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kinetic theory of gases
College Physics - Kinetic Theory of Gases, including the equilibrium state of state parameters of thermodynamic systems, the equation of state of the zeroth law of thermodynamics, the microscopic model and statistical regularity of matter, the energy equipartition theorem of degrees of freedom, the internal energy of ideal gases, and the microscopic description of ideal gases Elementary theory, Maxwell's velocity distribution law of gas molecules, mean free path of gas molecules and collision frequency.
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kinetic theory of gases
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kinetic theory of gases
thermodynamic system state parameters equilibrium state
thermodynamic system
isolated system
closed system
open system
State parameters: physical quantities used to describe the properties of the system
Volume V
The space that gas molecules can reach
Unit: cubic meter
Pressure p
The vertical force exerted by gas on the unit area of the container wall directed towards the container wall
Unit: Pa
Temperature T
Unit:K
equilibrium state
Definition: Without being affected by external conditions, after a long enough time, the system will reach a state that does not change with time from a macro perspective.
Note: The equilibrium state is an ideal model, which is a generalization and abstraction of the actual situation.
The zeroth law of thermodynamics equation of state
Insulating walls and thermal conductive walls
zeroth law of thermodynamics
definition
Objects A and B are in thermal equilibrium with object C, which is in a certain equilibrium state. Then A and B are also in equilibrium.
physical meaning
1) Objects that are in thermal equilibrium with each other must have the same characteristic, that is, their temperatures are the same. 2) The zeroth law of thermodynamics not only gives the concept of temperature, but also points out the method of judging whether the temperatures are the same.
ideal gas equation of state
pV=M/μ·RT
Notice
Only applicable to equilibrium state
Non-ideal gases do not comply with
Microscopic models and statistical regularities of matter
Thermal motion characteristics of gas molecules
Eternal motion, frequent collisions
Brownian motion reflects the thermal motion of fluid molecules
Due to the characteristics of molecular thermal motion
The physical quantities that characterize the properties of individual molecules are called microscopic quantities
The quantity that characterizes the collective characteristics of a large number of molecules is a macroscopic quantity
Characteristics of statistical laws
Use the average properties of a large number of molecules to represent the reality of individual molecules
Statistical laws fluctuate
Degrees of freedom Equipartition of energy theorem Internal energy of ideal gas
equipartition theorem of energy
The average kinetic energy of any degree of freedom of gas molecules is 1/2kT
degrees of freedom
The number of independent coordinates used to determine the position of an object in space
internal energy of ideal gas
The energy of gas molecules and the potential energy between molecules constitute the total energy inside the gas
E=3nRT
It can be seen that the internal energy of a certain amount of ideal gas depends entirely on the degree of freedom of molecular motion and temperature.
Elementary theory of microscopic description of ideal gases
ideal gas microscopic model
Based on the basic characteristics, we first make the following assumptions
Molecular size is negligible because the distance between gas molecules is much greater than the diameter
Taking into account the intermolecular interaction force is not considered
Collisions can be considered as perfectly elastic collisions
possessing molecular chaos
Derivation of ideal gas pressure formula
p=2/3nEk
The nature and statistical significance of temperature
Nature
p=nkT k represents Boltzmann’s constant
Ek=1/2m0v2=3/2kT
Statistical significance
The temperature of a gas is a measure of the average translational kinetic energy of the gas molecules
Therefore, temperature is a physical quantity that represents the degree of heat or coldness of an object when it is in thermal equilibrium.
Maxwell's gas molecular velocity distribution law
Gas molecular velocity distribution function
The velocity needs to be divided into several intervals according to its size, so that the distribution can be accurately defined f(v)=dN/Ndv
normalization condition
The area enclosed between 0 and ∞ is 1
Maxwell rate distribution
Maxwell derived the specific form of f(v) theoretically
Three statistical rates
Using the Maxwell rate distribution function, the statistical mean of a molecule can be calculated
Average velocity Root mean square velocity Most probable velocity
Mean free path and collision frequency of gas molecules
Study of molecular collisions
Average collision frequency: the average number of collisions between a molecule and other molecules per unit time
Mean free path: the average distance a molecule travels freely between two consecutive collisions
mean free path formula
average collision frequency formula