The relationship between pressure, temperature, volume and amount of gas moles ("mass" gas). Universal (molar) gas constant R. Clayperon Mendeleev equation \u003d the equation of the state of the ideal gas.
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Limitations of practical applicability:
Inside the range, the accuracy of the equation exceeds the accuracy of conventional modern engineering tools. It is important for the engineer to understand that for all gases there is a significant dissociation or decomposition when increasing the temperature. |
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Let's solve a couple of tasks regarding gas volumetric and mass expenses under the assumption that the gas composition does not change (the gas does not dissociate) - which is true for most gases in the above.
This task is mainly relevant, but not only, for applications and devices in which the gas volume is directly measured.
V 1. and V 2., at temperatures, respectively, T 1. and T 2. let it go T 1.< T 2. . Then we know that:
Naturally, V 1.< V 2.
How to deal with it? At least a simple temperature compensation is necessary, i.e. information from an additional temperature sensor should be given to the device.
This task is mainly mainly, but not only, for applications and devices in which the gas speed is directly measured.
Let the counter () at the delivery point gives voluminous accumulated costs V 1. and V 2., at pressures, respectively, P 1. and P 2. let it go P 1.< P 2. . Then we know that:
Naturally, V 1.>V 2. For identical amounts of gas under these conditions. Let's try to formulate several conclusions in practice for this case:
How to deal with it? At least a simple pressure compensation is necessary, i.e, the device should be given information from an additional pressure sensor.
In conclusion, I would like to note that, theoretically, each gas meter must have both temperature compensation and pressure compensation. Practically ......
Consider how the gas pressure on temperature depends when its mass and volume remain constant.
Take a closed vessel with gas and warm it up (Fig. 4.2). Gas temperature will be determined using a thermometer, and the pressure is a pressure gauge M.
First, place the vessel in the melting snow and the gas pressure at 0 ° C will be denoted and then we will gradually heat the outer vessel and write values \u200b\u200bfor the gas. It turns out that the schedule of dependence on the basis of such experience built on the basis of such experience, has the appearance of a straight line (Fig. 4.3, a). If you continue this schedule to the left, it will cross the abscissa axis at point A, corresponding to zero gas pressure.
From the similarity of triangles in Fig. 4.3, but you can write:
If you designate constant through y, then we get
In the sense, the proportionality coefficient in the described experiments should express the dependence of the gas pressure change from its kind.
The magnitude characterizing the dependence of the gas pressure change from its genus during the temperature of the temperature at a constant volume and the constant mass of the gas is called the temperature coefficient of pressure. The temperature coefficient shows which part of the gas pressure, taken at 0 ° C, its pressure changes when heated on
Withdraw a unit of temperature coefficient in C:
Repeating the described experience for different gases With different masses, it is possible to establish that within the errors of experiments, the point A for all charts is obtained in the same place (Fig. 4.3, b). In this case, the segment length of the OA is obtained equal in this way, for all cases, the temperature at which the gas pressure should turn to zero, is the same and equal to the temperature coefficient of pressure, we note that the exact value of the value in solving problems is usually used by the approximate value in equal
From the experiments, the value was first determined by the French physicist J. Charl, who in 1787 set the following law: the temperature coefficient of pressure does not depend on the genus of the gas and it is noted that it is true only for gases that have a small density, and with small temperature changes ; at high pressures or low temperatures It depends on the genus of gas. Accurately obeys the law of Charles only the perfect gas.
Throughout this leaf, we will adhere to the following assumption: mass I. chemical composition Gas remain unchanged. In other words, we believe that:
That is, there is no gas leak from the vessel or, on the contrary, the flow of gas into the vessel;
That is, gas particles do not have any changes (let's say there is no dissociation - the decay of molecules to atoms).
These two conditions are performed in very many physically interesting situations (for example, in simple models thermal motors) and therefore perfectly deserve separate consideration.
If the mass of the gas and its molar mass is fixed, then the state of the gas is determined three macroscopic parameters: pressure, volume and temperature. These parameters are associated with each other equation of state (the Mendeleev - Klapairone equation).
Thermodynamic process (or simply process) - This is a change in the state of the gas over time. During the thermodynamic process, the values \u200b\u200bof macroscopic parameters - pressure, volume and temperature are changed.
Of particular interest are isoprocessees - Thermodynamic processes in which the value of one of the macroscopic parameters remain unchanged. Alternately fixing each of the three parameters, we will get three types of isoprocesses.
1. Isothermal process It comes at a permanent gas temperature :.
2. Isobaric process It goes with constant pressure of the gas :.
3. Isochhore process It goes with a constant amount of gas :.
Isoproces are described by the very simple laws of Boyle - Mariotta, Gay Loussa and Charles. Let's move on to their study.
Let the ideal gas performs an isothermal process at temperatures. During the process, only gas pressure and its volume are changing.
Consider two arbitrary states of gas: in one of them, the values \u200b\u200bof macroscopic parameters are equal, and in the second. These values \u200b\u200bare connected by the Mendeleev-Klapairone equation:
As we said from the very beginning, the mass and molar mass are assumed unchanged.
Therefore, the right parts of the written equations are equal. Therefore, the leftists are equal:
(1)
Since the two states of the gas were chosen arbitrarily, we can conclude that during the isothermal process, the product of gas pressure on its volume remains constant:
(2)
This statement is called boyle's law - Mariotta.
Recovering the law of Boyl - Mariotta in the form
(3)
this wording can be given: in the isothermal process, the gas pressure is inversely proportional to its volume.. If, for example, with an isothermal expansion of the gas, it increases three times, then the gas pressure is triggered by three times.
How to explain the inverse dependence of pressure from an amount from a physical point of view? At a constant temperature, there remains unchanged average kinetic energy of gas molecules, that is, simply speaking, the force of blows of molecules about the wall of the vessel does not change. With increasing volume, the concentration of molecules is reduced, and accordingly, the number of blows of molecules per unit time per unit area of \u200b\u200bthe wall is reduced - the gas pressure drops. On the contrary, with a decrease in volume, the concentration of molecules increases, their blows will raw more often and gas pressure increases.
In general, the graphs of thermodynamic processes are customary in the following coordinate systems:
-Diagram: abscissa axis, ordinate axes;
-Diagram: abscissa axis, ordinate axis.
The graph of the isothermal process is called isotherma.
Isotherm on -Diagram is a graph inversely proportional dependence.
Such a chart is a hyperbole (remember the algebra - a function graph). The hyperbole isotherm is shown in Fig. one .
Fig. 1. Isotherm on -Diagram
Each isotherm meets a definite fixed temperature value. It turns out that the higher the temperature, the higher the corresponding isotherm on -diagram.
In fact, we consider two isothermal process performed by the same gas (Fig. 2). The first process is at temperatures, the second - at a temperature.
Fig. 2. The higher the temperature, the higher isotherm
Fix some value of volume. On the first isotherm, the pressure is responsible for him, on the second - class \u003d "Tex" alt \u003d "(! Lang: P_2\u003e P_1"> . Но при фиксированном объёме давление тем больше, чем выше температура (молекулы начинают сильнее бить по стенкам). Значит, class="tex" alt="T_2\u003e T_1."> .!}
In the remaining two systems, the coordinates of the isotherm looks very simple: it is a straight, perpendicular axis (Fig. 3):
Fig. 3. Isotherms on and -Diagram
Recall once again that the isobaric process is a process passing at constant pressure. In the course of the isobaric process, only gas and its temperature are changed.
A typical example of the isobaric process: gas is under a massive piston, which can move freely. If the weight of the piston and cross section piston, the gas pressure is always constantly and equal
where - atmospheric pressure.
Let the ideal gas performs the isobaric process at pressure. Consider two arbitrary gas states again; This time the values \u200b\u200bof macroscopic parameters will be equal and.
Representation equations:
Sharing them on each other, we get:
In principle, it could already be enough, but we will go a little further. We rewrite the resulting ratio so that only the parameters of the first state appear in one part, and in another part, only the parameters of the second state (in other words, "we will separate indexes" in different parts):
(4)
And hence now - in view of the arbitrariness of the choice of states! - Receive law Gay Lussa:
(5)
In other words, with constant gas pressure, its volume is directly proportional to the temperature:
(6)
Why increases volume with increasing temperature? When the temperature is raised, the molecule starts to beat more and lift the piston. In this case, the concentration of molecules falls, the blows become less likely, so as a result, the pressure retains its former value.
The graph of the isobaric process is called isobara. On -Diagram, Isobar is a straight line (Fig. 4):
Fig. 4. Isobar to -Diagram
The dotted portion of the graph means that in the case of real gas at sufficiently low temperatures, the model of the ideal gas (and with it the law of gay-lousha) ceases to work. In fact, when the temperature of the gas particle is reduced, everything is slower, and the forces of intermolecular interaction have an increasingly significant effect on their movement (analogy: a slow ball is easier to catch than fast). Well, at very low temperatures of gases and are completely converted into a liquid.
Let us describe now how the position of the isobar changes when the pressure changes. It turns out that the more pressure, the lower the isobar on -diagram.
To make sure that we consider two isobars with pressures and (Fig. 5):
Fig. 5. The lower the isobar, the greater the pressure
Fix some temperature value. We see that. But at a fixed temperature, the volume is the less, the more pressure (the law of Boyle is Mariotta!).
There was Class \u003d "Tex" alt \u003d "(! Lang: p_2\u003e p_1"> .!}
In the remaining two coordinates, the coordinates of the isobar is a direct line, perpendicular to the axis (Fig. 6):
Fig. 6. Isobaras on and -Diagram
Isochoor process, we recall, is a process passing at a constant volume. With a isochorine process, only gas pressure changes and its temperature.
The isochhore process to imagine is very simple: this is a process that goes in a rigid vessel of a fixed volume (or in a cylinder under the piston when the piston is fixed).
Let the perfect gas makes the isochoric process in the vessel volume. Again, consider two arbitrary states of gas with parameters and. We have:
We divide these equations to each other:
As with the conclusion of the Law of Gay-Loussak, "Drag" indexes in different parts:
(7)
In view of the arbitrariness of the selection of states, we come to charles law:
(8)
In other words, with a constant amount of gas, its pressure is directly proportional to the temperature:
(9)
An increase in the gas pressure of a fixed volume when it is heated - the thing is completely obvious from a physical point of view. You yourself easily explain this.
The graph of the isochlorine process is called izochora. On -Diagram of the isoker is a straight line (Fig. 7):
Fig. 7. Isochora on -Diagram
The meaning of the dotted plot is the same: the inadequacy of the model of the ideal gas at low temperatures.
Fig. 8. The lower the isoker, the greater the volume
Proof similar to the previous one. Fix the temperature and see that. But at a fixed temperature, the pressure is the less, the more volume (again the law of the boiler is Mariotta). It was Class \u003d "Tex" alt \u003d "(! Lang: V_2\u003e V_1"> .!}
In the remaining two systems, the coordinates of the isoker is a straight line, perpendicular axis (Fig. 9):
Fig. 9. Isochora on and -Diagram
Boyle's laws - Mariotta, Gay Loussa and Charles are also called gas laws.
We brought gas laws from the Mendeleev equation - Klapaireron. But historically everything was the opposite: gas laws were established experimentally, and much earlier. The state equation emerged later as their generalization.
Introduction
The state of the ideal gas is fully described by the measured values: pressure, temperature, volume. The relationship between these three values \u200b\u200bis determined by the main gas law:
purpose of work
Check the law of Boyl Mariotta.
Resolved tasks
Measurement of air pressure in the syringe when changing the volume considering that the gas temperature is constant.
Experimental installation
Instruments and accessories
Manometer
Manual vacuum pump
In this experiment, the law of Boyl - Mariotta is confirmed by the installation shown in Figure 1. The volume of air in the syringe is determined as follows:
where p 0 atmospheric pressure, the pressure measured using a pressure gauge.
Procedure for performing work
Install the syringe piston at 50 ml.
Tightly put on the free end of the connecting hose of the hand-made vacuum pump on the outlet of the syringe.
Having advanceed the piston, increase the volume with a step of 5 ml, fix the testimony of the machine to the black scale.
To determine the pressure under the piston, it is necessary to subtract the monometer testimony expressed in Pascal from the atmospheric pressure. Atmosphere pressure Equally, approximately 1 bar, which corresponds to 100,000 pa.
For processing measurement results, the availability of air in the connecting hose should be taken into account. To do this, measure calculate the volume of the connecting hose, measuring the length of the hose with a roulette, and the diameter of the hose caliper, given that the wall thickness is 1.5 mm.
Build a graph of the measured dependence of air from pressure.
Calculate the dependence of the volume from pressure at a constant temperature according to the law of the Mariott Boiler and build a schedule.
Compare theoretical and experimental dependencies.
Introduction
Consider the dependence of gas pressure on temperature under the condition of the constant volume of a certain mass of the gas. These studies were first produced in 1787 by Jacques Alexander Cesar Chalf (1746-1823). The gas was heated in a large flask connected to a mercury pressure gauge as a narrow curved tube. Neglecting an insignificant increase in the volume of the flask when heated and a minor change in the volume when mercury is displaced in a narrow pressure gauge. Thus, the volume of gas can be considered unchanged. Heated water in a vessel surrounding the flask, measured the temperature of the thermometer gas T., and the corresponding pressure r- on the manometer. Filling with vessel with melting ice, the pressure was determined r about , and the appropriate temperature T. about . It was found that if at 0 with pressure r about , then when heated by 1 with the increment of pressure will be in r about . The values \u200b\u200bof the same value (more precisely, almost the same thing) for all gases, namely 1/273 C -1. Perforce the temperature coefficient of pressure.
The Charles Act allows you to calculate the pressure of the gas at any temperature, if its pressure is known at a temperature of 0 C. Let the pressure of this mass of the gas at 0 CV p. o. , and the pressure of the same gas at temperatures t.p.. Temperature varies by t.and pressure changes to r about t., then pressure requally:
At very low temperatures, when the gas approaches the state of the liquefaction, as well as in the case of highly compressed gases, the Charles law is not applicable. The coincidence of the coefficients of i, which are included in the law of Charles and the law of Gay-Loursak, not by chance. Since the gases are subordinate to the law of Boyle - Mariott at a constant temperature, even to be equal to each other.
We substitute the value of the temperature coefficient in the temperature dependence formula of the pressure:
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Magnitude ( 273+ t.) It is possible to consider how the temperature value counted along the new temperature scale, the unit of which is the same as the Celsius scale, and for zero, the point laying on 273 below the point adopted for zero Celsius scale, i.e. ice melting points . Zero of this new scale is called absolute zero. This new scale is called a thermodynamic scale of temperatures, where T. t.+273 .
Then, at a constant volume, Challa's law is fair:
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purpose of work
Check Charles Law
Resolved tasks
Determination of gas pressure dependence on temperature at a constant volume
Determination of the absolute temperature scale by extrapolation towards low temperatures
Safety technique
ATTENTION: Glass is used in operation.
Be extremely accurate when working with a gas thermometer; Glass vessel and measuring cup.
Be extremely attentive when working with hot water.
Experimental installation
Instruments and accessories
Gas thermometer
Mobile Cassy Lab.
Thermocouple
Electric heating tile
Glass measuring glass
Glass vessel
Manual vacuum pump
When air pumping at room temperature with a manual pump, a pressure on the air p0 + will be created, where r 0 - external pressure. A drop of mercury also puts pressure on the air pole:
In this experiment, this law is confirmed using a gas thermometer. The thermometer is placed in water with a temperature of about 90 ° C and this system is gradually cooled. Pumping air from the gas thermometer using a hand-made vacuum pump, maintain constant air volume during cooling.
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Procedure for performing work
Open the gas thermometer plug, connect a manual vacuum pump to the thermometer.
Turn the thermometer carefully as shown on the left in fig. 2 and pump out the air from it using the pump so that the mercury droplet is at point a) (see Fig. 2).
After the droplet of mercury gathered at the point a), turn the thermometer with a hole upstairs and lower the faded air handle) on the pump (see Fig. 2) Caution to mercury it was not divided into several droplets.
Heat Water B. glass vessel On tile up to 90 ° C.
Pour hot water In a glass vessel.
Place a gas thermometer into the vessel, consolidating it on a tripod.
Place the thermocouple into water, gradually this system is cooled. Pumping the air from the gas thermometer using a manual vacuum nanos, support the constant volume of the air column during the entire cooling process.
Fix a pressure gauge reading rand temperature T..
Build the dependence of the total gas pressure p. 0 +p.+p. HG on temperature in about S.
Continue the schedule to the intersection with the abscissa axis. Determine the intersection temperature, explain the results obtained.
By tangent angle of inclination, determine the temperature coefficient.
Calculate the dependence of the pressure from temperature at a constant volume by the chalk law and build a schedule. Compare theoretical and experimental dependencies.
We make sure that the gas molecules are really located far enough from each other, and therefore gases are well compressed. Time syringe and position its piston approximately in the middle of the cylinder. The hole of the syringe is connected to the tube, the second end of which is tightly closed. Thus, some portion of air will be imprisoned in the syringe cylinder under the piston and in the tube. The cylinder under the piston is a certain amount of air. Now we put a car load on the movable piston. It is easy to see that the piston drops a little. This means that the volume of air has decreased in other words, the gases are easily compressed. Thus, there are large gaps between gas molecules. The room room on the piston causes a decrease in gas volume. On the other hand, after installing the cargo, the piston, slightly dropping, stops in the new position of the equilibrium. This means that air pressure force on the piston Increases and again backed up the increased weight of the piston with a cargo. And since the piston area at the same time remains unchanged, we come to an important conclusion.
With a decrease in the volume of gas, its pressure increases.
We will remember how the mass of the gas and its temperature during the experience remained unchanged. It is possible to explain the dependence of pressure from the volume as follows. With an increase in the volume of gas, the distance between its molecules increases. Each molecule now needs to go through a larger distance from one blow from the vessel wall to another. The average speed of movement of molecules remains unchanged. Related, the gas molecules are less likely to be hitting the vessel wall, and this leads to a decrease in gas pressure. And, on the contrary, with a decrease in the volume of gas, its molecule is more likely to hit the wall of the vessel, and the gas pressure increases. With a decrease in the volume of gas, the distance between its molecules is reduced
The dependence of gas pressure on temperature
In previous experiments, the gas temperature remained unchanged, and we studied the change in pressure due to changes in the volume of gas. Now consider the case when the volume of gas remains constant, and the gas temperature changes. The mass is also unchanged. You can create such conditions by placing a number of gas into a cylinder with a piston and consolidating the piston
Changing the temperature of this gas mass with a constant volume
The higher the temperature, the faster the gas molecules are moving.
Therefore
First, the molecules of the vessel wall occur more often;
Secondly, the average impact force of each molecule about the wall becomes greater. This leads us to another important conclusion. With increasing gas temperature, its pressure increases. We will remember that this assertion is true if the mass and volume of gas during the change of its temperature remain unchanged.
Storage and transportation of gases.
The dependence of gas pressure from volume and temperature is often used in the technique and in everyday life. If you need to carry a significant amount of gas from one place to another, or when the gases need to be kept for a long time, they are placed in special solid metal vessels. These vessels withstand high pressure, so with the help of special pumps there you can download significant gas masses, which in normal conditions would be hundreds of times more than a larger volume. Since the pressure of gases in the cylinders even at room temperature is very large, they will not be heated in any way or in any way to try to make a hole in them even after use.
Gas laws of physics.
The physics of the real world in the calculations is often reduced to several simplified models. The most applied such an approach to the description of the behavior of gases. The rules established by the experimental way were reduced by various researchers in the gas laws of physics and served as the appearance of the concept of "isoprocess". This is the passage of the experiment, in which one parameter retains a constant value. Gas laws of physics operate with the main parameters of the gas, more precisely, its physical condition. The temperature occupied by volume and pressure. All processes that refer to a change in one or more parameters are called thermodynamic. The concept of the isostatic process is reduced to the statement that during any state change, one of the parameters remains unchanged. This is the behavior of the so-called "ideal gas", which, with some reservations, can be applied to the real substance. As noted above, in reality everything is somewhat more complicated. However, with high reliability, the behavior of the gas at a constant temperature is characterized by the law of the Mariott law, which says:
The product of the gas pressure is permanent value. This statement is considered correct in the case when the temperature does not change.
This process is called "isothermal". In this case, two of the three parameters studied are changing. Physically, everything looks simple. Squeeze the inflated ball. The temperature can be considered unchanged. And as a result, the pressure will increase the pressure when the volume decreases. The magnitude of the work of two parameters will remain unchanged. Knowing the initial value of at least one of them, you can easily find out the second indicators. Another rule in the list "Gas laws of physics" is a change in the volume of gas and its temperature at the same pressure. This is called "isobaric process" and is described using the Gay Lusaka law. The ratio of volume and temperature of the gas is invariably. This is true under the condition of a constant pressure value in this mass of the substance. Physically, everything is simple. If at least once charged gas lighter Or enjoyed carbon dioxide fire extinguisher, seen the action of this law "Virgin". The gas coming out of the canister or the extinguisher is rapidly expanding. Its temperature drops sharply. You can frowned the skin of the hands. In the case of a fire extinguisher, whole flakes of carbon dioxide snow are formed, when the gas under the influence of a low temperature quickly turns into a solid state of gaseous. Thanks to the law of Gay-Lusaka, you can easily find out the gas temperature, knowing its volume at any time. Gas laws of physics describe and behavior under the condition of the consistent volume occupied. This process is called isoormal and described by the Charles law, which says: With a consistent volume occupied, the pressure ratio to the gas temperature remains unchanged at any time.In reality, everyone knows the rule: it is impossible to heat the splashes from air fresheners and other vessels containing gas under pressure. The case ends with an explosion. It is exactly what the Charles Act describes. The temperature grows. At the same time, the pressure is growing, since the volume does not change. There is a cylinder destruction at the moment when the indicators exceed the permissible. So, knowing the volume occupied and one of the parameters, you can easily set the value of the second. Although the gas laws of physics describe the behavior of a certain ideal model, they can be easily applied to predict gas behavior in real systems. Especially in everyday life, items can easily explain how the refrigerator works, why a cold jet of air flies out of the freshener's sprayer, because of which the camera or the ball is burst, how the sprayer works and so on.
Basics of MTT.
Molecular kinetic theory of substance- Method of explanation heat phenomenawhich binds the flow of thermal phenomena and processes with the peculiarities of the inner structure of the substance and studies the causes that cause heat movement. This theory was recognized only in the XX century, although it comes from ancient Greek atomic teaching on the structure of the substance.
Explains the thermal phenomena with the peculiarities of the movement and interaction of microparticles of the substance
Based on the laws of classical mechanics I. Newton, which allow to derive the equation of movement of microparticles. Nevertheless, in connection with their huge amounts (in 1 cm 3 of the substance there is about 10 23 molecules) is impossible every second with the help of the laws of classical mechanics to uniquely describe the movement of each molecule or atom. Therefore, methods of mathematical statistics are used to construct modern theory of heat, which explain the flow of thermal phenomena on the basis of the patterns of behavior of a significant number of microparticles.
Molecular kinetic theory Built on the basis of generalized equations of movement of a huge number of molecules.
Molecular kinetic theory Explains thermal phenomena from the standpoint of ideas about the inner structure of the substance, that is, it turns out their nature. This is a deeper, albeit a more complex theory, which explains the essence of thermal phenomena and causes the laws of thermodynamics.
Both existing approaches - thermodynamic approach and molecular kinetic theory - Scientifically proved and mutually complement each other, and do not contradict each other. In this regard, the study of heat phenomena and processes is usually considered from positions or molecular physics, or thermodynamics, depending on how it is easier to state the material.
Thermodynamic and molecular-kinetic approaches mutually complement each other when explaining heat phenomena and processes.
