Annotation: The concept of scaling. Existing species scales and their scope. Reasons for the appearance of scales.

SHKA "LA, s, and. [Latin. scala - stairs].- 1 . Ruler with divisions in various measuring instruments. W. thermometer. 2 . A series of values, digits in ascending or descending order (spec.). Sh. temperature of the patient. Sh. diseases. Sh. wages.

Scale types:

Measurement scales are usually classified according to the types of measured data, which determine the mathematical transformations allowed for a given scale, as well as the types of relationships displayed by the corresponding scale. The modern classification of scales was proposed in 1946 by Stanley Smith Stevens.

Name scale (nominal, classification)

Used to measure the values ​​of qualitative features. The value of such a feature is the name of the equivalence class to which the considered object belongs. Examples of values ​​for qualitative features are the names of states, colors, car brands, etc. Such signs satisfy the axioms of identity:

At large numbers classes use hierarchical naming scales. Most famous examples such scales are the scales used to classify animals and plants.

With the values ​​measured in the scale of names, you can perform only one operation - checking their coincidence or mismatch. Based on the results of such a check, it is possible to additionally calculate the filling frequencies (probabilities) for various classes that can be used to apply various methods statistical analysis - Chi-square goodness-of-fit test, Cramer's test for testing the hypothesis about the relationship of qualitative features, etc.

Ordinal scale (or rank)

Built on identity and order. The subjects in this scale are ranked. But not all objects can be subordinated to the relation of order. For example, one cannot say which is larger, a circle or a triangle, but one can single out a common property in these objects - area, and thus it becomes easier to establish ordinal relationships. For this scale, a monotonic transformation is allowed. Such a scale is crude because it does not take into account the difference between the subjects of the scale. An example of such a scale: performance scores (unsatisfactory, satisfactory, good, excellent), Mohs scale.

Interval scale

Here there is a comparison with the standard. The construction of such a scale allows most properties of existing numerical systems to attribute to numbers obtained on the basis of subjective assessments. For example, building a scale of intervals for reactions. For this scale, a linear transformation is acceptable. This allows you to bring the test results to common scales and thus compare the indicators. Example: Celsius scale.

Relationship scale

In the scale of ratios, the ratio "so many times more" operates. This is the only one of the four scales that has absolute zero. The zero point characterizes the absence of a measurable quality. This the scale admits a similarity transformation (multiplication by a constant). Determination of the zero point is a difficult task for research, imposing a limitation on the use of this scale. With the help of such scales, mass, length, strength, cost (price) can be measured. Example: Kelvin scale (temperatures measured from absolute zero, with the unit of measurement chosen by agreement of specialists - Kelvin).

difference scale

The origin is arbitrary, the unit of measurement is set. Valid transformations are shifts. Example: measuring time.

Absolute scale

It contains an additional feature - the natural and unambiguous presence of a unit of measurement. This scale has a single zero point. Example: the number of people in the audience.

Of the scales considered, the first two are non-metric, and the rest are metric.

The problem of the adequacy of methods for mathematical processing of measurement results is directly related to the question of the type of scale. In the general case, adequate statistics are those that are invariant with respect to admissible transformations of the used measurement scale.

Use in psychometry. Using various scales, various psychological measurements can be made. The very first methods of psychological measurements were developed in psychophysics. The main task of psychophysicists was how to determine how the physical parameters of stimulation correlate with the subjective assessments of sensations corresponding to them. Knowing this connection, one can understand what sensation corresponds to one or another sign. The psychophysical function establishes a relationship between the numerical value of the scale of the physical measurement of the stimulus and the numerical value of the psychological or subjective response to this stimulus.

Celsius

1701 in Sweden. His area of ​​interest: astronomy, general physics, geophysics. He taught astronomy at Uppsala University, founded an astronomical observatory there.

Celsius was the first to measure the brightness of stars, establishing the relationship between the northern lights and fluctuations in the Earth's magnetic field.

He took part in the Lapland expedition of 1736-1737 to measure the meridian. Upon his return from the polar regions, Celsius began active work on the organization and construction of an astronomical observatory in Uppsala and in 1740 became its director. Anders Celsius died on March 25, 1744. The mineral Celsian, a type of barium feldspar, is named after him.

In engineering, medicine, meteorology and everyday life, the Celsius scale is used, in which the temperature of the triple point of water is 0.01, and therefore the freezing point of water at a pressure of 1 atm is 0. Currently, the Celsius scale is determined through the Kelvin scale: the Celsius degree is equal to the Kelvin,. Thus, the boiling point of water, originally chosen by Celsius as a reference point of 100, has lost its value, and according to modern estimates, the boiling point of water at normal atmospheric pressure is about 99.975. 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, as it is associated with the freezing of atmospheric water. The scale was proposed by Anders Celsius in 1742.

Fahrenheit

Gabriel Fahrenheit. Daniel Gabriel Fahrenheit (Daniel Gabriel (1686–1736) - German physicist. Born May 24, 1686 in Danzig (now Gdansk, Poland). Studied physics in Germany, Holland and England. Lived almost all his life in Holland, where he was engaged in the manufacture of precise meteorological instruments In 1709 he made an alcohol, in 1714 - a mercury thermometer, using new way mercury purification. For mercury thermometer Fahrenheit built a scale with three fixed points: it corresponded to the temperature of the mixture of water - ice - ammonia, - body temperature healthy person, and the value for the ice melting point was taken as the control temperature. The boiling point of pure water on the Fahrenheit scale is . The Fahrenheit scale is used in many English-speaking countries, although it is gradually giving way to the Celsius scale. In addition to making thermometers, Fahrenheit also improved barometers and hygrometers. He also studied the dependence of the change in the boiling point of a liquid on atmospheric pressure and the content of salts in it, discovered the phenomenon of supercooling of water, compiled tables specific gravity tel. Fahrenheit died in The Hague on September 16, 1736.

In England, and especially in the USA, the Fahrenheit scale is used. Zero degrees Celsius is 32 degrees Fahrenheit, and a degree Fahrenheit is 5/9 degrees Celsius.

The following definition is currently accepted fahrenheit scale: this is a temperature scale, 1 degree of which (1) is equal to 1/180 of the difference between the boiling points of water and the melting of ice at atmospheric pressure, and the melting point of ice has a temperature of F. The Fahrenheit temperature is related to the Celsius temperature () by the relationship. Proposed by G. Fahrenheit in 1724.

Reaumur scale

René Réaumur. Rene Antoine de Reaumur was born on 28

February 1683 in La Rochelle, French naturalist, foreign honorary member of the St. Petersburg Academy of Sciences (1737). Works on regeneration, physiology, biology of insect colonies. He proposed a temperature scale named after him. He improved some methods of steel preparation, he was one of the first who made attempts to scientifically substantiate some casting processes, wrote the work "The Art of Turning Iron into Steel". He came to a valuable conclusion: iron, steel, cast iron, differ in the amount of some impurity. By adding this admixture to iron, by cementation or alloying with cast iron, Réaumur obtained steel. In 1814, K. Careten proved that this impurity is carbon.

Réaumur gave a method for preparing frosted glass.

Today, memory associates his name only with the invention of a long

temperature scale used. In fact, René Antoine Ferchant de Reaumur, who lived in 1683-1757, mainly in Paris, belonged to those scientists who versatility which in our time - the time of narrow specialization - is difficult to imagine. Réaumur was at the same time a technician, physicist and naturalist. He gained great fame outside of France as an entomologist. AT last years In his life, Réaumur came to the idea that the search for a mysterious transforming power should be carried out in those places where its manifestation is most obvious - during the transformation of food in the body, i.e. while assimilating it. He died on October 17, 1757 in the castle of Bermovdier near Saint-Julien-du-Terroux (Mayenne).

It was proposed in 1730 by R. A. Reaumur, who described the alcohol thermometer he invented.

The unit is the degree of Réaumur (), equal to 1/80 of the temperature interval between the reference points - the temperature of melting ice () and boiling water ()

At present, the scale has fallen into disuse; it has been preserved for the longest time in France, in the author's homeland.

Temperature scales, systems of comparable numerical values ​​of temperature. Temperature is not a directly measurable quantity; its value is determined by the temperature change of some physical property of a thermometric substance that is convenient for measuring. Having chosen a thermometric substance and property, it is necessary to set the starting point of reference and the size of the temperature unit - degrees. Thus, empirical temperature scales (hereinafter T.sh.) are determined. In T. sh. Usually, two main temperatures are fixed, corresponding to the points of phase equilibrium of one-component systems (the so-called reference or constant points), the distance between which is called the main temperature interval of the scale. The following are used as reference points: the triple point of water, the boiling points of water, hydrogen and oxygen, the solidification points of silver, gold, etc. The size of a single interval (temperature unit) is set as a certain fraction of the main interval. For the origin of T. sh. take one of the reference points. So you can determine the empirical (conditional) T. sh. for any thermometric property. If we assume that the relationship between and temperature is linear, then temperature , where , and are the numerical values ​​of the property at temperature , at the start and end points of the main interval, - the size of the degree, - the number of divisions of the main interval.

In the Celsius scale, for example, the temperature of solidification of water (melting of ice) is taken as the reference point, the main interval between the points of solidification and boiling of water is divided into 100 equal parts ().

T. sh. represents, therefore, a system of successive temperature values ​​associated linearly with the values ​​of the measured physical quantity (this quantity must be unambiguous and monotonic function temperature). In the general case, T. sh. can differ in thermometric properties (it can be thermal expansion of bodies, a change in the electrical resistance of conductors with temperature, etc.), in thermometric substance (gas, liquid, solid), and also depend on the reference points. In the simplest case, T. sh. differ in numerical values ​​taken for the same reference points. So, in the Celsius (), Reaumur () and Fahrenheit () scales, the points of melting ice and boiling water at normal pressure are assigned different meanings temperature. The ratio for converting temperature from one scale to another:

Direct recalculation for T. sh., Differing in basic temperatures, is impossible without additional experimental data. T. sh., differing in thermometric property or substance, are significantly different. An unlimited number of empirical T.sh. that do not coincide with each other is possible, since all thermometric properties are nonlinearly related to temperature and the degree of nonlinearity is different for different properties and the real temperature, measured according to the empirical T. w., is called the conditional ("mercury", "platinum" temperature, etc.), its unit is the conditional degree. Among empirical T. sh. a special place is occupied by gas scales, in which gases ("nitrogen", "hydrogen", "helium" gases) serve as thermometric substances. These T. sh. less than others depend on the gas used and can be (by introducing corrections) reduced to the theoretical gas temperature. Avogadro, fair for an ideal gas. Absolute empirical T. sh. called the scale, the absolute zero of which corresponds to the temperature at which numerical value physical properties (for example, in the Avogadro gas pipeline, the absolute zero temperature corresponds to the zero pressure of an ideal gas). temperatures (according to empirical T.sh.) and (according to absolute empirical T.sh.) are related by the relation , where is the absolute zero of the empirical T. sh. (the introduction of absolute zero is an extrapolation and does not imply its implementation).

The fundamental shortcoming of the empirical T. sh. - their dependence on the thermometric substance - is absent in the thermodynamic theory of thermodynamics, which is based on the second law of thermodynamics. When determining the absolute thermodynamic T. sh. (Kelvin scale) come from Carnot cycle. If in the Carnot cycle the body executing the cycle absorbs heat at a temperature and gives off heat at a temperature , then the ratio does not depend on the properties of the working fluid and allows you to determine the absolute temperature using the values ​​available for measurements. Initially, the main interval of this scale was set by the points of ice melting and water boiling at atmospheric pressure, the absolute temperature unit corresponded to a part of the main interval, and the ice melting point was taken as the reference point. In 1954, the 10th General Conference on Weights and Measures established the thermodynamic T. sh. one fiducial point- the triple point of water, the temperature of which is taken to be 273.16 K (exactly), which corresponds to . temperature in absolute thermodynamic T. sh. measured in kelvins (K). Thermodynamic temperature, in which the temperature is taken for the melting point of ice, is called centigrade. Relationships between temperatures expressed in the Celsius scale and absolute thermodynamic T. w.:

so the size of the units in these scales is the same. In the United States and some other countries where it is customary to measure temperature on the Fahrenheit scale, absolute T.sh. is also used. Rankin. The relationship between Kelvin and degrees Rankine: , according to the Rankine scale, the melting point of ice corresponds to , boiling point of water .

Any empirical T. sh. reduced to thermodynamic T. sh. the introduction of corrections that take into account the nature of the relationship between the thermometric property and the thermodynamic temperature. Thermodynamic T. sh. is carried out not directly (by carrying out the Carnot cycle with a thermometric substance), but with the help of other processes associated with thermodynamic temperature. In a wide range of temperatures (approximately from the boiling point of helium to the solidification point of gold), thermodynamic T. sh. coincide with T. sh. Avogadro, so that the thermodynamic temperature is determined by the gas temperature, which is measured with a gas thermometer. At lower temperatures, the thermodynamic T. sh. is carried out according to the temperature dependence of the magnetic susceptibility of paramagnets, at higher ones - the scale was redefined several times (MTSh-48, MPTSh-68, MTSh-90): the reference temperatures and interpolation methods changed, but the principle remained the same - the basis of the scale is a set of phase transitions of pure substances with certain values ​​of thermodynamic temperatures and interpolation devices graduated at these points. The ITS-90 scale is currently in effect. The main document (Regulations on the scale) establishes the definition of Kelvin, the values ​​of phase transition temperatures (reference points) and interpolation methods.

The temperature scales used in everyday life - both Celsius and Fahrenheit (used mainly in the USA) - are not absolute and therefore inconvenient when conducting experiments in conditions where the temperature drops below the freezing point of water, due to which the temperature has to be expressed negative number. For such cases, absolute temperature scales were introduced.

One of them is called the Rankin scale, and the other is called the absolute thermodynamic scale (Kelvin scale); temperatures are measured, respectively, in degrees Rankine () and kelvins (K). Both scales start at absolute zero. They differ in that the kelvin is equal to degrees Celsius, and the degree Rankine is equal to degrees Fahrenheit. The freezing point of water at standard atmospheric pressure corresponds to , , .

The scale of the Kelvin scale is tied to the triple point of water (273.16 K), while the Boltzmann constant depends on it. This creates problems with the accuracy of interpreting high temperature measurements. Now the BIPM is considering the possibility of moving to a new definition of the kelvin and fixing the Boltzmann constant, instead of linking to the temperature of the triple point.

Brief summary: the student got acquainted with the classification of scales and their scope.

Practice set

Questions:

1. When and by whom was the modern classification of scales proposed?
2. Define the word scale.
3. List all types of scales known to you and explain how they differ?
4. Why are scales used in psychometrics?
5. What scales are most used in England and America?
6. Which of the above scales appeared first?
7. Which country used the Réaumur scale the longest?
8. How is temperature measured on the absolute thermodynamic temperature scale?
9. Give examples of absolute temperature scales.
10. What is the ratio between kelvin and degree Rankine?

Exercises

1. Draw a diagram showing modern classification scales. Can you make scales by hierarchy.
2. Determine the temperature value in different temperature scales (Fahrenheit, Kelvin)

Why used in physics multiple temperature scales? Well, there is - "Celsius" - and that would be enough, and then - "according to Fahrenheit", "according to Reaumur", "according to Kelvin", and even "according to Rankin", "according to Newton" ... everyone wanted to stick into history and science.

Story

The word "temperature" arose at a time when people believed that hotter bodies contained large quantity special substance - caloric, than in less heated ones. Therefore, temperature was perceived as the strength of a mixture of body substance and caloric. For this reason, the units of measure for 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 molecular kinetic theory, so practical scales measure temperature in conventional units - degrees.

Kelvin scale (K)

It was proposed in 1848 by an English scientist William Thomson(aka Lord Kelvin) as a more accurate way to measure temperature. On this scale, the zero point, or absolute zero, is the lowest possible temperature, that is, a certain theoretical state of matter at which its molecules completely stop moving. this value was obtained by theoretical study of the properties of a gas under zero pressure. On a centigrade scale, absolute zero, or zero Kelvin, corresponds to -273.15ºС. Therefore, in practice, 0ºС can be equated to 273K. Until 1968, the unit of measure kelvin (K) was referred to as degrees Kelvin (ºK). Used in thermodynamics.

The temperature is measured from absolute zero (the state corresponding to the minimum theoretically possible internal energy body), and one kelvin is equal to 1/273.15 of the distance from absolute zero to the triple point of water (the state in which ice, water and water vapor are in equilibrium). The Boltzmann constant is used to convert kelvins to energy units. Derived units are also used: kilokelvin, megakelvin, millikelvin, etc.

Celsius (ºC)

In 1742 a Swedish astronomer Anders Celsius proposed his own scale, in which the temperature of a mixture of water and ice was taken as zero, and the boiling point of water was equated to 100º. The hundredth part of the interval between these reference points is taken as a degree. This scale is more rational than the Fahrenheit and Reaumur scales, and is widely used in science and in everyday life.

Since the freezing and boiling points of water are not well defined, the Celsius scale is currently defined in terms of the Kelvin scale: degrees Celsius equals Kelvin, absolute zero is taken to be -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 changes everything significantly.

Fahrenheit (ºF)

It was proposed in the winter of 1724 by a German scientist Gabriel Fahrenheit. According to this scale, the point was taken as zero, to which, on one very cold winter day (it was in Danzig and Fahrenheit lived there), the mercury in the scientist's thermometer dropped. As another starting point, he chose the temperature of the human body. This interval is divided into 100 degrees. According to this not too logical system, the freezing point of water (that is, zero degrees Celsius) at sea level turned out to be +32º, and the boiling point of water +212º. The scale is popular in the UK and especially in the US.

A degree Fahrenheit is 5/9 degrees Celsius.

The current definition of the Fahrenheit scale is as follows: it is a temperature scale, 1 degree (1 °F) of which is equal to 1/180 of the difference between the boiling point of water and the melting of ice at atmospheric pressure, and the melting point of ice is +32 °F. The temperature on the Fahrenheit scale is related to the temperature on the Celsius scale (t ° C) by the ratio t ° C = 5/9 (t ° F - 32), 1 ° F = 5/9 ° C.

Réaumur scale (ºR)

In 1731 a French scientist René Antoine de Réaumur proposed a temperature scale based on the use of alcohol, which has the property of expanding (together with a description by the alcohol thermometer he invented). The freezing point of water was taken as the lower reference point. Degree Réaumur arbitrarily defined as one thousandth of the volume that alcohol occupies in the tank and tube of the thermometer at zero point. Under normal conditions, the boiling point of water on this scale is 80º. The Réaumur scale is now universally out of use.

Unit - degree Réaumur (°R), 1 °R is equal to 1/80 of the temperature interval between the reference points - the temperature of melting ice (0 °R) and boiling water (80 °R)

1°R = 1.25°C.

At present, the scale has fallen into disuse; it has been preserved for the longest time in France, in the author's homeland.

Rankin scale (ºRa)

Was proposed by a Scottish engineer and physicist William Rankin (William John McWorn Rankin (Rankin)). Its zero coincides with the zero of the thermodynamic temperature, and in size 1ºRa it is equal to 5/9 K. That is, the principle is the same as in the Kelvin scale, only in dimension the Rankine scale does not coincide with the Celsius scale, but with the Fahrenheit scale. This temperature measurement system has not received distribution.

Comparison of temperature scales

¹ Normal human body temperature is 36.6°C ±0.7°C, or 98.2°F ±1.3°F. The commonly given value of 98.6 °F is an exact Fahrenheit conversion of the 19th century German value of 37 °C. Because this value is outside the normal temperature range for modern ideas, we can say that it contains excessive (incorrect) precision. Some values ​​in this table have been rounded.

Comparison of Fahrenheit and Celsius scales

(oF- Fahrenheit scale, o C- Celsius scale)

The most famous for this moment, temperature scales are Fahrenheit, Celsius and Kelvin.

temperature scale fahrenheit most popular in the US. The temperature is measured in degrees, for example 48.2°F (forty-eight and two degrees Fahrenheit), the symbol F indicates that the Fahrenheit scale is used.

Europeans are used to Celsius temperature scale, which also measures temperature in degrees, such as 48.2°C (forty-eight and two degrees Celsius), the symbol C indicates that the Celsius scale is used.

Scientists are more accustomed to operating with Kelvin temperature scale. Until 1968, the kelvin was officially called the degree Kelvin, then it was decided to refer to the temperature value measured on the Kelvin scale, simply in kelvins (without degrees), for example, 48.2 K (forty-eight and two kelvins).

Daniel Gabriel Fahrenheit He invented his scale in the 18th century while making thermometers in Amsterdam. For the zero point of temperature, Fahrenheit took the temperature of a frozen salt solution, which at that time was used to obtain low temperatures in the laboratory. The German physicist set a value of 32°F for the melting point of ice and the freezing point of water (when the temperature rises and falls, respectively). According to the resulting scale, the boiling point of water is 212°F.

In the same 18th century, a Swedish scientist Anders Celsius invented his own temperature scale, which is based on the freezing point (0°C) and boiling point (100°C) of pure water at normal atmospheric pressure.

The Kelvin scale was invented in the 19th century by a British scientist. William Thomson, who later received the honorary title of Baron Kelvin. Thomson based his temperature scale on the concept of absolute zero. Later, the Kelvin scale became the main one in physics, and now the Fahrenheit and Celsius systems are determined through it.

At its core, the temperature of any object characterizes the measure of movement of its molecules - the faster the molecules move, the higher the temperature of the object, and vice versa. The lower the temperature, the slower the molecules move. At absolute zero (0 K), the molecules stop (which cannot be in nature). For this reason, reaching absolute zero or even lower temperatures is impossible.

I must say that the graduation of the Kelvin and Celsius scales are the same (one degree Celsius is equal to one kelvin), and 0 K \u003d -273.15 ° C.

Thus, linking the Kelvin and Celsius temperature scales is very simple:

K=C+273.15 C=K-273.15

Let's try to connect the Celsius and Fahrenheit scales.

As you know, water freezes at 32°F and 0°C: 32°F=0°C. Boils water at 212°F and 100°C: 212°F=100°C.

Thus, for 180 degrees Fahrenheit there are 100 degrees Celsius (ratio 9/5): 212°F-32°F=100°C-0°C.

It should also be noted that the zero point of the Celsius scale corresponds to the 32-degree point of the Fahrenheit scale.

Given the above correspondences between the two scales, we derive the formula for converting temperature from one scale to another:

C \u003d (5/9) (F-32) F \u003d (9/5) C + 32

If you decide this system equations, you can find out that -40°C = -40°F- this is the only temperature at which the value of both scales coincide.

Acting the same way, we connect the Kelvin and Fahrenheit scales:

F = (9/5) (K-273.15)+32 = (9/5)K-459.67 K = (5/9) (F+459.67)

Temperature scales

The temperature scale is a specific functional numerical relationship of temperature with the values ​​of the measured thermometric property. In this regard, it seems possible to construct a temperature scale based on the choice of any thermometric property. At the same time, there is not a single thermometric property that varies linearly with

temperature change and does not depend on other factors in a wide range of temperature measurements. The first scales appeared in the 18th century. To build them, two reference or reference points were chosen. t1 and t2, which are the phase equilibrium temperatures of pure substances. temperature difference t 1 -t 2 called the main temperature range.

Fahrenheit (1715), Réaumur (1776) and Celsius (1742) based their scales on the assumption of a linear relationship between temperature t and thermometric property, which was used as the expansion of the liquid volume V(formula 14.27) /8/

t=a+bV,(14.27)

where a and b- constant coefficients.

Substituting into equation (14.27) V=V1 at t=t1 and V=V2 at t=t2, after transformations we obtain the equation (14.28) of the temperature scale /8/

In Fahrenheit, Réaumur and Celsius scales, the melting point of ice t1 corresponded to +32, 0 and 0 °, and the boiling point of water t2- 212, 80 and 100°. Basic spacing t2–t1 in these scales, respectively, is divided into N= 180, 80 and 100 equal parts, and 1/N part of each of the intervals is called degrees Fahrenheit - t° F, degrees Réaumur - t° R and degrees Celsius t °С. Thus, for scales built according to this principle, the degree is not a unit of measurement, but is a single interval - the scale scale.

To convert the temperature from one specified scale to another, use the relation (14.29)

t°С= 1.25° R=-(5/9)( - 32), (14.29)

Later it was found that the readings of thermometers that have different thermometric substances (for example, mercury, alcohol, etc.), using the same thermometric property and a uniform degree scale, coincide only at reference points, and at other points the readings diverge. The latter is especially noticeable when measuring temperatures, the values ​​of which are located far from the main interval.

This circumstance is explained by the fact that the relationship between temperature and thermometric properties is actually nonlinear and this nonlinearity is different for different thermometric substances. In particular, in the case under consideration, the nonlinearity between the temperature and the change in the liquid volume is explained by the fact that the temperature coefficient of the volumetric expansion of the liquid itself changes with temperature, and this change is different for different dropping liquids.

On the basis of the described principle of construction, any number of temperature scales can be obtained, which differ significantly from each other. Such scales are called conditional, and the scales of these scales are called conditional degrees. The problem of creating a temperature scale independent of the thermometric properties of substances was solved in 1848 by Kelvin, and the scale he proposed was called thermodynamic. Unlike conditional temperature scales, the thermodynamic temperature scale is absolute.

Thermodynamic temperature scale based on the second law of thermodynamics. In accordance with this law, the efficiency of a heat engine operating on a reversible Carnot cycle is determined only by the heater temperatures T N and refrigerator T X and does not depend on the properties of the working substance, thus the efficiency is calculated by the formula (14.30) /8/

(14.30)

where Q N and Q X- respectively, the amount of heat received by the working substance from the heater and given to the refrigerator.

Kelvin proposed to use the equation (14.31) /8/ to determine the temperature

T N / T X \u003d Q N / Q X , (14.31)

Therefore, by using one object as a heater and another as a refrigerator, and performing a Carnot cycle between them, one can determine the ratio of the temperatures of the objects by measuring the ratio of heat taken from one object and given to another. The resulting temperature scale does not depend on the properties of the working (thermometric) substance and is called the absolute temperature scale. To absolute temperature(and not just the ratio) had a certain value, it was proposed to accept the difference in thermodynamic temperatures between the boiling points of water T KV and melting ice T TL, equal to 100 °. The adoption of such a value of the difference pursued the goal of preserving the continuity of the numerical expression of the thermodynamic temperature scale from the centigrade Celsius temperature scale. Thus, denoting the amount of heat received from the heater (boiling water) and given to the refrigerator (melting ice), respectively, through Q HF and Q TL and accepting T KV - T TL == 100, using (14.31), we obtain the equality (14.32) and (14.33)

(14.32)

(14.33)

For any temperature T heater at a constant temperature T TL refrigerator and the amount of heat Q TL, given to it by the working substance of the Carnot machine, we will have the equality (14.34) /8/

(14.34)

Expression (14.34) is the equation centigrade thermodynamic temperature scale and shows that the temperature value T on this scale is linearly related to the amount of heat Q obtained by the working substance of the heat engine when it completes the Carnot cycle, and, as a result, does not depend on the properties of the thermometric substance. One degree of thermodynamic temperature is taken to be such a difference between the temperature of the body and the melting temperature of ice, at which the work done in the reversible Carnot cycle is equal to 1/100 of the work done in the Carnot cycle between the boiling point of water and the melting of ice (provided that in both cycles the amount of heat given off to the refrigerator is the same). From expression (14.30) it follows that at the maximum value should be equal to zero T X. This lowest temperature was called absolute zero by Kelvin. The temperature on the thermodynamic scale is denoted T K. If in an expression describing gas law Gay-Lussac: (where Ro- pressure at t=0 °C; - temperature coefficient of pressure), substitute the temperature value equal to - , then the gas pressure P t will become zero. It is natural to assume that the temperature at which the limiting minimum gas pressure is provided is itself the lowest possible, and is taken as zero on the absolute Kelvin scale. Therefore, the absolute temperature

From the Boyle-Mariotte law, it is known that for gases the temperature coefficient of pressure a is equal to the temperature coefficient of volume expansion. It was experimentally found that for all gases at pressures tending to zero, in the temperature range 0-100 ° C, the temperature coefficient of volume expansion = 1/273.15.

Thus, the zero value of the absolute temperature corresponds to °C. The melting temperature of ice on an absolute scale will be To\u003d\u003d 273.15 K. Any temperature in the absolute Kelvin scale can be defined as (where t temperature in °C). It should be noted that one degree Kelvin (1 K) corresponds to one degree Celsius (1 °C), since both scales are based on the same fixed points. The thermodynamic temperature scale based on two reference points (the melting temperature of ice and the boiling point of water) had insufficient measurement accuracy. In practice, it is difficult to reproduce the temperatures of these points, since they depend on pressure changes, as well as minor impurities in the water. Kelvin and, independently of him, D. I. Mendeleev expressed their views on the expediency of constructing a thermodynamic temperature scale from one reference point. In 1954, the Advisory Committee on Thermometry of the International Committee for Weights and Measures adopted a recommendation to move to the definition of a thermodynamic scale using one reference point - the triple point of water (the equilibrium point of water in the solid, liquid and gaseous phases), which is easily reproduced in special vessels with with an error of no more than 0.0001 K. The temperature of this point is taken equal to 273.16 K, i.e. above the temperature of the ice melting point by 0.01 K. This number was chosen so that the temperature values ​​on the new scale would practically not differ from the old Celsius scale with two fixed points. The second reference point is absolute zero, which is not experimentally realized, but has a strictly fixed position. In 1967, the XIII General Conference on Weights and Measures clarified the definition of the unit of thermodynamic temperature in the following edition: "Kelvin-1/273.16 part of the thermodynamic temperature of the triple point of water." Thermodynamic temperature can also be expressed in degrees Celsius: t= T- 273.15 K. The use of the second law of thermodynamics, proposed by Kelvin in order to establish the concept of temperature and construct an absolute thermodynamic temperature scale that does not depend on the properties of a thermometric substance, is of great theoretical and fundamental importance. However, the implementation of this scale using a heat engine operating according to a reversible Carnot cycle as a thermometer is practically impossible.

The thermodynamic temperature is equivalent to the gas thermal temperature used in the equations describing the laws of ideal gases. The gas-thermal temperature scale is built on the basis of a gas thermometer, in which a gas is used as a thermometric substance, approaching in properties to ideal gas. Thus, the gas thermometer is a real tool for reproducing the thermodynamic temperature scale. There are three types of gas thermometers: constant volume, constant pressure, and constant temperature. Usually a gas thermometer of constant volume is used (Figure 14.127), in which the change in gas temperature is proportional to the change in pressure. The gas thermometer consists of a cylinder 1 and connecting tube 2, filled through the valve 3 hydrogen, helium or nitrogen (for high temperatures). Connecting tube 2 connected to a tube 4 two-pipe pressure gauge, in which the tube 5 can be moved up or down thanks to the flexible connecting hose 6. When the temperature changes, the volume of the system filled with gas changes, and to bring it to its original value, the tube 5 move vertically until the level of mercury in the tube 4 not aligned with axis X-X. At the same time, the column of mercury in the tube 5, measured from the level X-X, will correspond to the gas pressure R in a balloon.

Figure 14.127 - Diagram of a gas thermometer

commonly measured temperature T determined relative to some reference point, for example, relative to the temperature of the triple point of water T0, at which the pressure of the gas in the cylinder will be Ro. The desired temperature is calculated by the formula (14.35)

(14.35)

Gas thermometers are used in the interval ~ 2- 1300 K. The error of gas thermometers is within 3-10-3 - 2-10-2 K depending on the measured temperature. Achieving such high precision measurements -difficult task, which requires taking into account numerous factors: deviations of the properties of a real gas from an ideal one, the presence of impurities in the gas, sorption and desorption of gas by the walls of the cylinder, diffusion of gas through the walls, change in the volume of the cylinder from temperature, temperature distribution along the connecting tube.

Due to the great complexity of working with gas thermometers, attempts were made to find more simple methods reproduction of the thermodynamic temperature scale.

On the basis of studies carried out in various countries at the VII General Conference on Weights and Measures in 1927, it was decided to replace the thermodynamic scale "practical" temperature scale and call her international temperature scale. This scale was consistent with the centigrade thermodynamic scale as closely as the level of knowledge of that time allowed.

To build the international temperature scale, six reproducible reference points were chosen, the temperatures of which on the thermodynamic scale were carefully measured in various countries using gas thermometers and the most reliable results were accepted. With the help of fiducial points, reference instruments are calibrated to reproduce the international temperature scale. In the intervals between the reference points, the temperature values ​​are calculated according to the proposed interpolation formulas that establish the relationship between the readings of standard instruments and the temperature on the international scale. In 1948, 1960 and 1968 a number of clarifications and additions were made to the provisions on the international temperature scale, since, on the basis of improved measurement methods, differences were found between this scale and the thermodynamic scale, especially at high temperatures, and also due to the need to extend the temperature scale to lower temperatures. At present, the improved scale adopted at the XIII Conference on Weights and Measures under the name "International Practical Temperature Scale 1968" (IPTP-68) is in force. The definition "practical" indicates that this temperature scale generally does not coincide with the thermodynamic one. MPTSh-68 temperatures are supplied with an index ( T68 or t68).

MPTSh-68 is based on 11 main reference points listed in Table 9. Along with the main ones, there are 27 secondary fixed points covering the temperature range from 13.956 to 3660 K (from -259.194 to 3387 °C). The numerical values ​​of temperatures given in Table 14.4 correspond to the thermodynamic scale and are determined using gas thermometers.

As a reference thermometer in the temperature range from 13.81 to 903.89 K (630.74 ° C - the solidification point of antimony - the secondary reference point), a platinum resistance thermal converter is taken. This interval is divided into five subintervals, for each of which interpolation formulas are defined in the form of polynomials up to the fourth degree. In the temperature range from 903.89 to 1337.58 K, a reference platinum-platinum-rhodium thermoelectric thermometer is used. The interpolation formula that relates the thermoelectromotive force to the temperature here is a polynomial of the second degree.

For temperatures above 1337.58 K (1064.43°C), MPTS-68 is reproduced using a quasi-monochromatic thermometer using Planck's radiation law.

Table 14.4 - Main fiducial points of IPTS-68

Measurement of heat and power quantities

Temperature is one of the most important heat and power quantities. Temperature is a physical quantity that characterizes the degree of heating of a body or its heat and energy potential. Almost all technological processes and various properties of matter depend on temperature.

Unlike such physical quantities as mass, length, etc., temperature is not an extensive (parametric), but an intensive (active) quantity. If a homogeneous body is divided in half, then its mass is also divided in half. Temperature, being an intensive quantity, does not possess such an additivity property, i.e. for a system in thermal equilibrium, any part of the system has the same temperature. Therefore, it does not appear possible creation temperature standard, just as the standards of extensive quantities are created.

The temperature can only be measured indirectly, based on the temperature dependence of such physical properties bodies that are directly measurable. These properties of bodies are called thermometric. These include length, density, volume, thermal emf, electrical resistance, etc. Substances with thermometric properties are called thermometric. The instrument for measuring temperature is called a thermometer. To create a thermometer, you must have a temperature scale.

The temperature scale is a specific functional numerical relationship of temperature with the values ​​of the measured thermometric property. In this regard, it seems possible to construct temperature scales based on the choice of any thermometric property. At the same time, there is no general thermometric property that is linearly related to temperature change and does not depend on other factors in a wide range of temperature measurements.

The first temperature scales appeared in the 18th century. To construct them, two reference (reference) points t 1 and t 2 were chosen, which are the phase equilibrium temperatures of pure substances. The temperature difference t 2 - t 1 is called main temperature range. The German physicist Gabriel Daniel Fahrenheit (1715), the Swedish physicist Anders Celsius (1742) and the French physicist Rene Antoine Réaumur (1776) based their scales on the assumption of a linear relationship between temperature t and thermometric property, which was used as the expansion of the liquid volume V, i.e.

t = a + bV, (1)

where a and b are constant coefficients.

Substituting into this equation V \u003d V 1 at t \u003d t 1 and V \u003d V 2 at t \u003d t 2, after transformation, we obtain the temperature scale equation:

In the scales of Fahrenheit, Reaumur and Celsius, the melting point of ice t 1 corresponded to +32 0, 0 0 and 0 0, and the boiling point of water t 2 - 212 0, 80 0 and 100 0. The main interval t 2 - t 1 in these scales is divided into N \u003d 180, 80 and 100 equal parts, respectively, and the 1 / N part of each of the intervals is called degrees Fahrenheit - t 0 F, degrees Reaumur t 0 R and degrees Celsius t 0 C Thus, for scales constructed according to the indicated principle, the degree is not a unit of measurement, but is a single interval - the scale scale.

To convert temperature from one scale to another, use the ratio:

(3)

Later it was found that the readings of thermometers with different thermometric substances (mercury, alcohol, etc.), using the same thermometric property and a uniform degree scale, coincide only at the reference points, and at other points the readings diverge. The latter is especially noticeable when measuring temperatures, the values ​​of which are located far from the main interval.

This circumstance is explained by the fact that the relationship between temperature and thermometric property is actually non-linear and this non-linearity is different for different thermometric substances. In particular, the non-linearity between temperature and liquid volume change is explained by the fact that the temperature coefficient of liquid volume expansion itself changes with temperature and this change is different for different dropping liquids.

On the basis of the described principle, it is possible to build any number of scales that differ significantly from each other. Such scales are called conditional, and the scales of these scales are called conditional degrees.

The problem of creating a temperature scale independent of the thermometric properties of substances was solved in 1848 by Kelvin, and the scale he proposed was called thermodynamic. Unlike conditional temperature scales, the thermodynamic temperature scale is absolute.

Thermodynamic temperature scale based on the second law of thermodynamics. In accordance with this law, the efficiency h of a heat engine operating according to the reverse Carnot cycle is determined only by the temperature of the heater T n and the refrigerator T x and does not depend on the properties of the working substance:

(4)

where Q n and Q x - respectively, the amount of heat received by the working substance from the heater and given to the refrigerator.

Kelvin proposed to use the equality to determine the temperature

Therefore, by using one object as a heater and another as a refrigerator, and running a Carnot cycle between them, one can determine the ratio of the temperatures of the objects by measuring the ratio of heat taken from one object and given to another. The resulting temperature scale does not depend on the properties of the working substance and is called the absolute temperature scale. In order for the absolute temperature to have a certain value, it was proposed to take the difference in thermodynamic temperatures between the boiling points of water T kv and melting ice T t equal to 100 0 . The adoption of such a difference pursued the goal of preserving the continuity of the numerical value of the thermodynamic temperature scale from the centigrade Celsius temperature scale. T.O., denoting the amount of heat received from the heater (boiling water) and given to the refrigerator (melting ice), respectively, through Q kv and Q tl, and assuming T kv - T tl \u003d 100, we get:

and (6)

For any temperature T of the heater at a constant value of T t of the refrigerator and the amount of heat Q t given to it by the working substance of the Carnot machine, we will have:

(7)

Equation (6) is the equation centigrade thermodynamic temperature scale and shows that the temperature value T on this scale is linearly related to the amount of heat Q received by the working substance of the heat engine when it performs the Carnot cycle, and, as a result, does not depend on the properties of the thermodynamic substance. One degree of thermodynamic temperature is taken to be such a difference between the temperature of the body and the melting temperature of ice, at which the work done in the reverse Carnot cycle is equal to 1/100 of the work done in the Carnot cycle between the boiling point of water and the melting of ice (provided that in both cycles the amount of heat given off to the refrigerator is the same).

From the definition of efficiency it follows that at the maximum value h=1 should be equal to zero T x. This lowest temperature was called absolute zero by Kelvin. The temperature on the thermodynamic scale is denoted by "K".

The thermodynamic temperature scale based on two fixed points has insufficient measurement accuracy. It is practically difficult to reproduce the temperatures of these points, since they depend on the pressure as well as on the salt content of the water. Therefore, Kelvin and Mendeleev expressed the idea of ​​the expediency of constructing a thermodynamic temperature scale from one reference point.

In 1954, the Advisory Committee on Thermometry of the International Committee for Weights and Measures adopted a recommendation to move to the definition of a thermodynamic scale using one reference point - the triple point of water (equilibrium points of water in the solid, liquid and gaseous phases), which is easily reproduced in special vessels with an error not more than 0.0001 K. The temperature of this point is taken equal to 273.16 K, i.e. above the melting temperature of ice by 0.01 K. This number was chosen so that the temperature values ​​on the new scale would practically not differ from the old Celsius scale with two fixed points. The second reference point is absolute zero, which is practically not implemented, but has a strictly fixed position.

In 1967, the XIII General Assembly on Weights and Measures clarified the definition of the unit of thermodynamic temperature in the following edition: " Kelvin- 1/273.16 of the thermodynamic temperature of the triple point of water. Thermodynamic temperature can also be expressed in degrees Celsius:

t = T– 273.15K (8)