The material in this article gives an idea of such an important concept as temperature. Let's give a definition, consider the principle of temperature change and the diagram for constructing temperature scales.
What is temperature
Definition 1Temperature is a scalar physical quantity that describes the state of thermodynamic equilibrium of a macroscopic system of bodies.
The concept of temperature is also used as a physical quantity that determines the degree of heating of a body, but only such an interpretation is not enough to understand the meaning of the term. All physical concepts are related to certain fundamental laws and are given meaning only in accordance with these laws. In this case, the term temperature is associated with the concept of thermal equilibrium and with the law of macroscopic irreversibility.
The phenomenon of thermodynamic equilibrium of the bodies that make up the system indicates the presence of the same temperature of these bodies. Temperature can be measured only indirectly, taking as a basis the dependence on temperature of such physical properties of bodies that can be measured directly.
Definition 2
Substances or bodies used to obtain a temperature value are called thermometric.
Let's say two thermally insulated bodies are brought into thermal contact. One body will transfer a flow of energy to another: the process of heat transfer will start. In this case, the body giving off heat has a correspondingly higher temperature than the body “receiving” the heat flow. It is obvious that after some time the heat transfer process will stop and thermal equilibrium will occur: it is assumed that the temperatures of the bodies are equalized relative to each other, their values will be somewhere in the interval between the initial temperature values. Thus, temperature serves as a marker of thermal equilibrium. It turns out that any value t that meets the requirements:
- t 1 > t 2 , when heat transfer occurs from the first body to the second;
- t 1 " = t 2 " = t , t 1 > t > t 2 , when thermal equilibrium is established, it can be taken as temperature.
We also note that the thermal equilibrium of bodies is subject to the law of transitivity.
Definition 3
Law of transitivity: when two bodies are in equilibrium with a third, then they are in thermal equilibrium with each other.
An important feature of this definition of temperature is its ambiguity. By choosing different quantities to meet the established requirements (which will affect the way temperature is measured), it is possible to obtain divergent temperature scales.
Definition 4
Temperature scale is a method of dividing a temperature interval into parts.
Let's look at an example.
Example 1
A well-known device for measuring temperature is a thermometer. For consideration, let’s take thermometers of various devices. The first is represented by a mercury column in the capillary of the thermometer, and the temperature value here is determined by the length of this column, which meets conditions 1 and 2 indicated above.
And one more way to measure temperature: using a thermocouple - an electrical circuit with a galvanometer and two junctions of dissimilar metals (Figure 1 ).
Figure 1
One junction is in an environment with a fixed temperature (in our example, this is melting ice), the other is in an environment whose temperature needs to be determined. Here, a sign of temperature is the emf of the thermocouple.
These methods of measuring temperature will not give the same results. And to transition from one temperature to another, a calibration curve should be constructed that will establish the dependence of the emf of the thermocouple on the length of the mercury column. In this case, the uniform scale of a mercury thermometer is converted into an uneven scale of a thermocouple (or vice versa). The uniform temperature measurement scales of a mercury thermometer and a thermocouple create two completely different temperature scales on which a body in the same state will have different temperatures. It is also possible to consider thermometers that are identical in design, but have different “thermal bodies” (for example, mercury and alcohol): we will not observe the same temperature scales in this case. The graph of the length of the mercury column versus the length of the alcohol column will not be linear.
From the above we can conclude that the concept of temperature, based on the laws of thermal equilibrium, is ambiguous. This temperature is empirical and depends on the measurement method. An arbitrary point is taken as the “zero” of the empirical temperature scale. According to the definition of empirical temperature, only the temperature difference or its change has physical meaning. Any empirical temperature scale is converted into a thermodynamic temperature scale using corrections that take into account the nature of the relationship between the thermometric property and thermodynamic temperature.
In order to construct a temperature scale for measurement, two fixed reference points are assigned to two numerical temperature values. After this, the difference in the numerical values assigned to the reference points is divided into the required number of parts chosen at random, resulting in a unit of temperature measurement.
The initial values used as the starting point and unit of measurement are the temperatures of transition of chemically pure substances from one state of aggregation to another, for example, the melting temperature of ice t 0 and the boiling point of water t k at normal atmospheric pressure (Pa ≈ 10 5 Pa ) . The quantities t 0 and t k have different meanings in different types of temperature measurement scales:
- According to the Celsius scale (centigrade scale): the boiling point of water tk = 100 ° C, the melting point of ice t0 = 0 ° C. In the Celsius scale, the temperature of the triple point of water is 0.01 ° C at a pressure of 0.06 atm.
Triple point of water- such a temperature and pressure at which all three states of aggregation of water can exist in equilibrium simultaneously: liquid, solid (ice) and steam.
- According to the Fahrenheit scale: the boiling point of water tk = 212 °F; melting temperature of ice t 0 = 32 ° C.
The difference in temperatures expressed in degrees Celsius and Fahrenheit is leveled according to the following expression:
t°C 100 = t°F - 32,180 or t°F = 1.8°C + 32.
Zero on this scale is defined as the freezing point of a mixture of water, ammonia and salt, taken in a 1: 1: 1 ratio.
- According to the Kelvin scale: boiling point of water t k = 373 K; melting temperature of ice t 0 = 273 K. Here the temperature is measured from absolute zero (t = 273.15 ° C) and is called thermodynamic or absolute temperature. T = 0 K – this temperature value corresponds to the absolute absence of thermal fluctuations.
Temperature values on the Celsius scale and on the Kelvin scale are related to each other according to the following expression:
T(K) = t°C + 273.15°C.
- According to the Reaumur scale: boiling point of water tk = 80 ° R; melting temperature of ice t 0 = 0 ° R. Reaumur's thermometer used alcohol; at the moment the scale is almost not used.
Temperatures expressed in degrees Celsius and degrees Réaumur are related as follows:
1°C = 0.8°R.
- According to the Rankine scale: boiling point of water t k = 671.67 ° R a ; melting temperature of ice t0 = 491.67 ° R a. The beginning of the scale corresponds to absolute zero. The number of degrees between the reference points of freezing and boiling water on the Rankine scale is identical to the Fahrenheit scale and is equal to 180.
Kelvin and Rankine temperatures are related by:
°R a = °F + 459.67.
Degrees Fahrenheit can be converted to degrees Rankine according to the formula:
°R a = °F + 459.67.
The Celsius scale is most applicable in everyday life and technical devices (the scale unit is degrees Celsius, denoted as °C).
In physics, they use thermodynamic temperature, which is not just convenient, but also carries a deep physical meaning, since it is defined as the average kinetic energy of a molecule. The unit of thermodynamic temperature is the degree Kelvin (until 1968) or now simply Kelvin (K), which is one of the basic units in CI. The temperature T = 0 K is called the absolute zero temperature, as mentioned above.
In general, modern thermometry is based on the ideal gas scale: pressure is taken as the thermometric value. The scale of the gas thermometer is absolute (T = 0, p = 0). When solving practical problems, it is most often necessary to use this temperature scale.
Example 2
It is accepted that a room temperature comfortable for a person is in the range from + 18 ° C to + 22 ° C. It is necessary to calculate the boundaries of the comfort temperature interval according to the thermodynamic scale.
Solution
Let's take as a basis the ratio T (K) = t ° C + 273.15 ° C.
Let's calculate the lower and upper limits of comfort temperature on a thermodynamic scale:
T = 18 + 273 ≈ 291 (K) ; T = 22 + 273 ≈ 295 (K) .
Answer: The boundaries of the comfort temperature interval on the thermodynamic scale are in the range from 291 K to 295 K.
Example 3
It is necessary to determine at what temperature the thermometer readings on the Celsius scale and on the Fahrenheit scale will be the same.
Solution
Figure 2
Let's take as a basis the ratio t ° F = 1.8 t ° C + 32.
According to the conditions of the problem, the temperatures are equal, then it is possible to formulate the following expression:
x = 1.8 x + 32.
Let us define the variable x from the resulting record:
x = - 32 0, 8 = - 40 ° C.
Answer: at a temperature of - 40 ° C (or - 40 ° F), the thermometer readings on the Celsius and Fahrenheit scales will be the same.
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Temperature is also called a physical quantity that characterizes the degree of heating of a body, but this is not enough to understand the meaning and meaning of the concept of temperature. In this phrase there is only a replacement of one term with another and no more understandable one. Usually physical concepts are associated with some fundamental laws and gain meaning only in connection with these laws. The concept of temperature is associated with the concept of thermal equilibrium and, therefore, with the law of macroscopic irreversibility.
Temperature change
In a state of thermodynamic equilibrium, all bodies forming the system have the same temperature. Temperature can only be measured indirectly, based on the temperature dependence of such physical properties of bodies that can be measured directly. The substances (bodies) used for this are called thermometric.
Let two thermally insulated bodies be brought into thermal contact. A flow of energy will rush from one body to another, and the process of heat transfer will occur. In this case, it is believed that the body that gives off heat has a higher temperature than the body to which the heat flow rushes. Naturally, after some time the energy flow stops and thermal equilibrium occurs. It is assumed that body temperatures equalize and settle somewhere in the interval between the initial temperature values. So, it turns out that temperature is a certain marker of thermal equilibrium. It turns out that any value t that meets the requirements:
- $t_1>t_2$, if the heat flow goes from the first body to the second;
- $t"_1=t"_2=t,\ t_1 > t > t_2$, can be taken as temperature when thermal equilibrium is established.
It is assumed that the thermal equilibrium of bodies obeys the law of transitivity: if two bodies are in equilibrium with a third, then they are in thermal equilibrium with each other.
The most important feature of the above definition of temperature is its ambiguity. We can choose the quantities that satisfy the requirements in different ways (which will be reflected in the ways we measure temperature) and end up with divergent temperature scales. Temperature scales are ways of dividing temperature intervals into parts.
Let's give examples. As you know, a device for measuring temperature is a thermometer. Let's consider two types of thermometers of different devices. In one, the role of body temperature is played by the length of the mercury column in the capillary of the thermometer, in the case when the thermometer is in thermal equilibrium with the body whose temperature we are measuring. The length of the mercury column satisfies conditions 1 and 2, which are given above and apply to temperature.
There is another way to measure temperature: using a thermocouple. A thermocouple is an electrical circuit with a galvanometer and two junctions of dissimilar metals (Fig. 1). One junction is placed in a medium with a fixed temperature, for example melting ice, the other in a medium whose temperature must be determined. In this case, the temperature indicator is considered to be the emf of the thermocouple. These two methods of measuring temperature will not give the same results. And in order to move from one temperature to another, it is necessary to construct a calibration curve that establishes the dependence of the emf of the thermocouple on the length of the mercury column. Then the uniform scale of the mercury thermometer is converted into an uneven scale of the thermocouple (or vice versa). The uniform scales of a mercury thermometer and a thermocouple form two completely different temperature scales, on which a body in the same state will have different temperatures. You can take thermometers of the same design, but with different “thermal bodies” (for example, mercury and alcohol). Their temperature scales will also not match. The graph of the length of the mercury column versus the length of the alcohol column will not be linear.
It follows that the concept of temperature, based on the laws of thermal equilibrium, is not unique. This temperature is called empirical, it depends on the method of measuring temperature. The zero of the empirical temperature scale is always set arbitrarily. According to the definition of empirical temperature, only the temperature difference, that is, its change, has physical meaning. Any empirical temperature scale is reduced to a thermodynamic temperature scale by introducing corrections that take into account the nature of the relationship between the thermometric property and thermodynamic temperature.
Temperature scales
To construct a temperature scale, numerical temperature values are assigned to two fixed reference points. Then divide the temperature difference between the reference points into a randomly selected number of parts, obtaining a unit of temperature measurement. As the initial values that serve when constructing a temperature scale to establish the origin and its unit - degrees, the transition temperatures of chemically pure substances from one state of aggregation to another are used, for example, the melting temperature of ice $t_0$ and the boiling point of water $t_k$ at normal atmospheric pressure ($\approx 10^5Pa).$ The quantities $t_0\ and\ t_k$ have different meanings:
- on the Celsius scale (centigrade scale): boiling point of water $t_k=100^0C$, melting point of ice $t_0=0^0C$. The Celsius scale is a scale in which the temperature of the triple point of water is 0.010C at a pressure of 0.06 atm. (The triple point of water is a certain temperature and pressure at which water, its steam and ice can simultaneously exist in equilibrium.);
- on the Fahrenheit scale, the boiling point of water $t_k=212^0F;$ $t_0$=3$2^0F$ -- the melting point of ice;
- on the Kelvin scale: temperature is measured from absolute zero (t=-273.50C) and is called thermodynamic or absolute temperature. T=0K is a state corresponding to the complete absence of thermal fluctuations. The boiling point of water on this scale is $t_k=373K$, the melting point of ice is $t_0=273K$. Relationship between Kelvin temperature and Celsius temperature: \
- according to the Reaumur scale, the boiling point of water is $t_k=80^0R$, the melting point of ice is $t_0=0^0R.$ The scale has practically fallen out of use. The relationship between temperatures expressed in degrees Celsius and degrees Réaumur: \
- according to the Rankine scale, the boiling point of water is $t_k=671.67^(0\ )Ra$, the melting point of ice is $t_0=(491.67)^0Ra.$ The scale starts from absolute zero. The number of degrees between the freezing and boiling points of water on the Fahrenheit and Rankine scales is the same and equal to 180.
The relationship between temperatures expressed in degrees Celsius and Fahrenheit is:
\[\frac(t^0C)(100)=\frac(t^0F-32)(180)\ \ or\ t^0F=1.8t^0C+32\ \left(1\right);\ ]
Zero on this scale is determined by the freezing point of a mixture of water, salt and ammonia in a 1:1:1 ratio.
Reaumur's thermometer used alcohol.
The relationship between kelvin and degree Rankine: 1K=1.$8^(0\ )Ra$, degrees Fahrenheit are converted to degrees Rankine using the formula:
\[^0Ra=^0F+459.67\left(4\right);\]
In technology and in everyday life, temperatures are used on the Celsius scale. The unit of this scale is called the degree Celsius ($^0C).\ $ In physics, they use thermodynamic temperature, which is not only more convenient, but also has a deep physical meaning, since it is determined by the average kinetic energy of the molecule. The unit of thermodynamic temperature, the degree kelvin (until 1968), or now simply kelvin (K), is one of the base units in the SI. Temperature T=0K is called absolute zero temperature. Modern thermometry is based on the ideal gas scale, where pressure is used as a thermometric quantity. The gas thermometer scale is absolute (T=0, p=0). When solving problems, you will most often have to use this temperature scale.
Temperature and temperature scales
Temperature - degree of heating of the substance. This concept is based on the ability of different bodies (substances) to transfer heat to each other at different degrees of heating and to be in a state of thermal equilibrium at equal temperatures. Moreover, heat is always transferred from a body with a higher temperature to a body with a lower temperature. Temperature can also be defined as a parameter of the thermal state of a substance, determined by the average kinetic energy of movement of its molecules. From here it is obvious that the concept of “temperature” is inapplicable for one molecule, because at any particular temperature the energy of one molecule cannot be characterized by an average value. From this provision it follows that the concept of “temperature” is statistical.
Temperature is measured by devices called thermometers, the basis of which can be based on various physical principles. The ability to measure temperature with such devices is based on the phenomenon of thermal exchange between bodies with different degrees of heating and changes in their physical (thermometric) properties when heated (cooled).
To quantitatively determine temperature, it is necessary to choose one or another temperature scale. Temperature scales are built on the basis of certain physical properties of a substance, which should not depend on extraneous factors and should be accurately and conveniently measured. In fact, there is not a single thermometric property for thermometric bodies or substances that would completely satisfy the specified conditions over the entire range of measured temperatures. Therefore, temperature scales are defined for different temperature ranges, based on the arbitrary assumption of a linear relationship
between the property of a thermometric body and temperature. Such scales are called conditional and the temperature measured by them -conditional.
4 The conventional temperature scale includes one of the most common scales - the Celsius scale. According to this scale, the melting points of ice and the boiling point of water at normal atmospheric pressure are taken as the boundaries of the conditional measurement range, and one hundredth of this scale is usually called one degree Celsius (\ WITH),
| However, constructing such a temperature scale without using liquid thermometers can lead to a number of difficulties associated with the properties of the thermometric liquids used. For example, the readings of mercury and alcohol thermometers operating on the principle of liquid expansion will be different when measuring the same temperature due to different coefficients of their volumetric expansion.
| Therefore, to improve the conventional temperature scale, it was proposed to use a gas thermometer using gases whose properties would differ slightly from the properties of an ideal gas (hydrogen, helium, nitrogen, etc.).
Using a gas thermometer, temperature measurement can be based on changes in the volume or pressure of gas in a closed thermal system.
In practice, a method based on measuring pressure at a constant volume has become more widespread, because is more accurate and easy to implement.
To create a unified temperature scale that is not related to the thermometric properties of various substances for a wide temperature range, Kelvin proposed a temperature scale based on the second law of thermodynamics. This scale is called thermodynamic temperature scale.
It is based on the following provisions:
If, during a reversible Carnot cycle, a body absorbs heat 0, at temperature T, and releases heat C? 3 at temperature T 2, then the following equality must be observed:
THAT,
n<Г (21)
According to the principles of thermodynamics, this ratio does not depend on the properties of the working fluid.
I The Kelvin thermodynamic temperature scale began to be used as the initial scale for other temperature scales that do not depend on the thermometric properties of the working substance. To determine one degree on this scale, the interval between the melting points of ice and the boiling point of water is divided, as in the centigrade Celsius scale, into one hundred equal parts. Thus, I П С turns out to be equal to ] °К
* According to this scale, commonly called absolute The zero point is taken to be a temperature 273.15° below the melting point of ice, called absolute zero. It has been theoretically proven that at this temperature all thermal movement of the molecules of any substance ceases, therefore this scale is to a certain extent theoretical in nature.
The following relationship applies between temperature T, expressed in Kelvin, and temperature *, expressed in degrees Celsius:
1=T-T 0 , (2.2)
where T 0 = 273.15 K.
Of the existing thermometers, gas thermometers most accurately implement the absolute temperature scale in the range of no higher than 1200 °C. The use of these thermometers at higher temperatures faces great difficulties; in addition, gas thermometers are quite complex and bulky devices, which is inconvenient for practical purposes. Therefore, for the practical and convenient reproduction of the thermodynamic scale in wide ranges of temperature changes, International practical standards are accepted and used
temperature cabinets (MPTS). Currently, the temperature scale MPTS-68, adopted in 1968, is in force, the construction of which is based on reference points determined by the phase state of substances. These reference points are used to standardize temperatures in various ranges, which are given in table. 2.1.
The most well-known temperature scales at the moment are the Fahrenheit, Celsius and Kelvin scales.
Fahrenheit temperature scale most popular in the USA. Temperature is measured in degrees, for example 48.2°F (forty-eight point two degrees Fahrenheit), the symbol F indicates that the Fahrenheit scale is used.
Europeans are accustomed to Celsius temperature scale, which also measures temperature in degrees, for example 48.2°C (forty-eight point 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, kelvin was officially called the Kelvin degree, then it was decided to name 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 invented his scale in the 18th century while making thermometers in Amsterdam. Fahrenheit took the temperature of a frozen salt solution, which at that time was used to obtain low temperatures in laboratory conditions, as the zero temperature point. The German physicist set the value of 32°F for the melting point of ice and the freezing point of water (with increasing and decreasing temperatures, 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 subsequently 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 happen in nature). For this reason, it is impossible to reach absolute zero or even lower temperatures.
It must be said that the graduations of the Kelvin and Celsius scales are the same (one degree Celsius is equal to one kelvin), and 0 K = -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. Water boils at 212°F and 100°C: 212°F=100°C.
Thus, for 180 degrees Fahrenheit there are 100 degrees Celsius (9/5 ratio): 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.
Taking into account the above correspondences between the two scales, we derive the formula for converting temperature from one scale to another:
C = (5/9) (F-32) F = (9/5) C+32
If you solve this system of equations, you can find out that -40°C = -40°F- this is the only temperature at which the values of both scales coincide.
Proceeding in a similar 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)
Humanity learned to measure temperature approximately 400 years ago. But the first instruments resembling today's thermometers appeared only in the 15th century. The inventor of the first thermometer was the scientist Gabriel Fahrenheit. In total, several different temperature scales were invented in the world, some of them were more popular and are still used today, others gradually fell out of use.
Temperature scales are systems of temperature values that can be compared with each other. Since temperature is not a quantity that can be directly measured, its value is associated with a change in the temperature state of a substance (for example, water). On all temperature scales, as a rule, two points are recorded corresponding to the transition temperatures of the selected thermometric substance into different phases. These are the so-called reference points. Examples include the boiling point of water, the solidification point of gold, etc. One of the points is taken as the origin. The interval between them is divided into a certain number of equal segments, which are single. One degree is universally accepted as a unit.
The most popular and widely used temperature scales in the world are the Celsius and Fahrenheit scales. However, let’s look at the available scales in order and try to compare them from the point of view of ease of use and practical usefulness. There are five most famous scales:
1. The Fahrenheit scale was invented by Fahrenheit, a German scientist. On one of the cold winter days of 1709, the mercury in the scientist’s thermometer dropped to a very low temperature, which he proposed to take as zero on the new scale. Another reference point was the temperature of the human body. The freezing point of water on his scale was +32°, and the boiling point +212°. The Fahrenheit scale is not particularly thoughtful or convenient. Previously, it was widely used at present - almost only in the USA.
2. According to the Reaumur scale, invented by the French scientist René de Reaumur in 1731, the lower reference point is the freezing point of water. The scale is based on the use of alcohol, which expands when heated; a degree was taken to be a thousandth of the volume of alcohol in the reservoir and tube at zero. This scale is now out of use.
3. On the Celsius scale (proposed by a Swede in 1742), the temperature of the mixture of ice and water (the temperature at which ice melts) is taken as zero; the other main point is the temperature at which water boils. It was decided to divide the interval between them into 100 parts, and one part was taken as the unit of measurement - degrees Celsius. more rational than the Fahrenheit scale and the Reaumur scale, and is now used everywhere.
4. The Kelvin scale was invented in 1848 by Lord Kelvin (English scientist W. Thomson). The zero point on it corresponded to the lowest possible temperature at which the movement of molecules of a substance stops. This value was theoretically calculated when studying the properties of gases. On the Celsius scale, this value corresponds to approximately - 273 ° C, i.e. zero Celsius is equal to 273 K. The unit of measurement of the new scale was one kelvin (originally called “degree Kelvin”).
5. (named after the Scottish physicist W. Rankin) has the same principle as the Kelvin scale, and the dimension is the same as the Fahrenheit scale. This system was practically not widespread.
The temperature values that the Fahrenheit and Celsius scales give us can be easily converted to each other. When converting “in your head” (i.e. quickly, without using special tables) Fahrenheit values into degrees Celsius, you need to reduce the original figure by 32 units and multiply by 5/9. Vice versa (from the Celsius to Fahrenheit scale) - multiply the original value by 9/5 and add 32. For comparison: temperature in Celsius is 273.15 °, in Fahrenheit - 459.67 °.
