The gas pressure is determined by the chaotic impact of the moving molecules. This means that the decrease in pressure upon cooling the gas can be explained by a decrease in the average energy of the translational motion of molecules (). The gas pressure reaches zero when, in accordance with the basic law of molecular kinetic theory:
The concentration of gas molecules n is considered to be a constant nonzero.
Ideal Gas Absolute Temperature
There is a limit for gas cooling. Absolute zero is the temperature at which the translational movement of molecules stops.
An ideal gas (unlike real gases) remains in a gaseous state at any temperature. The value of the temperature at which the translational motion of molecules will stop can be found from the law that was defined by J. Charles: the temperature coefficient of pressure of an ideal gas does not depend on the type of gas and is equal to 
... In this case, the pressure of an ideal gas at an arbitrary temperature is:
where t is the temperature on the Celsius scale; - pressure at. Let us equate the pressure in expression (2) to zero, express the temperature at which the molecules of the ideal gas stop their translational motion:
V. Kelvin suggested that the obtained value of absolute zero would correspond to the termination of the translational motion of molecules of any substance. Temperatures below absolute zero (T = 0 K) do not exist in nature. Since at a temperature of absolute zero it is impossible to take away the energy of the thermal motion of molecules and reduce the temperature of the body, since the energy of the thermal motion cannot be negative. In laboratories, a temperature close to absolute zero (about a thousandth of a degree) was obtained.
Thermodynamic temperature scale
On the thermodynamic temperature scale (also known as the Kelvin scale), the absolute zero of temperatures is considered the reference point. Temperature is designated with a capital T. The size of the degree is the same as the degree on the Celsius scale:
The derivatives will be the same if they are taken using different temperature feces:
When changing from Kelvin to Celsius, the definitions of the thermal expansion coefficients and the pressure coefficient are retained.
In the international system of units (SI), the unit of temperature is the basic one, it is called the kelvin (K). In the SI system, the thermodynamic temperature scale is used to read the temperature.
In accordance with international agreement, the size of the kelvin is determined from the following conditions: the temperature of the triple point of the ox is taken equal to 273.16 K. The triple point of water in Celsius corresponds to 0.01 o С, the melting temperature of ice in kelvin is equal to 273.15 K.
Temperature measured in kelvin is called absolute. The relationship between absolute temperature and Celsius temperature is reflected by the expression:
Absolute temperature, kinetic energy of molecules and pressure of an ideal gas
The value of the average energy of the translational motion of molecules is directly proportional to the gas temperature:
where is the Boltzmann constant. Formula (6) means that the average value of the kinetic energy of the translational motion of molecules does not depend on the kind of ideal gas, but is determined only by its temperature.
The pressure of an ideal gas is determined only by its temperature:
Examples of problem solving
EXAMPLE 1
| Exercise | At what temperature on the Celsius scale will the average kinetic energy of the translational motion of gas molecules be J? |
| Solution | As a basis for solving the problem, we will take the law relating the temperature on the thermodynamic scale and the average kinetic energy of molecules:
Let us express the absolute temperature from (1.1): Let's calculate the temperature:
Temperature in Kelvin and temperature in Celsius are related by the expression: We get the gas temperature is: |
| Answer |
EXAMPLE 2
| Exercise | How does the average kinetic energy of the translational motion of ideal gas molecules change, if the process can be represented by the graph in Fig. 1? |
| Solution | As a basis for solving the problem, we take the equation of state of an ideal gas in the form: |
History
The word "temperature" originated in those days when people believed that more heated bodies contain more of a special substance - caloric, than less heated ones. Therefore, temperature was perceived as the strength of a mixture of body matter and caloric. For this reason, the units for measuring the strength of alcoholic beverages and temperature are called the same - degrees.
From the fact that temperature is the kinetic energy of molecules, it is clear that it is most natural to measure it in energy units (i.e., in the SI system in joules). However, temperature measurement began long before the creation of the molecular kinetic theory, therefore practical scales measure temperature in arbitrary units - degrees.
Kelvin scale
In thermodynamics, the Kelvin scale is used, in which the temperature is measured from absolute zero (the state corresponding to the minimum theoretically possible internal energy of the body), and one kelvin is equal to 1 / 273.16 of the distance from absolute zero to the triple point of water (the state in which ice, water and water steam is in equilibrium). The Boltzmann constant is used to convert kelvin into energy units. Derivative units are also used: kilokelvin, megakelvin, millikelvin, etc.
Celsius
In everyday life, the Celsius scale is used, in which the freezing point of water is taken as 0, and the boiling point of water at atmospheric pressure is taken as 100 °. Since the freezing and boiling points of water are not well defined, currently the Celsius scale is determined through the Kelvin scale: Celsius is equal to Kelvin, absolute zero is taken as -273.15 ° C. The Celsius scale is practically very convenient, since water is very common on our planet and our life is based on it. Zero Celsius is a special point for meteorology, since the freezing of atmospheric water significantly changes everything.
Fahrenheit
In England, and especially in the United States, the Fahrenheit scale is used. On this scale, the interval from the temperature of the coldest winter in the city where Fahrenheit lived to the temperature of the human body is divided by 100 degrees. Zero degrees Celsius is 32 degrees Fahrenheit and Fahrenheit is 5/9 degrees Celsius.
The current definition of the Fahrenheit scale is that it is a temperature scale with 1 degree (1 ° F) equal to 1/180 of the difference between the boiling points of water and ice melting at atmospheric pressure, and the melting point of ice is + 32 ° F. Fahrenheit temperature is related to Celsius temperature (t ° C) by t ° C = 5/9 (t ° F - 32), that is, a 1 ° F change in temperature corresponds to a 5/9 ° C change. Proposed by G. Fahrenheit in 1724.
Reaumur scale
Proposed in 1730 by R.A. Reaumur, who described the alcohol thermometer invented by him.
Unit - Degree Reaumur (° R), 1 ° R is equal to 1/80 of the temperature interval between the reference points - the temperature of ice melting (0 ° R) and boiling water (80 ° R)
1 ° R = 1.25 ° C.
At present, the scale has fallen out of use; it has been preserved for the longest time in France, in the author's homeland.
|
Conversion of temperature between main scales |
|||
|
Kelvin |
Celsius |
Fahrenheit |
|
|
Kelvin (K) |
C + 273.15 |
= (F + 459.67) / 1.8 |
|
|
Celsius (° C) |
K - 273.15 |
= (F - 32) / 1.8 |
|
|
Fahrenheit (° F) |
K 1.8 - 459.67 |
C 1.8 + 32 |
|
Comparison of temperature scales
|
Description |
Kelvin | Celsius |
Fahrenheit |
Newton | Reaumur |
|
Absolute zero |
−273.15 |
−459.67 |
−90.14 |
−218.52 |
|
|
Melting temperature of Fahrenheit mixture (equal amounts of salt and ice) |
255.37 |
−17.78 |
−5.87 |
−14.22 |
|
| Freezing point of water (normal conditions) |
273.15 |
||||
|
Average human body temperature ¹ |
310.0 |
36.8 |
98.2 |
12.21 |
29.6 |
|
Boiling point of water (normal conditions) |
373.15 |
||||
| Sun surface temperature |
5800 |
5526 |
9980 |
1823 |
4421 |
¹ Normal human body temperature is 36.6 ° C ± 0.7 ° C, or 98.2 ° F ± 1.3 ° F. The commonly quoted value of 98.6 ° F is the exact conversion to Fahrenheit of 37 ° C in 19th century Germany. Since this value is not included in the range of normal temperature according to modern concepts, we can say that it contains excessive (incorrect) accuracy. Some values in this table have been rounded.
Comparison of the Fahrenheit and Celsius scales
(o F- Fahrenheit scale, o C- Celsius scale)
|
oF |
oC |
oF |
oC |
oF |
oC |
oF |
oC |
|||
|
459.67 |
273.15 |
60 |
51.1 |
4 |
20.0 |
20 |
6.7 |
To convert degrees Celsius to Kelvin, you need to use the formula T = t + T 0 where T is the temperature in kelvin, t is the temperature in degrees Celsius, T 0 = 273.15 kelvin. A degree Celsius is the same size as Kelvin.
Temperature is a scalar physical quantity characterizing the average kinetic energy of particles of a macroscopic system in a state of thermodynamic equilibrium per one degree of freedom.
The SI derived quantities, which have a special name, include the Celsius temperature, measured in Celsius degrees. In practice, degrees Celsius are often used due to the historical link to the important characteristics of water - the temperature of ice melting (0 ° C) and the boiling point (100 ° C). This is convenient, since most climatic processes, processes in wildlife, etc., are associated with this range. A change in temperature by one degree Celsius is identical to a change in temperature by one Kelvin. Therefore, after the introduction in 1967 of a new definition of Kelvin, the boiling point of water ceased to play the role of a constant reference point and, as accurate measurements show, it is no longer equal to 100 ° C, but close to 99.975 ° C
Absolute Temperature Scale- Thermodynamic Temperature Scale or International Practical Temperature Scale, by which temperature is measured from absolute zero in degrees Kelvin (Kelvin)
The absolute temperature scale was introduced into science not only to give the gas laws a more convenient farm. It has a deep physical meaning.
The absolute temperature scale or Kelvin scale or thermodynamic temperature scale is recognized by the International Committee for Weights and Measures as the main one. The definition of the thermodynamic temperature scale is based on the second law of thermodynamics and uses the Carnot cycle. One of the most important properties of the thermodynamic scale is its independence from the thermometric substance.
To determine the degree of the scale, one reference point is used - the triple point of water, and the lower limit of the temperature range is the point of absolute zero. The triple point of water is assigned a temperature of 273-15 K precisely. Kelvin is equal to / 273.16 of the thermodynamic temperature of the triple point of water.
The absolute temperature scale has a zero point at -273 (G 273 O.
An absolute temperature scale is a scale in which the point of absolute zero temperature is taken as the reference point. The Kelvin value is uniquely determined by the requirement that the temperature of the triple point of water (the reference temperature point at which liquid, solid and gaseous phases of a substance exist in equilibrium) should be equal to 273 16 K. Then the normal melting points of ice and boiling of water on an absolute scale correspond to temperatures of 273 15 and 373 15 K, and the temperature range of 1 K is equal to the temperature range of 1 C.
The absolute temperature scale is called the temperature scale, which is determined by the thermodynamic method in such a way that it does not depend on the choice of thermometric substance. The zero point of this scale is defined as the lowest thermodynamically possible temperature. The absolute temperature scale, which is currently used in thermal physics, was introduced by Lord Kelvin (William Thomson) in 1848 and is therefore also called the Kelvin scale.
There is also an absolute temperature scale that uses degrees Fahrenheit.
The desirability of establishing an absolute temperature scale, independent of the properties of any particular substance, has already been indicated in Ch.
The Kelvin and Rankine scales are absolute temperature scales based on the laws of thermodynamics and the concept of an absolute temperature pool.
The absolute thermodynamic temperature scale is identical to the empirical absolute temperature scale.
In this regard, two absolute temperature scales were proposed - Kelvin and Rankine, differing in the value of the temperature measurement unit adopted in them.
At the beginning of this article, it was noted that the absolute temperature scale can be established using any relationship based on the second law of thermodynamics and connecting the temperature T with other parameters of state.
In addition to the centigrade scale, the absolute temperature scale is used in science and technology.
Based on these findings, a temperature scale was created, called the absolute temperature scale.
7. Internal energy.
Internal energy body (denoted as E or U) is the sum of the energies of molecular interactions and thermal motions of the molecule. Internal energy is an unambiguous function of the state of the system. This means that whenever the system is in a given state, its internal energy takes on the value inherent in this state, regardless of the system's history. Consequently, the change in internal energy during the transition from one state to another will always be equal to the difference between its values in the final and initial states, regardless of the path along which the transition was made.
§ - chemical potential
§ - the number of particles in the system
Every person is faced with the concept of temperature on a daily basis. The term has become firmly established in our everyday life: we heat food in a microwave oven or cook food in the oven, we are interested in the weather outside or find out if the water in the river is cold - all this is closely related to this concept. And what is temperature, what does this physical parameter mean, how is it measured? We will answer these and other questions in the article.
Physical quantity
Let's look at what temperature is in terms of an isolated system in thermodynamic equilibrium. The term comes from the Latin language and means "proper mixing", "normal state", "proportion". This value characterizes the state of thermodynamic equilibrium of any macroscopic system. In the case when it is out of equilibrium, over time there is a transition of energy from more heated objects to less heated ones. The result is an equalization (change) of temperature throughout the system. This is the first postulate (zero principle) of thermodynamics.
Temperature determines the distribution of the constituent particles of the system by energy levels and by velocities, the degree of ionization of substances, the properties of equilibrium electromagnetic radiation of bodies, and the total volumetric density of radiation. Since the listed parameters are equal for a system that is in thermodynamic equilibrium, it is customary to call them the temperature of the system.
Plasma
In addition to equilibrium bodies, there are systems in which the state is characterized by several temperature values that are not equal to each other. Plasma is a good example. It consists of electrons (light charged particles) and ions (heavy charged particles). When they collide, there is a rapid transfer of energy from electron to electron and from ion to ion. But there is a slow transition between heterogeneous elements. Plasma can be in a state in which electrons and ions individually are close to equilibrium. In this case, you can take the individual temperatures of each type of particles. However, these parameters will differ among themselves.
Magnets
In bodies in which particles have a magnetic moment, the transfer of energy usually occurs slowly: from translational to magnetic degrees of freedom, which are associated with the possibility of changing the directions of the moment. It turns out that there are states in which the body is characterized by a temperature that does not coincide with the kinetic parameter. It corresponds to the translational motion of elementary particles. The magnetic temperature determines some of the internal energy. It can be either positive or negative. During the alignment process, energy will be transferred from particles with a higher value to particles with a lower temperature value if they are both positive and negative. Otherwise, this process will proceed in the opposite direction - the negative temperature will be "higher" than the positive one.
Why is this necessary?
The paradox is that the average person, in order to carry out the measurement process both in everyday life and in industry, does not even need to know what temperature is. It will be sufficient for him to understand that this is the degree of heating of an object or environment, especially since we are familiar with these terms since childhood. Indeed, most of the practical instruments designed to measure this parameter actually measure other properties of substances that change with the level of heating or cooling. For example, pressure, electrical resistance, volume, etc. Further, such readings are manually or automatically recalculated to the desired value.
It turns out that in order to determine the temperature, there is no need to study physics. Most of the population of our planet lives by this principle. If the TV is working, then there is no need to understand the transient processes of semiconductor devices, study, in the outlet or how it is fed to the signal. People are used to the fact that in every area there are specialists who can fix or debug the system. The layman does not want to strain his brain, because it is much better to watch a soap opera or soccer on the TV while sipping cold beer.
I want to know
But there are people, most often students, who, either to the extent of their curiosity, or by necessity, are forced to study physics and determine what temperature really is. As a result, in their search, they fall into the jungle of thermodynamics and study its zero, first and second laws. In addition, an inquiring mind will have to comprehend entropy. And at the end of his journey, he probably admits that defining temperature as a parameter of a reversible thermal system, which does not depend on the type of working substance, will not add clarity to the perception of this concept. And all the same, the visible part will be some degrees adopted by the international system of units (SI).
Temperature as kinetic energy
More "tangible" is the approach that is called molecular kinetic theory. From it, the idea is formed that heat is considered as one of the forms of energy. For example, the kinetic energy of molecules and atoms, a parameter averaged over a huge number of chaotically moving particles, turns out to be a measure of what is commonly called the temperature of a body. So, the particles of a heated system move faster than a cold one.
Since the term under consideration is closely related to the averaged kinetic energy of a group of particles, it would be quite natural to use joule as a unit for measuring temperature. Nevertheless, this does not happen, which is explained by the fact that the energy of the thermal motion of elementary particles is very small in relation to the joule. Therefore, using it is inconvenient. Thermal motion is measured in units derived from joules by means of a special conversion factor.
Temperature units
Today, there are three main units used to display this parameter. In our country, it is customary to determine the temperature in degrees Celsius. This unit of measurement is based on the solidification point of water - an absolute value. She is the starting point. That is, the water temperature at which ice begins to form is zero. In this case, water serves as an exemplary yardstick. This convention has been adopted for convenience. The second absolute value is the temperature of the vapor, that is, the moment when water changes from a liquid to a gaseous state.
The next unit is degrees Kelvin. The starting point of this system is considered to be a point. So, one degree of Kelvin is equal to one. The only difference is the starting point. We get that zero in Kelvin will be equal to minus 273.16 degrees Celsius. In 1954, the General Conference on Weights and Measures decided to replace the term "Kelvin" for the unit of temperature with "Kelvin".
The third common unit of measurement is Fahrenheit. Until 1960, they were widely used in all English-speaking countries. However, today in everyday life in the United States they use this unit. The system is fundamentally different from those described above. The freezing point of a mixture of salt, ammonia and water in a ratio of 1: 1: 1 is taken as the starting point. So, on the Fahrenheit scale, the freezing point of water is plus 32 degrees, and the boiling point is plus 212 degrees. In this system, one degree is equal to 1/180 of the difference between these temperatures. So, the range from 0 to +100 degrees Fahrenheit corresponds to the range from -18 to +38 Celsius.
Absolute zero temperature
Let's see what this parameter means. Absolute zero is the value of the limiting temperature at which the pressure of an ideal gas will vanish for a fixed volume. This is the lowest value in nature. As Mikhailo Lomonosov predicted, "this is the greatest or last degree of cold." From this follows chemical in equal volumes of gases under the condition of the same temperature and pressure, the same number of molecules is contained. What follows from this? There is a minimum gas temperature at which its pressure or volume will vanish. This absolute value corresponds to zero Kelvin, or 273 degrees Celsius.
Some interesting facts about the solar system
The temperature at the surface of the Sun reaches 5,700 Kelvin, and in the center of the core - 15 million Kelvin. The planets of the solar system are very different from each other in terms of heating. So, the temperature of the core of our Earth is about the same as on the surface of the Sun. The hottest planet is Jupiter. The temperature at the center of its core is five times higher than at the surface of the Sun. But the lowest value of the parameter was recorded on the surface of the Moon - it was only 30 kelvin. This value is even lower than on the surface of Pluto.
Earth Facts
1. The highest temperature recorded by a person was 4 billion degrees Celsius. This value is 250 times higher than the temperature of the Sun's core. The record was set by the Brookhaven New York Natural Laboratory in the ion collider, which is about 4 kilometers long.
2. The temperature on our planet is also not always ideal and comfortable. For example, in the city of Verkhnoyansk in Yakutia, the temperature in winter drops to minus 45 degrees Celsius. But in the Ethiopian city of Dallol, the situation is reversed. There, the average annual temperature is plus 34 degrees.
3. The most extreme conditions under which people work are recorded in gold mines in South Africa. Miners work at a depth of three kilometers at a temperature of plus 65 degrees Celsius.
Characterizing the thermal state of bodies.
In the world around us, various phenomena occur associated with the heating and cooling of bodies. They are called thermal phenomena... So, when heated, cold water first becomes warm, and then hot; the metal part taken out of the flame gradually cools down, etc. The degree of heating of the body, or its thermal state, we denote by the words "warm", "cold", "hot". To quantify this state, it serves temperature.
Temperature is one of the macroscopic parameters of the system. In physics, bodies consisting of a very large number of atoms or molecules are called macroscopic... The dimensions of macroscopic bodies are many times greater than the dimensions of atoms. All surrounding bodies - from a table or gas in a balloon to a grain of sand - are macroscopic bodies.
The quantities characterizing the state of macroscopic bodies without taking into account their molecular structure are called macroscopic parameters... These include volume, pressure, temperature, particle concentration, mass, density, magnetization, etc. Temperature is one of the most important macroscopic parameters of a system (gas, in particular).
Temperature is a characteristic of the thermal equilibrium of the system.
It is known that to determine the temperature of the environment, a thermometer should be placed in this environment and wait until the temperature of the thermometer stops changing, taking a value equal to the ambient temperature. In other words, it takes some time to establish thermal equilibrium between the medium and the thermometer.
Teplovym, or thermodynamic, equilibrium is called a state in which all macroscopic parameters remain unchanged for an arbitrarily long time. This means that the volume and pressure in the system do not change, phase transformations do not occur, and the temperature does not change.
However, microscopic processes do not stop at thermal equilibrium: the velocities of molecules change, they move, collide.
Any macroscopic body or group of macroscopic bodies - thermodynamic system- can be in various states of thermal equilibrium. In each of these states, the temperature has its own well-defined value. Other quantities can have different (but constant) values. For example, the pressure of a compressed gas in a cylinder will differ from the pressure in the room and with the temperature equilibrium of the entire system of bodies in this room.
Temperature characterizes the state of thermal equilibrium of a macroscopic system: in all parts of the system that are in a state of thermal equilibrium, the temperature has the same value (this is the only macroscopic parameter that has this property).
If two bodies have the same temperature, heat exchange does not occur between them, if different, heat exchange occurs, and heat is transferred from a more heated body to a less heated one until the temperatures are completely equalized.
Temperature measurement is based on the dependence of a physical quantity (for example, volume) on temperature. This dependence is used in the temperature scale of a thermometer - a device used to measure temperature.
The action of a thermometer is based on the thermal expansion of a substance. When heated, the column of the substance used in the thermometer (for example, mercury or alcohol) increases, when cooled, it decreases. Thermometers used in everyday life allow you to express the temperature of a substance in degrees Celsius (° C).
A. Celsius (1701-1744) - Swedish scientist who suggested using the centigrade temperature scale. In the Celsius temperature scale, zero (since the middle of the 18th century) is the temperature of melting ice, and 100 degrees is the boiling point of water at normal atmospheric pressure.
Since different liquids expand in different ways with increasing temperature, the temperature scales in thermometers with different liquids are different.
Therefore, in physics they use ideal gas temperature scale based on the dependence of the volume (at constant pressure) or pressure (at constant volume) of gas on temperature.
