Ideal gas equation of state
allows us to take as a thermometric quantity either p, or V, which can be measured with great accuracy.
As the experiment shows, sufficiently rarefied gases are very close to ideal. Therefore, they can be taken directly as a thermometric body.
In this way, one arrives at the ideal-gas temperature scale. The ideal gas temperature is the temperature measured by a gas thermometer filled with a rarefied gas. The advantage of the ideal gas temperature scale over all other empirical temperature scales is that, as experience shows, the temperature T, determined by formula (4), very weakly depends on the chemical nature of the gas with which the tank of the gas thermometer is filled. Indications various gases thermometers when measuring the temperature of the same body differ very little from each other.
In practice, a gas thermometer is usually implemented in the following way: volume of gas V is maintained constant, then the measured pressure serves as an indicator of temperature p.
Charles's law for reference points in this case will have the form:
where p 1 - pressure of a certain mass of gas, close to ideal, at the temperature of melting ice T 1 ; R 2 - pressure at the boiling point of water T 2 .
The degree of temperature, by definition, can be chosen such that the difference between the indicated temperatures is equal to 100, i.e.
It has been experimentally established that the pressure R 2 is 1.3661 times greater than R one . Therefore, to calculate T 2 and T 1 we have two equations: K and . Their solution gives T 1 = 273.15 K; T 2 \u003d 373.15 K.
To determine the temperature of a body, it is brought into contact with a gas thermometer and, after thermal equilibrium is established, the pressure is measured. R gas in a thermometer. In this case, the body temperature is determined by the formula
It follows from this that when T=0 R=0. The temperature corresponding to zero pressure ideal gas is called absolute zero, and the temperature measured from absolute zero is called absolute temperature. Here the concept of absolute zero temperature is introduced on the basis of extrapolation. In reality, as we approach absolute zero, there are more and more noticeable deviations from the laws ideal gases the gases begin to condense. A rigorous proof of the existence of absolute zero temperature is based on the second law of thermodynamics.
Kelvin scale
(absolute thermodynamic temperature scale)
In SI, it was agreed to determine the temperature scale by one reference point, which was taken as the triple point of water. In the so-called absolute thermodynamic temperature scale, or the Kelvin scale, it is assumed by definition that the temperature of this point is exactly 273.16 K.
Such a choice numerical value made so that the interval between the normal melting points of ice and the boiling point of water is, as accurately as possible, 100 K, using an ideal gas thermometer. This establishes the continuity of the Kelvin scale with the previously used scale with two fixed points. The measurements showed that the temperatures of the normal melting points of ice and the boiling points of water in the described scale are approximately 273.15 and 373.15 K, respectively.
The temperature scale defined in this way does not depend on the individual properties of the thermometric substance.
Absolute thermodynamic temperature T, counted on this scale, is a measure of the intensity of the chaotic motion of molecules and is a monotonic function of internal energy. For an ideal gas is directly related to the internal energy ().
It received the name "thermodynamic" because it can be derived completely independently from purely thermodynamic calculations on the basis of the second law of thermodynamics.
The absolute thermodynamic scale is the main temperature scale in physics. In the temperature range where a gas thermometer is suitable, this scale practically does not differ from the ideal gas temperature scale.
Celsius temperature ( t, ) connected with T(in K) equality
And K.
Types of thermometers
The temperature cannot be measured directly. Therefore, the action of thermometers is based on various physical phenomena, depending on temperature: on thermal expansion of liquids, gases and solids, changes in gas or saturated vapor pressure with temperature, electrical resistance, thermal emf, magnetic susceptibility, etc.
The main units of all devices for measuring temperature are a sensitive element, where a thermometric property is realized, and a measuring device associated with it (pressure gauge, potentiometer, measuring bridge, millivoltmeter, etc.).
The standard of modern thermometry is a gas thermometer of constant volume (pressure is a thermometric quantity). With the help of gas thermometers, the temperature is measured in a wide range: from 4 to 1000 K. Gas thermometers are usually used as primary instruments, according to which secondary thermometers used directly in experiments are calibrated.
Of the secondary thermometers, liquid thermometers, resistance thermometers, and thermoelements (thermocouples) are most widely used.
In liquid thermometers, the thermometric body is usually mercury or ethyl alcohol. Typically, liquid thermometers are used in the temperature range from 125 to 900 K. The lower limit of the measured temperatures is determined by the properties of the liquid, the upper limit - by the properties of the capillary glass.
In resistance thermometers, the thermometric body is a metal or semiconductor whose resistance changes with temperature. The change in resistance with temperature is measured using bridge circuits (see Fig.). Resistance thermometers from metals are used in the temperature range from 70 to 1300 K, from semiconductors (thermistors) - in the range from 150 to 400 K, and carbon ones - up to liquid helium temperatures. | |
Widespread in temperature measurements received thermometers based on thermocouples. Here, two junctions of dissimilar metals serve as a thermometric body. If two conductors are connected according to the scheme (see Fig.), Then the voltmeter in the circuit will register voltage, meaning |
which is proportional to the temperature difference between junctions 1 and 2. If the temperature of one of the junctions is maintained constant, then the voltmeter readings will depend only on the temperature of the second junction. These thermometers are especially useful in the field of high temperatures- about 700-2300 K.
At very high temperatures, the materials melt and the described types of thermometers are not applicable. In this case, the body itself, the temperature of which must be measured, is taken as the thermometric body, and the electromagnetic energy emitted by the body is taken as the thermometric quantity. According to the known laws of radiation, a conclusion is made about the temperature of the body. The International Committee for Weights and Measures established the thermodynamic scale at temperatures above 1064 precisely on the basis of the laws of radiation. Instruments that measure radiation energy are called pyrometers.
At very low temperatures (> 1 K), it is also not possible to apply the usual methods of measuring temperatures, since the equalization of temperatures upon contact occurs very slowly and, in addition, the usual thermometric values become unsuitable (for example, the gas pressure becomes very low, the resistance is practically independent of temperature ). Under these conditions, the body itself is also taken as a thermometric body, and the characteristics of its properties, for example, magnetic ones, are taken as a thermometric quantity.
To get rid of this difficulty, consider the case where the thermometric substance is a gas. It is clear that it is impossible to use it in exactly the same way as a liquid. The gas completely fills the entire vessel containing it. It does not form a free surface or interface. Its volume is equal to the volume of the vessel in which it is located. However, with an increase in the degree of heating, the gas will expand, i.e., increase its volume if the vessel has elastic walls, so that the pressure of the gas can remain constant. Conversely, if the volume is kept constant, then the pressure of the gas increases with increasing degree of heating. Such empirical observations, made by the French physicists J. A. C. Charles (1787) and J. L. Gay-Lussac (1802), became the basis of the gas laws, which we will discuss in the next chapter. Now we simply state that the pressure of a gas at constant volume increases with increasing temperature.
In the device shown in Fig. 2.3, a line is engraved on the glass tube (indicated by an arrow); it defines the volume of gas whose pressure changes with the temperature of the surrounding liquid. The observed thermometric quantity is the pressure corresponding to a given volume at various temperatures, i.e. the pressure required to maintain the meniscus (gas-liquid interface) at the engraved mark. Pressure is measured by the weight of the liquid column in a manometer, which is a U-shaped tube filled with liquid. (See Appendix I for more information on measuring pressure with pressure gauges.) In fig. 2.3 the gas thermometer is shown only schematically. In fact, a gas thermometer is an extremely complex and difficult instrument to use. It is necessary to take into account the change in the volume of the flask itself with a change in temperature, the contribution made to the total pressure by the vapors of the liquid used to determine the volume, the change in the density of the liquid with temperature, etc.
Rice. 2.3. Constant volume gas thermometer. An accurate (albeit cumbersome) instrument that can be used to determine absolute temperature.
However, despite the practical difficulties, the principle remains simple.
It is clear that the pressure shown on the pressure gauge will be higher when the tank contains boiling water than when it contains a mixture of water and ice. It is also clear that one can arbitrarily define the temperature ratio in terms of the pressure ratio:
where the indices s and i mean the boiling point and freezing point of water (from English words steam - "steam" and ice - "ice"). If we determine this ratio for various gases, say for helium, nitrogen, argon and methane, starting each time with a pressure approximately equal to the atmospheric pressure at the freezing point of water, i.e. p = 760 mm Hg. while we get approximately the same value regardless of the gas used in the thermometer. This constancy convinces us that the determination of the temperature ratio is almost independent of specific choice thermometric substance, at least for these few gases.
Let us now assume that the amount of gas in the flask can be varied, so that the pressure at the freezing point can be any predetermined value. We will find that the ratio of the pressures at the boiling point and at the freezing point will depend to some extent on the amount of gas in the flask, that is, on the pressure at the freezing point. Having spent quite a lot of time, we will find a pattern established by a number of conscientious researchers, namely, it turns out that with a decrease in the initial pressure, the ratio of pressures for various gases converges to the same value. Having plotted the dependences of this ratio on pressure (which is determined by the amount of gas in the flask) for various gases, we will obtain the graph shown in Fig. 2.4.
When tending to zero, i.e. when extrapolating the values to the vertical axis, for all gases exactly the same limit value equal to 1.36609 ± 0.00004 is obtained. This circumstance, which is confirmed for all gases studied, means that the temperature ratio has the same value, regardless of chemical composition gas. Thus, we can now define the temperature scale, using the condition that for two temperatures the relation holds
This ratio does not fully define the scale, since we have two unknown quantities and only one ratio between them. Let us also introduce the condition
This condition sets the same degree value as in the Celsius scale, in which Having solved equations (2) and (3) together, it is easy to find that .
For any other temperature corresponding to pressure, one can write
In other words, to find the temperature of a body on the gas thermometric scale, one must determine the pressure p, of a gas of a given volume, which will be established after the gas has been in contact with the body for a time sufficient to achieve thermal equilibrium (in practice, this means that the pressure should stop changing over time).
Rice. 2.4. Results of measurements made with a constant volume gas thermometer. Within a very low pressure(density) all gases give the same extrapolated value of the ratio
In addition, it is necessary to determine the pressure p, the same amount of gas enclosed in the same volume and in thermal equilibrium with a mixture of ice and water. The temperature T can then be found by multiplying the pressure ratio by 273.16. To have an accurate result, it is necessary to take the limiting value of this ratio with a decrease in the amount of gas in a given volume.
The thermometer is special device, designed to measure the current temperature of a particular medium in contact with it.
Depending on the type and design, it allows you to determine the temperature regime of air, the human body, soil, water, and so on.
Modern thermometers are divided into several types. The gradation of devices depending on the scope of application looks like this:
There are also thermometers
Each of these devices has its own design, differs in the principle of operation and scope.
The liquid thermometer is based on an effect known as the expansion of liquid media when heated. Most often, alcohol or mercury is used in such devices. Although the latter is systematically abandoned due to the increased toxicity of this substance. But still, this process this is not fully completed, since mercury provides better measurement accuracy by expanding in a linear fashion.
In meteorology, devices filled with alcohol are more often used. This is explained by the properties of mercury: at a temperature of +38 degrees and above, it begins to thicken. In turn, alcohol thermometers allow you to evaluate the temperature regime of a particular medium heated to 600 degrees. The measurement error does not exceed a fraction of one degree.
Mechanical thermometers are bimetallic or delatometric (rod, wand). The principle of operation of such devices is based on the ability metal bodies expand when heated. They differ high reliability and accuracy. The production cost of mechanical thermometers is relatively low.
These devices are mainly used in specific equipment: alarm systems, automatic temperature control systems.
The principle of operation of the thermometer is based on the same properties as the devices described above. Except that in this case an inert gas is used. In fact, such a thermometer is an analogue of a manometer, which serves to measure pressure. gas appliances are used to measure high- and low-temperature environments (the range is -271 - +1000 degrees). They provide relatively low accuracy, which is why they are abandoned in laboratory measurements.
It is also called a resistance thermometer. The principle of operation of this device is based on the change in the properties of the semiconductor embedded in the design of the device, with an increase or decrease in temperature. The dependence of both indicators is linear. That is, as the temperature rises, the resistance of the semiconductor increases, and vice versa. The level of the latter directly depends on the type of metal used in the manufacture of the device: platinum "works" at -200 - +750 degrees, copper at -50 - +180 degrees. Electric thermometers are rarely used, since it is very difficult to calibrate the scale during production.
Also known as a pyrometer. It is a non-contact device. The pyrometer works with temperatures from -100 to +1000 degrees. Its operating principle is based on measuring the absolute value of the energy emitted by a particular object. The maximum range at which the thermometer is able to evaluate temperature indicators depends on its optical resolution, the type of aiming device and other parameters. Pyrometers are different enhanced security and measurement accuracy.
The action of a thermoelectric thermometer is based on the Seebeck effect, by which the potential difference is estimated when two semiconductors are in contact, resulting in the formation electricity. The temperature measurement range is -100 - +2000 degrees.
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In general, Thermometer- a device for measuring the current temperature. Galileo is considered the inventor of the thermometer: in his own writings there is no description of this device, but it is known that already in 1597 he created a device resembling a thermometer. The scheme of the prototype of the thermometer was as follows: it was a vessel with a tube containing air, separated from the atmosphere by a column of water; he changed his readings both from changes in temperature and from changes in atmospheric pressure. In the 18th century, the air thermometer was improved. modern shape the thermometer was given by the scientist Fahrenheit, who described his method of making a thermometer in 1723. Initially, he filled his tubes with alcohol and only at the end of his research switched to mercury. The final permanent points of melting ice and boiling water were established by the Swedish physicist Celsius in 1742. The surviving copies of the Fahrenheit and Celsius thermometers are distinguished by their meticulous workmanship.
There are a huge number of types of thermometers - electronic thermometers, digital, resistance thermometers, bimetallic thermometers, infrared thermometers (IR thermometers), remote thermometers, electrocontact thermometers. And, of course, the most popular - alcohol and mercury thermometers. In addition to thermometers, frames for thermometers, manometric thermometers (thermomanometers), portable pyrometers, hygrometers, thermometers, thermometers, barometers, tonometers, thermometers, thermocouples and other equipment are widely available for sale.
The question of where to buy a thermometer is now practically not worth it. The widest range of thermometers on the market for various purposes, including household ones: outdoor thermometers for any windows (both wooden and plastic), room thermometers for home and office, thermometers for baths and saunas. You can buy thermometers for water, for tea, even for wine and beer, for an aquarium, special thermometers for soil, for incubators, facade and car thermometers. There are thermometers for refrigerators, freezers and cellars. In a word, there is everything! The price depends on the type of thermometer. The price range is as wide as the range of thermometer types. Many companies are engaged in the wholesale and retail sale of thermometers of Russian and foreign manufacturers, there are specialized stores and online stores that sell these devices and are able to satisfy the need for devices of almost any kind of this type. The most popular production and sale simple models measuring equipment. The prices for such devices are more than affordable. A wide range of temperature control and measurement technology and complex solutions in the field of metrology are now offered not only in Moscow, but in many major cities Russia.
Installing a thermometer, as a rule, is not technologically complicated. But do not forget that reliable and durable fastening of the thermometer is guaranteed only by the installation performed in accordance with all the rules, do not neglect this. Remember also that the thermometer is an inertial device, and the settling time for its readings is 10 - 20 minutes, depending on the required accuracy. Therefore, you should not expect the thermometer to change its readings as soon as you take it out of the package or install it.
In FIG. 75c shows a thermometer that measures the expansion of a gas. A drop of mercury locks a volume of dry air in a capillary with a sealed end. When measuring, the entire thermometer must be immersed in the medium. The movement of a drop of mercury in a capillary indicates a change in the volume of the gas; the capillary has a scale with marks 0 and 100 for the points of melting ice and boiling water, as with a mercury thermometer.
Such a thermometer is not suitable for very accurate measurements. We want to talk about a gas thermometer to clarify the general idea. A thermometer of this type is shown in Fig. 75b. The mercury barometer AB measures the pressure of a constant volume of gas in cylinder C. But instead of marking the height of the mercury column in the barometer in units of pressure, we mark it with 0 when the cylinder is in melting ice and 100 when in boiling water, I plot on them the whole Celsius scale. Using Boyle's law, it can be shown that the scale of the thermometer shown in Fig. 75b should be the same as that of the thermometer in FIG. 75 a.
Application of gas thermometer
When calibrating the gas thermometer shown in Fig. 76, we immerse the cylinder in melting ice and mark 0 on the barometer scale. Then we repeat the whole procedure, replacing the ice with boiling water; we get a mark of 100. Using the scale defined in this way, we build a graph of pressure versus temperature. (If you like, the pressure can be expressed in units of the height of the mercury column.) Then draw a straight line through the points O and 100 and, if necessary, continue it. This will be a straight line that determines the temperature in the gas scale and gives standard values 0 and 100 at the points where ice melts and water boils. Now a gas thermometer will allow us to measure the temperature if we know the pressure of the gas in the cylinder at that temperature. The dotted line in Fig. 76 shows how to find the water temperature at which the gas pressure is 0.6 mHg.
After we have chosen a gas thermometer as a standard, we can compare mercury and glycerin with it. So it was found that the expansion of most liquids, depending on the temperature measured by a gas thermometer, is somewhat non-linear. The readings of the two types of thermometers diverged between the points 0 and 100, agreement in which is obtained by definition. But mercury, oddly enough, gives an almost straight line. Now we can formulate the “dignity” of mercury: “On the gas temperature scale, mercury expands evenly.” This amazing coincidence shows that at one time we made a very good choice - that is why now ordinary mercury thermometers can be used to directly measure temperature.
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