The basis for describing processes in pneumatic automation elements is the first law of thermodynamics. The first law of thermodynamics is a special case of the law of conservation of energy. This law states that in an isolated system the sum of all types of energy is a constant value.
The relationship between heat and work was established by Robert Mayer in 1842
In the SI system, the thermal equivalent of work is A = 1.
German physician and physicist Julius Robert von Mayer was born in Heilbronn into the family of a pharmacist. Having received medical education, he worked for several months in clinics in Paris, after which he went as a ship's doctor to the island. Java. During a year-long voyage (1840–1841), the doctor Mayer came to his great discovery. According to him, this conclusion was prompted by observations of changes in the color of blood in people in the tropics. While carrying out numerous bloodlettings on the roadstead in Batavia, Mayer noticed that “the blood released from the hand vein was of such extraordinary redness that, judging by the color, I might have thought that I had hit an artery.” He concluded from this that “the temperature difference between the body’s own heat and the heat environment must be in quantitative relation to the difference in color of both types of blood, i.e. arterial and venous... This difference in color is an expression of the amount of oxygen consumed or the strength of the combustion process occurring in the body.”
At the time of Mayer, the doctrine of the vital force of the organism (vitalism) was widespread: a living organism acts due to the presence of a special vital force in it. Thus, physiological processes were excluded from the sphere of physical and chemical laws and were determined by a mysterious vital force. Mayer showed through his observations that the body is governed by natural physical and chemical laws, and above all by the law of conservation and transformation of energy. Returning from the trip, he immediately wrote an article entitled “On the quantitative and qualitative determination of forces,” which he sent on June 16, 1841 to the journal “Annals...” to I. Poggendorff. This work of Mayer, despite some inconsistencies, contains a very definite and clear formulation of the law of conservation and transformation of force, i.e. energy. Poggendorff, however, did not print the article and did not return it to the author; it lay in his desk for 36 years, where it was discovered after Poggendorff's death. In 1842, Mayer published another article in the journal Annals of Chemistry and Pharmacy.
This work of Mayer is rightfully considered fundamental in the history of the law of conservation and transformation of energy. Particularly important is Mayer's idea of the qualitative transformation of forces (energy) while maintaining their quantitative conservation. Mayer analyzes in detail all possible forms of energy transformation in the brochure “Organic motion in its connection with the metabolism of matter,” published in Heilbronn in 1845. Mayer first thought of publishing his article in the same “Annals of Chemistry and Pharmacy,” but their editor, J. Liebig, citing the overload of the journal with chemical articles, he advised sending the article to Poggendorff’s Annals. Mayer, realizing that Poggendorff would treat it the same way as with the article of 1841, decided to publish the article as a pamphlet at his own expense.
In his pamphlet, Mayer calculates in detail the mechanical equivalent of heat; he provides data on the calorific value of carbon and draws attention to the low efficiency of heat engines, the maximum value of which in modern machines was 5–6%, and in locomotives did not reach one percent. Considering electrification by friction and the action of the electrophore, Mayer points out that here “the mechanical effect is converted into electricity.” He concludes: the expenditure of a mechanical effect causes both electrical and magnetic stress. Mayer concludes his analysis with “chemical force.” It is interesting that he combines the question of chemical energy with the question of energy solar system. He points out that the flow of solar energy (force), which also appears on our Earth, “is that constantly winding spring that maintains the mechanism of all activities occurring on Earth in a state of motion.”
Mayer completed the development of his ideas by 1848, when in the brochure “Dynamics of the Sky in a Popular Presentation” he posed and attempted to solve the most important problem about the source of solar energy. Mayer realized that chemical energy was not sufficient to replenish the enormous energy expenditure of the Sun. However, only mechanical energy was known among other energy sources in his time. And Mayer concluded that the heat of the Sun is replenished by the bombardment of meteorites falling on it from all sides continuously from the surrounding space. In his 1851 work, “Notes on the Mechanical Equivalent of Heat,” Mayer briefly and popularly outlines his ideas about the conservation and transformation of force.
Mayer's work went unnoticed for a long time: the first article was not published at all, the second was published in a chemical journal not read by physicists, and the third in a private brochure. It is quite clear that Mayer’s discovery did not reach physicists, and the law of conservation of energy was discovered independently of him and in other ways by other authors, primarily J. Joule and G. Helmholtz. Mayer became embroiled in a dispute over priority that took its toll on him; only in 1862 did R. Clausius and J. Tyndall pay attention to Mayer's research. The assessment of Mayer's merits in creating the mechanical theory of heat at one time caused a fierce debate between Clausius, Tyndall, Joule and Dühring.
Mayer, forced to defend his priority in the discovery of the law of conservation of energy, did so in a calm and dignified tone, hiding that deep mental trauma, which was inflicted on him by the “petty envy of shop scientists” and “ignorance of the environment,” according to K. A. Timiryazev. Suffice it to say that in 1850 he tried to commit suicide by jumping out of a window and remained lame for the rest of his life. He was hounded in the newspapers, accused of being a modest and honest scientist of delusions of grandeur, and subjected to forced “treatment” in a psychiatric hospital.
Mayer died on March 20, 1878. Shortly before his death, in 1874, a collection of his works on the law of conservation and transformation of energy was published under the title “Heat Mechanics.” In 1876, his last works “On the Torricelli Emptiness” and “On the Liberation of Forces” were published. (See below).
The first law of thermodynamics states that heat dq, supplied to the TDS goes to perform work dl this system and the change in internal energy du TDS.
dq = du + dl.
The internal energy of a thermodynamic system is understood as all the energy contained in this system. This energy is determined by the energy of translational, rotational and vibrational motion of molecules, as well as the energy of interaction between molecules and atoms. The absolute value of the internal energy of a close-body system is not determined by thermodynamic methods. In technical thermodynamics, it is customary to consider the internal energy of a close body at zero temperature to be equal to zero and to consider the increase in internal energy relative to this level.
,where is the universal gas constant, is the molar heat capacity at constant pressure, and is the molar heat capacity at constant volume.
Mayer's equation follows from the first law of thermodynamics, applied to an isobaric process in an ideal gas:
in this case:
Obviously, Mayer's equation shows that the difference in the heat capacities of a gas is equal to the work done by one mole of an ideal gas when its temperature changes by 1, and explains the meaning of the universal gas constant R- mechanical equivalent of heat.
Wikimedia Foundation. 2010.
See what "Mayer's Formula" is in other dictionaries:
For any ideal gas, the Mayer relation is valid: , where is the universal gas constant, the molar heat capacity at constant pressure, the molar heat capacity at constant volume. Mayer's equation follows from... ... Wikipedia
Wikipedia has articles about other people with this surname, see Mayer. Julius Robert von Mayer Julius Robert von Mayer ... Wikipedia
Von Mayer, Julius Robert Wikipedia has articles about other people with the surname Mayer. Robert Mayer Julius Robert von Mayer (German: Julius Robert von Mayer; ... Wikipedia
OBLITERATION- (lat. obliteratio destruction), a term used to designate the closure, destruction of a particular cavity or lumen through the proliferation of tissue coming from the walls of a given cavity formation. The specified growth is more often... ... Great Medical Encyclopedia
Its essence can be expressed in a few words. According to this theory, gases consist of a huge number of individual very small particles moving in all possible directions and at all possible speeds; these particles are interconnected...
This article is about the substance; about the drug, see: Morphine ( medicine). The request for "Morphine" is redirected here; see also other meanings. Morphine ... Wikipedia
Bodies characterized by the desire to fill any space and devoid of their own form. The doctrine of geology represents a brilliant page in modern natural science. The once elusive shape of the body, which, according to the concepts of the ancients, occupied... ... Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron
Characterized by the desire to fill any space and devoid of their own form. The doctrine of geology represents a brilliant page in modern natural science. The once seemingly elusive shape of the body, which according to the concepts of the ancients occupied the middle... ... Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron
A branch of applied physics or theoretical thermal engineering that studies the transformation of motion into heat and vice versa. Thermodynamics deals not only with the distribution of heat, but also with physical and chemical changes associated... Collier's Encyclopedia
English FIFA World Cup ... Wikipedia
DEFINITION
Mayer's equation connects the molar heat capacity for an ideal gas in an isochoric process, and the molar heat capacity at in an isobaric process.
It is in this simple equation that the physical essence of the quantity is contained - the universal gas constant, equal to 8.31 J / (mol K).
Writing the Mayer equation
Mayer's equation is written as:
In it, c p is the molar heat capacity at constant, and c v, respectively, under conditions of constant volume.
Molar heat capacity indicates how much heat in Joules must be supplied to one mole of gas to heat it by 1 Kelvin. The molar heat capacity of an isochoric process can be determined by the following formula:
where i is the number of degrees of freedom for a gas molecule. Taking into account the Mayer equation, we obtain a formula for calculating the isobaric molar heat capacity:
Calculations using Mayer's equation
In practical calculations, specific mass heat capacity is often used, and it is precisely this that is usually given in tables of thermophysical quantities. By multiplying the molar heat capacity of a gas by its molar mass, we obtain the specific mass heat capacity:
Why was it necessary to distinguish between isochoric and isobaric heat capacities?
In an isobaric process (a process with constant pressure), the first law of thermodynamics is represented by the formula:
where is the amount of heat supplied to the gas, 
– change in gas, – expansion made by gas.
This means that the heat supplied to the gas in an isobaric process will be spent on changing its internal energy and working on its expansion.
If the gas is closed in a closed volume (isochoric process), then no work will be done to expand it (), and all the supplied heat will be spent on changing the internal energy:
If we subtract the second from the first expression, we get:
Thus, the gas constant R determines the work expended on the expansion of one mole of gas when it is heated by 1 Kelvin at constant pressure.
Basically, Mayer's equation is used in the theory of heat engines and thermal hydraulics to determine the thermophysical characteristics of working fluids. However, it has also found application in quantum physics: Planck’s constant, which relates the energy of a light quantum to its frequency, was obtained taking into account physical meaning universal gas constant.
Examples of problem solving
EXAMPLE 1
| Exercise | The molar isochoric heat capacity of carbon dioxide is 28.825 J/(mol K). Find the heat capacity of 1 liter at constant pressure. |
| Solution | Let's find the isobaric molar heat capacity using Mayer's formula: J/(mol K) Knowing the heat capacity of 1 mole of carbon dioxide, we find the isobaric heat capacity of 1 liter of carbon dioxide: |
| Answer | 831.8 J/K. This means that to heat 1 liter of carbon dioxide by 1 Kelvin, you need to spend 831.8 J |
EXAMPLE 2
| Exercise | The gas mixture consists of 5 kg of CO 2 dioxide and 8 kg of dinitrogen N 2. The isobaric molar heat capacities of the indicated gases at temperature T = 298.15 K are equal to J/mol K, J/mol K. Calculate the specific mass isochoric heat capacity of the mixture, J/kg K. |
| Solution | 1) Determine the molar masses of each of the components of the mixture: 2) Determine the amount of substance of each of the components of the mixture (in moles): |
The physical meaning of Mayer's equation is that when a gas is heated isobarically, more heat must be supplied to it than for the same isochoric heating. The heat difference must be equal to the work done by the gas during isobaric expansion.
10. Circular process. Carnot cycle. Efficiency of a heat engine.
Thermodynamic cycles are circular processes in thermodynamics, that is, processes in which the initial and final parameters that determine the state of the working fluid (pressure, volume, temperature, entropy) coincide.
Thermodynamic cycles are models of processes occurring in real heat engines to convert heat into mechanical work.
The Carnot cycle is an ideal thermodynamic cycle. A Carnot heat engine operating in this cycle has the highest efficiency of all machines in which the maximum and minimum temperatures of the cycle being carried out coincide, respectively, with the maximum and minimum temperatures of the Carnot cycle. Consists of 2 adiabatic and 2 isothermal processes.
The Carnot cycle is named after the French military engineer Sadi Carnot, who first studied it in 1824.
One of the important properties of the Carnot cycle is its reversibility: it can be carried out both in the forward and in the reverse direction, while the entropy of an adiabatically isolated (without heat exchange with the environment) system does not change.
Efficiency factor (efficiency) is a characteristic of the efficiency of a system (device, machine) in relation to the conversion or transmission of energy. It is determined by the ratio of usefully used energy to the total amount of energy received by the system; usually denoted η (“this”). η = Wpol/Wcym. Efficiency is a dimensionless quantity and is often measured as a percentage. Mathematically, the definition of efficiency can be written as:
where A is useful work and Q is work expended.
Due to the law of conservation of energy, efficiency is always less than or equal to unity, that is, it is impossible to obtain more useful work than the energy expended.
The efficiency of a heat engine is the ratio of the complete useful work of the engine to the energy received from the heater. The efficiency of a heat engine can be calculated using the following formula
,
where is the amount of heat received from the heater, is the amount of heat given to the refrigerator. The highest efficiency among cyclic machines operating at given temperatures of a hot source T 1 and a cold source T 2 is achieved by heat engines operating according to the Carnot cycle; this marginal efficiency is equal to
.
11. Electric field strength and potential. Coulomb's law.
Electric field strength is a vector physical quantity that characterizes the electric field at a given point and is numerically equal to the ratio of the force acting on a stationary test charge placed at a given point in the field to the magnitude of this charge:
Potential is an energy characteristic of the field. It is numerically equal to the work that must be expended against the forces of the electric field when transferring a unit positive point charge from infinity to a given point in the field. The unit of measurement for potential is volt. Taking into account (1.16)
Coulomb's law is a law that describes the interaction forces between point electric charges.
It was discovered by Charles Coulomb in 1785. After conducting a large number of experiments with metal balls, Charles Coulomb gave the following formulation of the law:
Modulus of the force of interaction between two point charges in a vacuum is directly proportional to the product of the moduli of these charges and inversely proportional to the square of the distance between them
Otherwise: Two point charges in a vacuum act on each other with forces that are proportional to the product of the moduli of these charges, inversely proportional to the square of the distance between them and directed along the straight line connecting these charges. These forces are called electrostatic (Coulomb).
It is important to note that in order for the law to be true, it is necessary:
point-like charges - that is, the distance between charged bodies is much larger than their sizes - however, it can be proven that the force of interaction of two volumetrically distributed charges with spherically symmetrical non-intersecting spatial distributions is equal to the force of interaction of two equivalent point charges located at centers of spherical symmetry;
their immobility. Otherwise, additional effects come into force: the magnetic field of a moving charge and the corresponding additional Lorentz force acting on another moving charge;
interaction in a vacuum.
However, with some adjustments, the law is also valid for interactions of charges in a medium and for moving charges.
In vector form in the formulation of C. Coulomb, the law is written as follows:
where is the force with which charge 1 acts on charge 2; - magnitude of charges; - radius vector (vector directed from charge 1 to charge 2, and equal, in absolute value, to the distance between charges - ); - proportionality coefficient. Thus, the law indicates that like charges repel (and unlike charges attract).
Let's place 1 kg of the same gas with the same parameters in identical cylinders and try to heat this gas to the same temperature T. In the first cylinder, the piston is welded to the walls, and in the second, it does not encounter resistance when moving.
To do this, you need to supply heat to the first cylinder q v , and in the second – q p . Wherein q v =c v (T 2 - T 1 ), q p =c p (T 2 - T 1 ).
It's obvious that q p > q v, since in the second case the heat will be spent not only on heating the gas, but also on doing work (Fig. 6).
In this case
(see Fig. 4). In turn, since p v = RT,
From here we get Mayer's law:
With p -With v = R. (37)
In thermotechnical calculations the relation is used With p /With v =k, which is called the adiabatic exponent. Because With p > with v , That k>1.
With satisfactory engineering accuracy, for all diatomic gases and air, we can consider With p and With v constant and equal:
With p = 1.004 kJ/kg deg ; With v = 0.716 kJ/kg deg.
Then To=
3.3 First law of thermodynamics
According to the law of conservation and transformation of energy, the latter can neither be created nor destroyed, but can only be transformed from one type to another through various physical and chemical processes.
Historically, different units were adopted to measure certain types of energy - calories, kgm, joules, kWh, hp h, etc. In this regard, the transformation of energy occurs not in numerically equal, but in equivalent ratios. The thermal equivalent of a unit of work is known from physics: 1 kgm = 1/427 kcal.
The following ratios are also known: 1 hp h = 632.3 kcal = 0.735 kWh; 1 kWh = 860 kcal.
Previously, we noted that the first law is a special case of the general law of conservation and transformation of energy in relation to processes occurring in thermodynamic systems. In the general case, the first law can be formulated as follows: “The total energy of an isolated thermodynamic system remains unchanged for any processes occurring in the system.”
Only 100 years after Lomonosov’s conclusions, after his general formulation of the law of conservation of energy, in 1842, Robert Mayer, based on experiments, established direct proportionality between the expended heat Q and the work received L and determined the quantitative relationship between them (if Q And L expressed in J):
Q = L. (38)
Once heat is expended, it disappears, and as a result, work is obtained and vice versa. Those. in relation to thermal and mechanical phenomena, the first law can be formulated as follows:
“When a certain amount of thermal energy disappears, an equivalent amount of mechanical energy appears (in the form of work done) and vice versa.”
The approval of the first law contributed to the cessation of attempts to build an engine that produces mechanical energy without consuming any other type of energy (for example, released during the combustion of fuel) - “perpetuum mobile of the first kind.”
The equation of the first law in this form does not fully characterize the energy balance in the processes of changing the state of the gas. These processes usually occur during heat exchange with gas, so let’s consider the components of this heat exchange.
Let an infinitesimal amount of heat be supplied to 1 kg of gas in a cylinder with a moving piston dq. In this case, the kinetic energy will increase forward movement molecules, as a result of which the gas will do work (expressed by the movement of the piston)
. In addition, all types of energy inherent in the state of molecules will change - i.e. the internal energy of the gas will change. Thus, heat is spent on changing internal energy and doing work
dq = du + d
From the description of the operation of heat engines it is clear that thermodynamics considers two sharply different groups of physical changes in gas. In piston engines, gas movement is not significant and can be neglected.In rotary heat engines (for example, a steam turbine), a change in the state of the gas is accompanied by intense (with high speed W) movement of the working fluid. For this case, the first law of thermodynamics will be written in the form
(For example, in internal combustion engines W 1 = 0.1 m/sec, W 2 = 10 m/sec, in vocational school W 1 = 0.1 m/sec W 2 = 1000 m/sec).
Loading...