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Most often in practice, the dependence of the volume of liquid (mercury or alcohol) on temperature is used.
When calibrating a thermometer, the temperature of melting ice is usually taken as the reference point (0); the second constant point (100) is considered the boiling point of water at normal atmospheric pressure(Celsius).
Since different liquids expand differently when heated, the scale thus established will depend to some extent on the properties of the liquid in question.
Of course, 0 and 100°C will coincide for all thermometers, but 50°C will not coincide.
Unlike liquids, all rarefied gases expand equally when heated and change their pressure equally when the temperature changes. Therefore, in physics, to establish a rational temperature scale, they use a change in the pressure of a certain amount of rarefied gas at a constant volume or a change in the volume of a gas at a constant pressure.
This scale is sometimes called the ideal gas temperature scale.
At thermal equilibrium, the average kinetic energy of the translational motion of the molecules of all gases is the same. Pressure is directly proportional to the average kinetic energy of translational motion of molecules: p = n
In thermal equilibrium, if the pressure of a gas of a given mass and its volume are fixed, the average kinetic energy of the gas molecules must have a strictly defined value, as does the temperature.
Because concentration of molecules in the volume of gas n = , then p = or = .
Let us denote = Θ.
The value of Θ increases with increasing temperature and does not depend on anything other than temperature.
The ratio of the product of gas pressure and its volume to the number of molecules at the same temperature is the same for almost all rarefied gases (close in properties to an ideal gas):
At high pressures the ratio is broken.
The temperature determined in this way is called absolute.
Based on the formula, a temperature scale is introduced that does not depend on the nature of the substance used to measure temperature.
The most important macroscopic parameter characterizing the stationary equilibrium state of any body is temperature.
Temperature is a measure of the average kinetic energy of the chaotic translational motion of molecules. bodies.
The most important corollary follows from the basic MKT equation in the form = and the definition of temperature in the form = kT:
Absolute temperature is a measure of the average kinetic energy of molecular motion.
The average kinetic energy of the chaotic translational motion of molecules is proportional to the thermodynamic (or absolute temperature):
KT Þ = kT Þ == kT
The higher the temperature, the faster the molecules move.
k = 1.38*10-23 J/K – Boltzmann’s constant
Boltzmann's constant is a coefficient that converts temperature from degrees (K) to energy (J) and vice versa.
Unit of thermodynamic temperature – K (Kelvin)
Kinetic energy cannot be negative. Therefore, thermodynamic temperature cannot be negative. It becomes zero when the kinetic energy of the molecules becomes zero.
Absolute zero (0K) is the temperature at which the movement of molecules should stop.
To estimate the speed of thermal movement of molecules in a gas, we calculate the mean square of the speed:
The product kNa = R = 8.31 J/(mol*K) is called the molar gas constant
Root mean square speed of molecules:
This speed is close in value to the average and most probable speed and gives an idea of the speed of thermal motion of molecules in an ideal gas.
At the same temperature, the speed of thermal movement of gas molecules is higher, the lower its M. (At 0°C, the speed of molecules is several hundred m/s)
At the same pressures and temperatures, the concentration of molecules of all gases is the same:
KT Þ p = nkT, where n = N/V is the concentration of molecules in a given volume
This implies Avogadro's law:
Equal volumes of gases at the same temperatures and pressures contain the same number of molecules.
Celsius scale – reference point – ice melting temperature 0°C, water boiling point – 100°C
Kelvin scale - reference point - absolute zero - 0°K (-273.15°C)
tоК = tоС -273
Fahrenheit scale - reference point - the lowest temperature that Fahrenheit managed to obtain from a mixture of water, ice and sea salt– 0оF, upper reference point – human body temperature - 96 оF
SPECIFY
CLIPERON-MENDELEEV EQUATION (grade 10, pp. 248-251)
(Ideal gas equation of state)
Basic equation of the molecular kinetic theory of an ideal gas (10th grade, pp. 247-248)
Transition from microscopic gas parameters to macroscopic ones
Loschmidt's constant - meaning and units of measurement
Average distance between ideal gas particles
Equation of state of an ideal gas – Clayperon-Mendeleev
Universal gas constant
Physical meaning of the Clayperon-Mendeleev equation
p = n - basic equation of MKT ideal gas
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Like all bodies, gases expand when heated, and quite noticeably even with slight heating. This is easy to discover in the following simple experiment.
Flask A is connected to a horizontal tube CD, which is fixed along the scale. Inside this tube is a small column of mercury. It is enough to touch the flask with your hand and the column of mercury in the CD tube will begin to move.
When the flask is cooled, the mercury column moves to the left, and when heated, it moves to the right; Consequently, gas contracts when cooled and expands when heated. Knowing the volume of the flask and the diameter of the tube, you can measure the increase in gas volume.
By gradually heating the gas in the flask, it can be established that at constant pressure, the change in the volume of a given mass of gas is directly proportional to the change in temperature. Therefore, the thermal expansion of a gas, as well as other bodies, can be characterized using the coefficient of volumetric expansion.
Let at a temperature of 0° C the volume of gas be equal to V 0, and at a temperature t - the volume V t. The increase in volume per each unit of volume taken at 0° C when heated by one degree will be equal to:
? = V t – V 0 /V 0 t
V t = V 0 (1 + ?t) (1)
The quantity a included in the formulas written above is called coefficient of volumetric expansion of gas.
Joseph Louis Gay-Lussac (1778–1850) is one of the outstanding French chemists and physicists. He discovered a number of important chemical and physical laws, of which the law of equal expansion of gases and vapors with the same increase in temperature is widely known in physics.
The French scientist Gay-Lussac, experimentally studying the thermal expansion of gases, discovered that the coefficient of volumetric expansion for all gases at constant pressure is the same and is numerically equal to 1/273 deg -1.
In this respect, the expansion of gases when heated differs from the expansion of solids and liquids, where the coefficient of volumetric expansion depends on chemical composition tel.
Let us put in formula (1):
t = 1°С, ? = 273 deg -1
We get: V t = V 0 + 1 / 273 · V 0 from which it follows that when heated by 1 degree under constant pressure, the volume of a given mass of gas increases by 1 / 273 of the volume that the gas occupied at 0°C. This law was called Gay-Lussac's law.
Processes similar to the one considered, occurring at constant pressure, are called isobaric.
Formula (1) shows that the volume of gas at temperature equal to the product its volume, taken at 0°C, by the binomial of volumetric expansion (1 + ?t).
Example 1. The volume of a certain mass of gas at 0° C is 10 liters. Find its volume at t = 273° C, if the pressure is constant.
According to the conditions of the problem, we know the volume of gas at 0 ° C, i.e. V 0 = 10 l; Substituting the numerical data of the problem into the formula V t = V 0 (1 + ?t), we find that
V t = 10 (1 + 273 / 273) l = 20 l
Example 2. At a temperature of 273° C, the volume of a certain mass of gas is 10 liters. What will happen equal to volume of this gas at a temperature t 2 = 546° C, if the pressure is constant?
We know the volume of gas at a temperature of 273 ° C; to determine the volume of this gas at t 2 = 546° C, we must first find its volume at 0° C.
We find this volume from the equality:
10 l = V 0 (1 + 1 / 273 273) l
V 0 = 10 l / 2 = 5 l
Let us now find the volume of gas at 546° C:
V t = 5 (1 + 1 / 273 546) l = 15 l
You can verify the validity of Gay-Lussac’s law using a device already known to us (see Fig. 3.7). To do this, after noticing the pressure gauge readings, you should measure the temperature of the gas in the corrugated vessel and the volume of the vessel. Then you need to heat the gas by placing the vessel in hot water, and by rotating the screw, ensure that the pressure gauge readings remain the same. Measure the temperature and volume of the gas again. After this, change the temperature again, achieve the initial pressure value and measure the temperature and volume of the gas for the third time.
Isobars
Using the found gas volume values at different temperatures and the same pressure, you can plot the dependence V from t. This dependence will be represented by a straight line - an isobar, as it should be according to formula (3.6.4).
Different pressures correspond to different isobars (Fig. 3.10). Since the volume of a gas at a constant temperature decreases with increasing pressure (Boyle-Mariotte law), the isobar corresponding to a higher pressure r 2 , lies below the isobar corresponding to more low pressure p 1
Ideal gas
If we continue the isobars into the region of low temperatures, where measurements were not carried out, then all straight lines intersect the temperature axis at a point corresponding to a volume equal to zero (dotted straight lines in Fig. 3.10). But this does not mean that the volume of gas actually goes to zero. After all, all gases turn into liquids when strongly cooled, and neither the Gay-Lussac law nor the Boyle-Mariotte law are applicable to liquids.
Real gases obey the basic gas laws only approximately and the less accurately, the higher the density of the gas and the lower its temperature. A gas that exactly obeys the gas laws is called ideal.
Gas temperature scale
The fact that the numerical value of the temperature coefficient of volumetric expansion in the limiting case of low densities is the same for all gases makes it possible to establish a temperature scale that does not depend on the substance - the ideal gas temperature scale.
Taking the Celsius scale as a basis, you can determine the temperature from the relationship (3.6.1)
(3.6.5)
Where V 0 is the volume of gas at 0 °C, and V - its volume at temperature t.
Thus, using formula (3.6.5), a determination of temperature is carried out that does not depend on the substance of the thermometer.
A definition of an ideal gas is given as a gas that exactly obeys the Boyle-Mariotte and Gay-Lussac laws. An ideal gas temperature scale, independent of the substance, was introduced.
§ 3.7. Absolute temperature
Not everything in the world is relative. So, there is absolute zero temperature. There is also an absolute temperature scale. Now you will know about it
As the temperature increases, the volume of the gas increases without limit. There is no limit to temperature rise*. On the contrary, low temperatures have a limit.
* The highest temperatures on Earth - hundreds of millions of degrees - were obtained during explosions of thermonuclear bombs. Even higher temperatures are typical for the inner regions of some stars.
According to Gay-Lussac's law (3.6.4), as the temperature decreases, the volume tends to zero. Since the volume cannot be negative, the temperature cannot be less than a certain value (negative on the Celsius scale).
Ideal gas law.
Experimental:
The main parameters of gas are temperature, pressure and volume. The volume of gas depends significantly on the pressure and temperature of the gas. Therefore, it is necessary to find the relationship between the volume, pressure and temperature of the gas. This ratio is called equation of state.
It was experimentally discovered that for given quantity gas, to a good approximation, the following relation holds: at constant temperature, the volume of gas is inversely proportional to the pressure applied to it (Fig. 1):
V~1/P , at T=const.
For example, if the pressure acting on a gas doubles, the volume will decrease to half its original volume. This relationship is known as Boyle's law (1627-1691)-Mariotte (1620-1684), it can be written like this:
This means that when one of the quantities changes, the other will also change, and in such a way that their product remains constant.
The dependence of volume on temperature (Fig. 2) was discovered by J. Gay-Lussac. He discovered that at constant pressure, the volume of a given amount of gas is directly proportional to the temperature:
V~T, at Р =const.
The graph of this dependence passes through the origin of coordinates and, accordingly, at 0K its volume will become equal to zero, which obviously has no physical meaning. This has led to the suggestion that -273 0 C is the minimum temperature that can be achieved.
The third gas law, known as Charles's law named after Jacques Charles (1746-1823). This law states: at constant volume, gas pressure is directly proportional to absolute temperature (Fig. 3):
P ~T, at V=const.
A well-known example of this law is an aerosol can that explodes in a fire. This happens due to sharp increase temperature at constant volume.
These three laws are experimental, fulfilling well in real gases only as long as the pressure and density are not very high, and the temperature is not too close to the condensation temperature of the gas, so the word "law" is not very suitable for these properties of gases, but it has become generally accepted.
Gas laws Boyle-Mariotte, Charles and Gay-Lussac can be combined into one more general relationship between volume, pressure and temperature, which is valid for a certain amount of gas:
This shows that when one of the quantities P, V or T changes, the other two quantities will also change. This expression turns into these three laws when one value is taken as constant.
Now we should take into account one more quantity, which until now we considered constant - the amount of this gas. It has been experimentally confirmed that: at constant temperature and pressure, the closed volume of a gas increases in direct proportion to the mass of this gas:
This dependence connects all the main quantities of gas. If we introduce a proportionality factor into this proportionality, we get equality. However, experiments show that this coefficient is different in different gases, so instead of mass m, the amount of substance n (number of moles) is introduced.
As a result we get:
Where n is the number of moles, and R is the proportionality coefficient. The quantity R is called universal gas constant. To date, the most accurate value of this value is:
R=8.31441 ± 0.00026 J/mol
Equality (1) is called equation of state of an ideal gas or ideal gas law.
Avogadro's number; ideal gas law at the molecular level:
That the constant R has the same value for all gases is a magnificent reflection of the simplicity of nature. This was first realized, albeit in a slightly different form, by the Italian Amedeo Avogadro (1776-1856). He experimentally established that equal volumes volumes of gas at the same pressure and temperature contain same number molecules. First: from equation (1) it can be seen that if different gases contain equal number moles have the same pressure and temperature, then, provided R is constant, they occupy equal volumes. Secondly: the number of molecules in one mole is the same for all gases, which directly follows from the definition of a mole. Therefore, we can say that the value of R is constant for all gases.
The number of molecules in one mole is called Avogadro's numberN A. It has now been established that Avogadro's number is equal to:
N A =(6.022045 ± 0.000031) 10 -23 mol -1
Since total number molecules N of gas is equal to the number of molecules in one mole multiplied by the number of moles (N = nN A), the ideal gas law can be rewritten as follows:
Where k is called Boltzmann constant and has the same value:
k= R/N A =(1.380662 ± 0.000044) 10 -23 J/K
Directory of compressor equipment
In relation to liquids, it makes sense to talk only about volumetric expansion. For liquids it is much greater than for solids. As experience shows, the dependence of the volume of liquid on temperature is expressed by the same formula as for solids.
If at 0° C a liquid occupies a volume V 0, then at a temperature t its volume V t will be:
V t = V 0 (1 + ?t)
To measure the coefficient of expansion of a liquid, a thermometric glass vessel is used, the volume of which is known. The ball and tube are filled to the top with liquid and the entire device is heated to a certain temperature; in this case, part of the liquid pours out of the vessel. Then the vessel with the liquid is cooled in melting ice to 0°. In this case, the liquid will no longer fill the entire vessel, and the unfilled volume will show how much the liquid expanded when heated. Knowing the coefficient of expansion of glass, it is possible to fairly accurately calculate the coefficient of expansion of the liquid.
Expansion coefficients of some liquids
Ether – 0.00166
Alcohol – 0.00110
Kerosene – 0.00100
Water (from 20° C and above) – 0.00020
Water (from 5 to 8° C) – 0.00002
Thermal expansion
From the table of linear expansion coefficients in the article linear expansion of solids, it can be seen that the expansion coefficients of solids are very small. However, the most insignificant changes in the size of bodies with temperature changes cause the appearance of enormous forces.
Experience shows that even for a small elongation solid huge external forces are required. So, to increase the length of a steel rod with a cross-section of 1 cm 2 by approximately 0.0005 of its original length, it is necessary to apply a force of 1000 kg. But the same magnitude of expansion of this rod is obtained when it is heated by 50 degrees. It is therefore clear that, expanding when heated (or contracting when cooling) by 50 degrees, the rod will exert a pressure of about 1000 kg/cm 2 on those bodies that will prevent its expansion (compression).
The enormous forces that arise during the expansion and compression of solids are taken into account in technology. For example, one of the ends of the bridge is not fixedly fixed, but installed on rollers; railway rails are not laid closely, but a gap is left between them; steam pipelines are suspended on hooks, and compensators are installed between individual pipes, bending as the steam pipeline pipes lengthen. For the same reason, the boiler of a steam locomotive is fixed only at one end, while its other end can move freely.
Linear expansion of solids
A solid at a given temperature has a certain shape and certain linear dimensions. An increase in the linear dimensions of a body when heated is called thermal linear expansion.
Measurements show that the same body expands at different temperatures in different ways: at high temperatures usually stronger than at low levels. But this difference in expansion is so small that with relatively small changes in temperature it can be neglected and it can be assumed that the change in body size is proportional to the change in temperature.
Volume expansion of solids
With the thermal expansion of a solid body, as the linear dimensions of the body increase, its volume also increases. Similar to the linear expansion coefficient, the volumetric expansion coefficient can be entered to characterize volumetric expansion. Experience shows that, just as in the case of linear expansion, it can be assumed without much error that the increase in the volume of a body is proportional to the increase in temperature.
Denoting the volume of the body at 0° C by V 0, the volume at temperature t° by V t, and the coefficient of volumetric expansion by α, we find:
α = V t – V 0: V 0 t (1)
At V 0 = 1 unit. volume and t = 1 o C the value of α is equal to V t – V 0, i.e. the coefficient of volumetric expansion is numerically equal to the increase in the volume of a body when heated by 1 degree, if at 0°C the volume was equal to a unit volume.
Using formula (1), knowing the volume of a body at a temperature of 0 ° C, you can calculate its volume at any temperature t °:
V t = V 0 (1 + αt)
Let us establish the relationship between the coefficients of volumetric and linear expansion.
Law of conservation and transformation of energy
Let us consider the Joule experiment described above in more detail. In this experiment, the potential energy of falling weights was converted into kinetic energy of rotating blades; Thanks to the work against frictional forces, the kinetic energy of the blades was converted into internal energy of water. We are faced here with the case of the transformation of one type of energy into another. The potential energy of falling weights is converted into internal energy of water, the amount of heat Q serves as a measure of the converted energy. Thus, the amount of energy is conserved when it is converted into other types of energy.
It is natural to ask the question: is the amount of energy conserved during transformations of other types of energy, for example kinetic, electrical, etc.? Let us assume that a bullet of mass m is flying with speed v. Its kinetic energy is equal to mv 2 / 2. The bullet hit an object and got stuck in it. The kinetic energy of the bullet is converted into the internal energy of the bullet and the object, measured by the amount of heat Q, which is calculated by well-known formula. If kinetic energy is not lost when converted into internal energy, then the equality must hold:
mv 2 / 2 = Q
where kinetic energy and amount of heat are expressed in the same units.
Experience confirms this conclusion. The amount of energy is conserved.
Mechanical equivalent of heat
IN early XIX V. Steam engines are being widely introduced into industry and transport. At the same time, opportunities are being sought to improve their efficiency. In this regard, physics and technology are faced with a question of great practical importance: how to do as much work as possible in a car with the least amount of fuel consumed.
The first step in solving this problem was made by the French engineer Sadi Carnot in 1824, studying the question of the coefficient useful action steam engines.
In 1842, the German scientist Robert Mayer theoretically determined how much mechanical work could be obtained by expending one kilocalorie of heat.
Mayer based his calculations on the difference in the heat capacities of gas.
Gases have two heat capacities: heat capacity at constant pressure (c p) and heat capacity at constant volume (c v).
The heat capacity of a gas at constant pressure is measured by the amount of heat that goes into heating a given mass of gas by 1 degree without changing its pressure.
The heat capacity at a constant volume is numerically equal to the amount of heat used to heat a given mass of gas by 1 degree without changing the volume occupied by the gas.
Dependence of the volume of bodies on temperature
Particles of a solid body occupy certain positions relative to each other, but do not remain at rest, but oscillate. When a body heats up, the average speed of particle movement increases. At the same time, the average distances between particles increase, therefore the linear dimensions of the body increase, and therefore its volume increases.
When cooling, the linear dimensions of the body are reduced and its volume decreases.
As is known, when heated, bodies expand, and when cooled, they contract. The qualitative side of these phenomena has already been discussed in initial course physics.
