy (for example, to drive a smoke exhauster, a fan, feed pumps, fuel supply and dust preparation mechanisms, etc.), so the consumption for own needs includes the consumption of all types of energy spent on production of steam or hot water.
The gross efficiency of a boiler unit characterizes the degree of its technical excellence, and net efficiency - commercial profitability.
Gross efficiency of the boiler unit ŋ br, %, can be determined by the direct balance equation
ŋ br \u003d 100 (Q floor / Q p p)
or by the inverse balance equation
ŋ br \u003d 100-(q y.g + q x.n + q m.n + q n.o + q f.sh),
Where Q floor useful heat used to generate steam (or hot water); Q p p- available heat of the boiler unit; q c.g +q c.n +q m.n +q n.o +q f.sh- relative heat losses by items of heat consumption.
The net efficiency according to the reverse balance equation is defined as the difference
ŋ net = ŋ br -q s.n.,
Where q s.n- relative energy consumption for own needs, %.
The efficiency factor according to the direct balance equation is used mainly when reporting for a certain period (decade, month), and the efficiency factor according to the reverse balance equation is used when testing boiler units. Definition of efficiency according to the inverse balance, it is much more accurate, since the errors in measuring heat losses are smaller than in determining fuel consumption, especially when burning solid fuels.
Thus, to improve the efficiency of boiler units, it is not enough to strive to reduce heat losses; it is also necessary to reduce in every possible way the cost of heat and electric energy for own needs. Therefore, a comparison of the efficiency of the operation of various boiler units should ultimately be carried out according to their net efficiency.
In general, the efficiency of the boiler unit varies depending on its load. To build this dependence, it is necessary to subtract from 100% successively all the losses of the boiler unit Sq sweat \u003d q y.g + q x.n + q m.n + q n.o which depend on the load.
As can be seen from Figure 1.14, the efficiency of the boiler unit at a certain load has a maximum value, i.e. the operation of the boiler at this load is the most economical.
Figure 1.14 - Dependence of the boiler efficiency on its load: q c.g, q x.n, q m.s., q n.o.,S q sweat- heat losses with exhaust gases, from chemical incomplete combustion, from mechanical incomplete combustion, from external cooling and total losses
