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The presentation about Molecule-kinetic theory

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  • Pressure Buildup in a Bottle of Champagne

    22 слайд

    Pressure Buildup in a Bottle of Champagne

  • GasGases are composed of particles that are moving around very fast in their...

    23 слайд

    Gas
    Gases are composed of particles that are moving around very fast in their container(s).

    These particles moves in straight lines until they collides with either the container wall or another particle, then they bounce off.

    A snapshot of these particles in a gas, will reveal that there is a lot of empty space
    in there.

  • Gas PressureJust as a ball exerts a force when it bounces against a wall, a g...

    24 слайд

    Gas Pressure
    Just as a ball exerts a force when it bounces against a wall, a gaseous atom or molecule exerts a force when it collides with a surface.

    The result of many of these molecular collisions is pressure.

    Pressure is the force exerted per unit area by gas molecules as they strike the surfaces around them.

  • Gas PressureGas pressure is a result of the constant movement of the gas mole...

    25 слайд

    Gas Pressure
    Gas pressure is a result of the constant movement of the gas molecules and their collisions with the surfaces around them.

    The pressure of a gas depends on several factors:
    Number of gas particles in a given volume
    Volume of the container
    Average speed of the gas particles

  • Gas PressureThe total pressure exerted by a gas depends on several factors, i...

    26 слайд

    Gas Pressure
    The total pressure exerted by a gas depends on several factors, including the concentration of gas molecules in the sample.
    The higher the concentration, the greater the pressure.
    As volume increases, concentration of gas molecules decreases (number of molecules does not change, but since the volume increases, the concentration goes down).
    This in turn results in fewer molecular collisions, which results in lower pressure.

  • Atmospheric Pressure EffectsVariation in pressure in Earth’s atmosphere creat...

    27 слайд

    Atmospheric Pressure Effects
    Variation in pressure in Earth’s atmosphere creates wind, and changes in pressure help us to predict weather.
    The H’s in this map indicate regions of high pressure, usually associated with clear weather.

    The L’s indicate regions of low pressure, usually associated with unstable weather.
    The number of gas particles in a given volume decreases with increasing altitude.
    Hence, pressure decreases with increasing altitude.

  • Pressure exerted by a gas is dependent on the number of gas particles in a gi...

    28 слайд

    Pressure exerted by a gas is dependent on the number of gas particles in a given volume.
    The fewer the gas particles, the lower the force per unit area and the lower the pressure.
    A low density of gas particles results in low pressure. A high density of gas particles results in high pressure.

  • Pressure Imbalance in the EarIf there is a difference
	in pressure across the...

    29 слайд

    Pressure Imbalance in the Ear
    If there is a difference
    in pressure across the eardrum membrane,
    the membrane will be
    pushed out—what we
    commonly call a
    “popped eardrum.”

  • The ManometerThe pressure of a gas trapped in a container can be measured wit...

    30 слайд

    The Manometer
    The pressure of a gas trapped in a container can be measured with an instrument called a manometer.
    Manometers are U-shaped tubes partially filled with a liquid that are connected to the gas sample on one side and open to the air on
    the other.
    A competition is established between the pressures of the atmosphere and the gas.
    The difference in the liquid levels is a measure
    of the difference in pressure between the gas and the atmosphere.

  • The ManometerFor this sample the gas pressure is greater than atmospheric pre...

    31 слайд

    The Manometer
    For this sample the gas pressure is greater than atmospheric pressure, the mercury level on the left side of the tube is higher than the level on the right.

  • Blood PressureBlood pressure is the force within arteries that drives the cir...

    32 слайд

    Blood Pressure
    Blood pressure is the force within arteries that drives the circulation of blood throughout the body.

    Blood pressure is measured with an instrument called a sphygmomanometer—an inflatable cuff equipped with a pressure gauge and a stethoscope.

  • Blood Pressure

    33 слайд

    Blood Pressure

  • The Simple Gas LawsBoyle’s Law 
Charles’s Law 
Avogadro’s Law
There are four...

    34 слайд

    The Simple Gas Laws
    Boyle’s Law
    Charles’s Law
    Avogadro’s Law
    There are four basic properties of a gas: pressure (P), volume (V), temperature (T), and amount in moles (n).
    These properties are interrelated—when one changes, it affects the others.
    The simple gas laws describe the relationships between pairs of these properties.

  • Boyle’s Law: Robert Boyle (1627–1691)Robert Boyle and Robert Hooke used a J-t...

    35 слайд

    Boyle’s Law: Robert Boyle (1627–1691)
    Robert Boyle and Robert Hooke used a J-tube to measure the volume of a sample of gas at different pressures.

    They trapped a sample of air in the J-tube and added mercury to increase the pressure on the gas.
    They observed an inverse relationship between volume and pressure.
    Hence, an increase in one causes a decrease in
    the other.

  • Boyle’s Law

    36 слайд

    Boyle’s Law

  • Boyle’s LawPressure of a gas is inversely proportional to its volume.
Constan...

    37 слайд

    Boyle’s Law
    Pressure of a gas is inversely proportional to its volume.
    Constant T and amount of gas
    Graph P vs. V is curve
    Graph P vs. 1/V is straight line
    As P increases, V decreases by the same factor.
    P × V = constant
    P1 × V1 = P2 × V2

  • Molecular Interpretation of Boyle’s LawAs the volume of a gas sample is decre...

    38 слайд

    Molecular Interpretation of Boyle’s Law
    As the volume of a gas sample is decreased, gas molecules collide with surrounding surfaces more frequently, resulting in greater pressure.

  • Boyle’s Law and DivingFor every 10 m of depth, a diver experiences approximat...

    39 слайд

    Boyle’s Law and Diving
    For every 10 m of depth, a diver experiences approximately one additional atmosphere of pressure due to the weight of the surrounding water.

    At 20 m, for example, the diver experiences approximately 3 atm of pressure.

  • Boyle’s Law and DivingIf a diver holds his or her breath and rises to the sur...

    40 слайд

    Boyle’s Law and Diving
    If a diver holds his or her breath and rises to the surface quickly, the outside pressure drops to 1 atm.
    According to Boyle’s law, what should happen to the volume of air in the lungs?
    Because the pressure is decreasing by a factor of 3, the volume will expand by a factor of 3, causing damage to internal organs.
    Always exhale when rising!

  • Charles’s Law: Volume and TemperatureThe volume of a fixed amount of gas at a...

    41 слайд

    Charles’s Law: Volume and Temperature
    The volume of a fixed amount of gas at a constant pressure increases linearly with increasing temperature in kelvins:
    The volume of a gas increases with increasing temperature.
    Kelvin T = Celsius T + 273
    V = constant × T
    (if T measured in Kelvin)

  • Charles’s LawThe extrapolated lines cannot be measured experimentally because...

    42 слайд

    Charles’s Law
    The extrapolated lines cannot be measured experimentally because all gases condense into liquids before –273.15 °C is reached.
    If the lines are extrapolated back to a volume of “0,” they all show the same temperature, −273.15 °C = 0 K, called absolute zero

  • Charles’s Law – A Molecular ViewIf we move a balloon from an ice water bath t...

    43 слайд

    Charles’s Law – A Molecular View
    If we move a balloon from an ice water bath to a boiling water bath, its volume expands as the gas particles within the balloon move faster (due to the increased temperature) and collectively occupy more space.

  • Charles’s Law – A Molecular ViewWhen the temperature of a gas sample increase...

    44 слайд

    Charles’s Law – A Molecular View
    When the temperature of a gas sample increases, the gas particles move faster.
    Collisions with the walls are more frequent.
    The force exerted with each collision is greater.
    The only way for the pressure (the force per unit area) to remain constant is for the gas to occupy a larger volume so that collisions become less frequent and occur over a larger area.

  • Charles’s Law

    45 слайд

    Charles’s Law

  • Avogadro’s Law, Amedeo Avogadro (1776–1856)Volume directly proportional to th...

    46 слайд

    Avogadro’s Law, Amedeo Avogadro (1776–1856)
    Volume directly proportional to the number of gas molecules
    V = constant × n
    Constant P and T
    More gas molecules = larger volume
    Count number of gas molecules by moles.
    Equal volumes of gases contain equal numbers of molecules.
    The gas doesn't matter.

  • Avogadro’s LawThe volume of a gas sample increases linearly with the number o...

    47 слайд

    Avogadro’s Law
    The volume of a gas sample increases linearly with the number of moles of gas in the sample.
    When the amount of gas in a sample increases at constant temperature and pressure, its volume increases in direct proportion because
    the greater number
    of gas particles fill more space.

  • Ideal Gas LawThe relationships that we have discussed so far can be combined...

    48 слайд

    Ideal Gas Law
    The relationships that we have discussed so far can be combined into a single law that encompasses all of them.




  • Ideal Gas LawBy combining the gas laws we can write a general equation.
R is...

    49 слайд

    Ideal Gas Law
    By combining the gas laws we can write a general equation.
    R is called the gas constant.
    The value of R depends on the units of P and V.
    We will use and convert P to atm and V
    to liters.
    The other gas laws are found in the ideal gas law if two variables are kept constant.
    The ideal gas law allows us to find one of the variables if we know the other three.

  • Ideal Gas Law

    50 слайд

    Ideal Gas Law

  • Standard ConditionsBecause the volume of a gas varies with pressure and tempe...

    51 слайд

    Standard Conditions
    Because the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy.
    We call these standard conditions.
    STP
    Standard pressure = 1 atm
    Standard temperature = 273 K = 0 °C

  • Molar VolumeThe volume occupied by one mole of a substance is its molar volum...

    52 слайд

    Molar Volume
    The volume occupied by one mole of a substance is its molar volume at STP
    (T =273 K or 0 °C and P = 1atm).

  • Molar Volume at STPSolving the ideal gas equation for the volume of 1 mol of...

    53 слайд

    Molar Volume at STP
    Solving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L.
    6.022 × 1023 molecules of gas
    Notice that the gas is immaterial.
    We call the volume of 1 mole of gas at STP the molar volume.
    It is important to recognize that one mole measure of different gases have different masses, even though they have the same volume.

  • Molar Volume at STP

    54 слайд

    Molar Volume at STP

  • Density of a Gas at STPDensity is the ratio of mass to volume.
Density of a g...

    55 слайд

    Density of a Gas at STP
    Density is the ratio of mass to volume.
    Density of a gas is generally given in g/L.
    The mass of 1 mole = molar mass.
    The volume of 1 mole at STP = 22.4 L.

  • Density of a Gas at STPFor example, the densities of helium and nitrogen gas...

    56 слайд

    Density of a Gas at STP
    For example, the densities of helium and nitrogen gas at STP are as follows:

  • Gas DensityDensity is directly proportional to molar mass.

    57 слайд

    Gas Density
    Density is directly proportional to molar mass.

  • Molar Mass of a GasOne of the methods chemists use to determine the molar mas...

    58 слайд

    Molar Mass of a Gas
    One of the methods chemists use to determine the molar mass of an unknown substance is to heat a weighed sample until it becomes a gas; measure the temperature, pressure, and volume; and use the ideal gas law.

  • Mixtures of GasesMany gas samples are not pure, but are mixtures of gases.
Dr...

    59 слайд

    Mixtures of Gases
    Many gas samples are not pure, but are mixtures of gases.
    Dry air, for example, is a mixture containing nitrogen, oxygen, argon, carbon dioxide, and a few other gases in trace amounts.

  • Mixtures of GasesTherefore, in certain applications, the mixture can be thoug...

    60 слайд

    Mixtures of Gases
    Therefore, in certain applications, the mixture can be thought of as one gas.

    Even though air is a mixture, we can measure the pressure, volume, and temperature of air as if it were a pure substance.

    We can calculate the total moles of molecules in an air sample, knowing P, V, and T, even though they are different molecules.

  • Partial PressureThe pressure of a single gas in a mixture of gases is called...

    61 слайд

    Partial Pressure
    The pressure of a single gas in a mixture of gases is called its partial pressure.
    We can calculate the partial pressure of a gas if
    we know what fraction of the mixture it composes and the total pressure,
    or we know the number of moles of the gas in a container of known volume and temperature.
    The sum of the partial pressures of all the gases in the mixture equals the total pressure:
    Dalton’s law of partial pressures
    Gases behave independently

  • Partial PressureThe pressure due to any individual component in a gas mixture...

    62 слайд

    Partial Pressure
    The pressure due to any individual component in a gas mixture is its partial pressure (Pn).
    We can calculate partial pressure from the ideal gas law by assuming that each gas component acts independently.

  • Dalton’s Law of Partial PressuresFor a multicomponent gas mixture, we calcula...

    63 слайд

    Dalton’s Law of Partial Pressures
    For a multicomponent gas mixture, we calculate the partial pressure of each component from the ideal gas law and the number of moles of that component ( nn ) as follows:
    The sum of the partial pressures of the components in a gas mixture equals the total pressure:

  • Dalton’s Law of Partial PressuresP total is the total pressure and Pa, Pb, Pc...

    64 слайд

    Dalton’s Law of Partial Pressures
    P total is the total pressure and Pa, Pb, Pc, . . . are the partial pressures of the components. This relationship is known as Dalton’s law of partial pressures.

  • Mole FractionThe ratio of the partial pressure a single gas contributes and t...

    65 слайд

    Mole Fraction
    The ratio of the partial pressure a single gas contributes and total pressure is equal to the mole fraction.


    The number of moles of a component in a mixture divided by the total number of moles in the mixture, is the mole fraction.

  • Mole FractionThe partial pressure of a component in a gaseous mixture is its...

    66 слайд

    Mole Fraction
    The partial pressure of a component in a gaseous mixture is its mole fraction multiplied by the total pressure.
    For gases, the mole fraction of a component is equivalent to its percent by volume divided
    by 100%.
    Nitrogen has a 78% composition of air; find its partial pressure.

  • Deep-Sea Diving and Partial PressuresWhen a diver breathes compressed air, th...

    67 слайд

    Deep-Sea Diving and Partial Pressures
    When a diver breathes compressed air, the abnormally high partial pressure of oxygen in the lungs leads to an elevated concentration of oxygen in body tissues.

  • Collecting GasesGases are often collected by having them displace water from...

    68 слайд

    Collecting Gases
    Gases are often collected by having them displace water from a container.
    The problem is that because water evaporates, there is also water vapor in the collected gas.
    The partial pressure of the water vapor, called the vapor pressure, depends only on the temperature.

    You can use a table to find out the partial pressure of the water vapor in the gas you collect.

    If you collect a gas sample with a total pressure of
    758.2 mmHg* at 25 °C, the partial pressure of the water vapor will be 23.78 mmHg, so the partial pressure of the dry gas will be 734.4 mmHg.
    See Table 5.4*

  • Vapor Pressure of Water

    69 слайд

    Vapor Pressure of Water

  • Collecting Gas by Water Displacement

    70 слайд

    Collecting Gas by Water Displacement

  • Molar Volume and StoichiometryHow many grams of water form when 1.24 L of ga...

    71 слайд

    Molar Volume and Stoichiometry
    How many grams of water form when
    1.24 L of gas H2 at STP completely reacts with O2?
    2H2 (g) + O2 (g) 2H2O (g)

  • Properties of GasesExpand to completely fill their container
Take the shape o...

    72 слайд

    Properties of Gases
    Expand to completely fill their container
    Take the shape of their container
    Low density
    Much less than solid or liquid state
    Compressible
    Mixtures of gases are always
    homogeneous fluid

  • Kinetic Molecular TheoryThe simplest model for the behavior of gases is the k...

    73 слайд

    Kinetic Molecular Theory
    The simplest model for the behavior of gases is the kinetic molecular theory.
    In this theory, a gas is modeled as a collection of particles (either molecules or atoms, depending on the gas) in constant motion.

  • Kinetic Molecular TheoryThe particles of the gas (either atoms or molecules)...

    74 слайд

    Kinetic Molecular Theory
    The particles of the gas (either atoms or molecules) are constantly moving.
    The attraction between particles is negligible.
    When the moving gas particles hit another gas particle or the container, they do not stick; but they bounce off and continue moving in another direction.
    Like billiard balls
    There is a lot of empty space between the gas particles compared to the size of the particles.

  • Kinetic Molecular TheoryThe average kinetic energy of the gas particles is di...

    75 слайд

    Kinetic Molecular Theory
    The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature.
    As you raise the temperature of the gas, the average speed of the particles increases.
    But not all the gas articles are moving at the
    same speed!
    The collision of one particle with another (or with the walls of its container) is completely elastic. 
    This means that when two particles collide, they may exchange energy, but there is no overall loss of energy.
    Any kinetic energy lost by one particle is completely gained by the other.

  • Kinetic Molecular Theory

    76 слайд

    Kinetic Molecular Theory

  • The Nature of PressureBecause the gas particles are constantly moving, they s...

    77 слайд

    The Nature of Pressure
    Because the gas particles are constantly moving, they strike the sides of the container with a force.
    The result of many particles in a gas sample exerting forces on the surfaces around them is a constant pressure.

  • Gas Laws Explained – Boyle’s LawBoyle’s Law says that the volume of a gas is...

    78 слайд

    Gas Laws Explained – Boyle’s Law
    Boyle’s Law says that the volume of a gas is inversely proportional to the pressure
    Decreasing the volume forces the molecules into a smaller space.
    More molecules will collide with the container at any one instant, increasing the pressure.

  • Gas Laws Explained – Charles’s LawCharles’s Law says that the volume of a gas...

    79 слайд

    Gas Laws Explained – Charles’s Law
    Charles’s Law says that the volume of a gas is directly proportional to the absolute temperature.
    According to kinetic molecular theory, when we increase the temperature of a gas, the average speed, and thus the average kinetic energy, of the particles increases.
    The greater volume spreads the collisions out over a greater surface area, so that the pressure is unchanged.

  • Gas Laws Explained – Avogadro’s LawAvogadro’s Law says that the volume of a g...

    80 слайд

    Gas Laws Explained – Avogadro’s Law
    Avogadro’s Law says that the volume of a gas is directly proportional to the number of gas molecules.
    Increasing the number of gas molecules causes more of them to hit the wall at the same time.
    To keep the pressure constant, the volume must then increase.

  • Gas Laws Explained – Dalton’s LawDalton’s law: the total pressure of a gas mi...

    81 слайд

    Gas Laws Explained – Dalton’s Law
    Dalton’s law: the total pressure of a gas mixture is the sum of the partial pressures.
    According to kinetic molecular theory, the particles have negligible size and they do not interact.
    Particles of different masses have the same average kinetic energy at a given temperature.
    Because the average kinetic energy is the same, the total pressure of the collisions is the same.

  • Kinetic Molecular Theory and The Ideal Gas LawThe kinetic molecular theory i...

    82 слайд

    Kinetic Molecular Theory and The Ideal
    Gas Law
    The kinetic molecular theory is a quantitative model that implies PV = nRT.
    The pressure on a wall of a container occupied by particles in constant motion is the total force on the wall (due to the collisions) divided by the area of the wall.

  • Temperature and Molecular VelocitiesAverage kinetic energy of the gas molecul...

    83 слайд

    Temperature and Molecular Velocities
    Average kinetic energy of the gas molecules depends on the average mass and velocity.

    Gases in the same container have the same temperature, therefore they have the same average kinetic energy.
    If they have different masses, the only way for them to have the same kinetic energy is to have different average velocities.
    Lighter particles will have a faster average velocity than more massive particles.

  • Molecular Speed versus Molar MassTo have the same average kinetic energy, hea...

    84 слайд

    Molecular Speed versus Molar Mass
    To have the same average kinetic energy, heavier molecules must have a slower average speed.

  • Temperature and Molecular VelocitiesKEavg = ½NAmu2

NA is Avogadro’s number....

    85 слайд

    Temperature and Molecular Velocities
    KEavg = ½NAmu2

    NA is Avogadro’s number.
    KEavg = (3/2)RT

    R is the gas constant in energy units, 8.314 J/mol ∙ K.
    1 J = 1 kg ∙ m2/s2
    Equating and solving we get the following:

    NA ∙ mass = molar mass in kg/mol
    As temperature increases, the average velocity increases.

  • Temperature versus Molecular Speed  As the temperature of a gas sample increa...

    86 слайд

    Temperature versus Molecular Speed  
    As the temperature of a gas sample increases, the velocity distribution of the molecules shifts toward higher velocity.
    The distribution function “spreads out,” resulting in more molecules with faster speeds.

  • Mean Free PathMolecules in a gas travel in straight lines until they collide...

    87 слайд

    Mean Free Path
    Molecules in a gas travel in straight lines until they collide with another molecule or the container.
    The average distance a molecule travels between collisions is called the mean
    free path.
    Mean free path decreases as the pressure increases.

  • Diffusion and EffusionThe process of a collection of molecules spreading out...

    88 слайд

    Diffusion and Effusion
    The process of a collection of molecules spreading out from high concentration to low concentration is called diffusion.
    The process by which a collection of molecules escapes through a small hole into a vacuum is called effusion.
    The rates of diffusion and effusion of a gas are both related to its rms average velocity.
    For gases at the same temperature, this means that the rate of gas movement is inversely proportional to the square root of its molar mass.

  • Effusion

    89 слайд

    Effusion

  • Graham’s Law of EffusionFor two different gases at the same temperature, the...

    90 слайд

    Graham’s Law of Effusion
    For two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:

  • Real GasesReal gases often do not behave like ideal gases at high pressure or...

    91 слайд

    Real Gases
    Real gases often do not behave like ideal gases at high pressure or low temperature.
    Ideal gas laws assume
    1.no attractions between gas molecules.
    2.gas molecules do not take up space.
    Based on the kinetic-molecular theory
    At low temperatures and high pressures these assumptions are not valid.

  • The Effect of the Finite Volume of Gas ParticlesAt low pressures, the molar v...

    92 слайд

    The Effect of the Finite Volume of Gas Particles
    At low pressures, the molar volume of argon is nearly identical to that of an ideal gas.
    But as the pressure increases, the molar volume of argon becomes greater than that of an ideal gas.
    At the higher pressures, the argon atoms themselves occupy a significant portion of the gas volume, making the actual volume greater than that predicted by the ideal gas law.

  • Real Gas BehaviorBecause real molecules take up space, the molar volume of a...

    93 слайд

    Real Gas Behavior
    Because real molecules take up space, the molar volume of a real gas is larger than predicted by the ideal gas law at high pressures.

  • Modification of the Ideal Gas Equation In 1873, Johannes van der Waals (1837–...

    94 слайд

    Modification of the Ideal Gas Equation
    In 1873, Johannes van der Waals (1837–1923) modified the ideal gas equation to fit the behavior of real gases at high pressure.

    The molecular volume makes the real volume larger than the ideal gas law would predict.

    van der Waals modified the ideal gas equation to account for the molecular volume.
    b is called a van der Waals constant and is different for every gas because their molecules are different sizes.

  • The Effect of Intermolecular AttractionsAt high temperature, the pressure of...

    95 слайд

    The Effect of Intermolecular Attractions
    At high temperature, the pressure of the gases is nearly identical to that of an
    ideal gas.
    But at lower temperatures, the pressure of gases is less than that of an ideal gas.
    At the lower temperatures, the gas atoms spend more time interacting with each other and less time colliding with the walls, making the actual pressure less than that predicted by the ideal gas law.

  • The Effect of Intermolecular AttractionsVan der Waals modified the ideal gas...

    96 слайд

    The Effect of Intermolecular Attractions
    Van der Waals modified the ideal gas equation to account for the intermolecular attractions.
    a is another van der Waals constant and is different for every gas because their molecules have different strengths of attraction.

  • Van der Waals’s EquationCombining the equations to account for molecular volu...

    97 слайд

    Van der Waals’s Equation
    Combining the equations to account for molecular volume and intermolecular attractions we get the following equation.
    Used for real gases

  • Real GasesA plot of PV/RT versus P for 1 mole of a gas shows the difference b...

    98 слайд

    Real Gases
    A plot of PV/RT versus P for 1 mole of a gas shows the difference between real and
    ideal gases.

    It reveals a curve that shows the PV/RT ratio for a real gas is generally lower than ideal for “low” pressures—meaning that the most important factor is the intermolecular attractions.

    It reveals a curve that shows the PV/RT ratio for a real gas is generally higher than ideal for “high” pressures—meaning that the most important factor is the molecular volume.

  • PV/RT Plots

    99 слайд

    PV/RT Plots

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Самостоятельная работа по физике по теме: "Основное уравнение МКТ"
  • Учебник: «Физика (базовый уровень)», Мякишев Г.Я., Буховцев Б.Б., Сотский Н.Н. / Под ред. Парфентьевой Н.А.
  • Тема: § 63. Основное уравнение молекулярно-кинетической теории газов
  • 08.04.2021
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«Физика (базовый уровень)», Мякишев Г.Я., Буховцев Б.Б., Сотский Н.Н. / Под ред. Парфентьевой Н.А.

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    Мединаев Данияр Аманович
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