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Physics_NIS_Kinetic_Molecular_Theory.pptx
Что делает ИДЕАЛЬНЫЙ газ ИДЕАЛЬНЫМ?
отaничoхе
вдноиеакоы
угепуро
незначительны
меъбo
ныеунркуилевтмляро ысли
хаотичное
одинаковые
упругое столкновение
объем
внутримолекулярные силы
знать основные положения молекулярно-кинетической теории газов;
объяснять, как движущиеся молекулы газа создают давление, вывести формулу: p=1/3 (nm0 〈v〉2)
выводить зависимость cредней кинетической энергии поступательного движения молекул от температуры
ENRICHMENT
Activity
Kinetic Molecular Theory
All gases are made up of identical atoms or molecules.
All atoms or molecules move randomly.
The volume of the atoms or molecules is negligible when compared with the volume occupied by the gas.
The intermolecular forces are negligible except during collisions.
Inter-atomic or molecular collisions are elastic.
The duration of a collision is negligible compared with the time spent travelling between collisions.
Atoms and molecules move with constant speed between collisions. Gravity has no effect on molecular motion.
Think
Together
PRESSURE on Microscopic Level
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Together
Motion of an IDEAL particle
A particle of mass 𝑚 is confined in a cube with side 𝑑.
Let us focus on one component of its velocity (𝑽𝑽𝒙𝒙).
Изменение импульса молекул
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Together
Motion of an IDEAL particle
After collision with wall A, the change in momentum is given by:
The total distance traveled for the particle before its next collision to wall A is 2𝑑.
∆ 𝑝 𝑥 𝑝𝑝 𝑝 𝑥 𝑥𝑥 𝑝 𝑥 =−𝑚𝑚 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 −𝑚𝑚 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥
∆ 𝑝 𝑥 𝑝𝑝 𝑝 𝑥 𝑥𝑥 𝑝 𝑥 =−2𝑚𝑚 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥
𝑑
The total time for this entire trip is:
∆𝑡𝑡= 2𝑑 𝑣 𝑥 2𝑑𝑑 2𝑑 𝑣 𝑥 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 2𝑑 𝑣 𝑥
A
B
A
B
Think
Together
Motion of an IDEAL particle
If Fx1 is the magnitude of the average force exerted by a molecule on the wall in the time t, thus by applying Newton’s second law of motion gives
𝐹 𝑥1 𝐹𝐹 𝐹 𝑥1 𝑥𝑥1 𝐹 𝑥1 = ∆ 𝑝 𝑥 ∆𝑡 ∆ 𝑝 𝑥 ∆ 𝑝 𝑥 𝑝𝑝 𝑝 𝑥 𝑥𝑥 𝑝 𝑥 ∆ 𝑝 𝑥 ∆ 𝑝 𝑥 ∆𝑡 ∆𝑡𝑡 ∆ 𝑝 𝑥 ∆𝑡 = 2𝑚 𝑣 𝑥 2𝑑 𝑣 𝑥 2𝑚𝑚 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 2𝑚 𝑣 𝑥 2𝑑 𝑣 𝑥 2𝑑 𝑣 𝑥 2𝑑𝑑 2𝑑 𝑣 𝑥 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 2𝑑 𝑣 𝑥 2𝑚 𝑣 𝑥 2𝑑 𝑣 𝑥 = 𝑚 𝑑 𝑚𝑚 𝑚 𝑑 𝑑𝑑 𝑚 𝑑 𝑣 𝑥 2 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2
𝑑
A
B
A
B
For N number of particles:
𝐹 𝑥 𝐹𝐹 𝐹 𝑥 𝑥𝑥 𝐹 𝑥 = 𝑚 𝑑 𝑚𝑚 𝑚 𝑑 𝑑𝑑 𝑚 𝑑 𝑣 𝑥1 2 𝑣 𝑥1 𝑣𝑣 𝑣 𝑥1 𝑥𝑥1 𝑣 𝑥1 𝑣 𝑥1 2 2 𝑣 𝑥1 2 + 𝑚 𝑑 𝑚𝑚 𝑚 𝑑 𝑑𝑑 𝑚 𝑑 𝑣 𝑥2 2 𝑣 𝑥2 𝑣𝑣 𝑣 𝑥2 𝑥𝑥2 𝑣 𝑥2 𝑣 𝑥2 2 2 𝑣 𝑥2 2 + …+ 𝑚 𝑑 𝑚𝑚 𝑚 𝑑 𝑑𝑑 𝑚 𝑑 𝑣 𝑥𝑁 2 𝑣 𝑥𝑁 𝑣𝑣 𝑣 𝑥𝑁 𝑥𝑥𝑁𝑁 𝑣 𝑥𝑁 𝑣 𝑥𝑁 2 2 𝑣 𝑥𝑁 2
𝐹 𝑥 𝐹𝐹 𝐹 𝑥 𝑥𝑥 𝐹 𝑥 = 𝑚 𝑑 𝑚𝑚 𝑚 𝑑 𝑑𝑑 𝑚 𝑑 (𝑣 𝑥1 2 (𝑣 𝑥1 (𝑣𝑣 (𝑣 𝑥1 𝑥𝑥1 (𝑣 𝑥1 (𝑣 𝑥1 2 2 (𝑣 𝑥1 2 + 𝑣 𝑥2 2 𝑣 𝑥2 𝑣𝑣 𝑣 𝑥2 𝑥𝑥2 𝑣 𝑥2 𝑣 𝑥2 2 2 𝑣 𝑥2 2 + … 𝑣 𝑥𝑁 2 𝑣 𝑥𝑁 𝑣𝑣 𝑣 𝑥𝑁 𝑥𝑥𝑁𝑁 𝑣 𝑥𝑁 𝑣 𝑥𝑁 2 2 𝑣 𝑥𝑁 2 )
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Together
Motion of an IDEAL particle
The mean value of the square of the velocity in the x direction for N molecules is
𝐹 𝑥 𝐹𝐹 𝐹 𝑥 𝑥𝑥 𝐹 𝑥 = 𝑚 𝑑 𝑚𝑚 𝑚 𝑑 𝑑𝑑 𝑚 𝑑 (𝑣 𝑥1 2 (𝑣 𝑥1 (𝑣𝑣 (𝑣 𝑥1 𝑥𝑥1 (𝑣 𝑥1 (𝑣 𝑥1 2 2 (𝑣 𝑥1 2 + 𝑣 𝑥2 2 𝑣 𝑥2 𝑣𝑣 𝑣 𝑥2 𝑥𝑥2 𝑣 𝑥2 𝑣 𝑥2 2 2 𝑣 𝑥2 2 + … 𝑣 𝑥𝑁 2 𝑣 𝑥𝑁 𝑣𝑣 𝑣 𝑥𝑁 𝑥𝑥𝑁𝑁 𝑣 𝑥𝑁 𝑣 𝑥𝑁 2 2 𝑣 𝑥𝑁 2 )
𝑣 𝑥 2 𝑣 𝑥 2 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 𝑣 𝑥 2 = (𝑣 𝑥1 2 + 𝑣 𝑥2 2 + … 𝑣 𝑥𝑁 2 ) 𝑁 (𝑣 𝑥1 2 (𝑣 𝑥1 (𝑣𝑣 (𝑣 𝑥1 𝑥𝑥1 (𝑣 𝑥1 (𝑣 𝑥1 2 2 (𝑣 𝑥1 2 + 𝑣 𝑥2 2 𝑣 𝑥2 𝑣𝑣 𝑣 𝑥2 𝑥𝑥2 𝑣 𝑥2 𝑣 𝑥2 2 2 𝑣 𝑥2 2 + … 𝑣 𝑥𝑁 2 𝑣 𝑥𝑁 𝑣𝑣 𝑣 𝑥𝑁 𝑥𝑥𝑁𝑁 𝑣 𝑥𝑁 𝑣 𝑥𝑁 2 2 𝑣 𝑥𝑁 2 ) (𝑣 𝑥1 2 + 𝑣 𝑥2 2 + … 𝑣 𝑥𝑁 2 ) 𝑁 𝑁𝑁 (𝑣 𝑥1 2 + 𝑣 𝑥2 2 + … 𝑣 𝑥𝑁 2 ) 𝑁
𝑁𝑁 𝑣 𝑥 2 𝑣 𝑥 2 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 𝑣 𝑥 2 = (𝑣 𝑥1 2 (𝑣 𝑥1 (𝑣𝑣 (𝑣 𝑥1 𝑥𝑥1 (𝑣 𝑥1 (𝑣 𝑥1 2 2 (𝑣 𝑥1 2 + 𝑣 𝑥2 2 𝑣 𝑥2 𝑣𝑣 𝑣 𝑥2 𝑥𝑥2 𝑣 𝑥2 𝑣 𝑥2 2 2 𝑣 𝑥2 2 + … 𝑣 𝑥𝑁 2 𝑣 𝑥𝑁 𝑣𝑣 𝑣 𝑥𝑁 𝑥𝑥𝑁𝑁 𝑣 𝑥𝑁 𝑣 𝑥𝑁 2 2 𝑣 𝑥𝑁 2 )
Thus, the x component for the total force exerted on the wall of the cubical container is:
𝐹 𝑥 𝐹𝐹 𝐹 𝑥 𝑥𝑥 𝐹 𝑥 = 𝑚 𝑑 𝑚𝑚 𝑚 𝑑 𝑑𝑑 𝑚 𝑑 𝑁𝑁 𝑣 𝑥 2 𝑣 𝑥 2 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 𝑣 𝑥 2
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Motion of an IDEAL particle
For velocity 𝒗𝒗 and its components:
Then, it follows:
𝑣 2 𝑣𝑣 𝑣 2 2 𝑣 2 = 𝑣 𝑥 2 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 + 𝑣 𝑦 2 𝑣 𝑦 𝑣𝑣 𝑣 𝑦 𝑦𝑦 𝑣 𝑦 𝑣 𝑦 2 2 𝑣 𝑦 2 + 𝑣 𝑧 2 𝑣 𝑧 𝑣𝑣 𝑣 𝑧 𝑧𝑧 𝑣 𝑧 𝑣 𝑧 2 2 𝑣 𝑧 2
𝑣 2 𝑣 2 𝑣𝑣 𝑣 2 2 𝑣 2 𝑣 2 = 𝑣 𝑥 2 𝑣 𝑥 2 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 𝑣 𝑥 2 + 𝑣 𝑦 2 𝑣 𝑦 2 𝑣 𝑦 𝑣𝑣 𝑣 𝑦 𝑦𝑦 𝑣 𝑦 𝑣 𝑦 2 2 𝑣 𝑦 2 𝑣 𝑦 2 + 𝑣 𝑧 2 𝑣 𝑧 2 𝑣 𝑧 𝑣𝑣 𝑣 𝑧 𝑧𝑧 𝑣 𝑧 𝑣 𝑧 2 2 𝑣 𝑧 2 𝑣 𝑧 2
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Motion of an IDEAL particle
𝑣 𝑥 2 𝑣 𝑥 2 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 𝑣 𝑥 2 = 𝑣 𝑦 2 𝑣 𝑦 2 𝑣 𝑦 𝑣𝑣 𝑣 𝑦 𝑦𝑦 𝑣 𝑦 𝑣 𝑦 2 2 𝑣 𝑦 2 𝑣 𝑦 2 = 𝑣 𝑧 2 𝑣 𝑧 2 𝑣 𝑧 𝑣𝑣 𝑣 𝑧 𝑧𝑧 𝑣 𝑧 𝑣 𝑧 2 2 𝑣 𝑧 2 𝑣 𝑧 2
Since the velocities of the molecules in the ideal gas are completely random, there is no preference to one direction or another. Hence:
𝑣 2 𝑣 2 𝑣𝑣 𝑣 2 2 𝑣 2 𝑣 2 = 𝑣 𝑥 2 𝑣 𝑥 2 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 𝑣 𝑥 2 + 𝑣 𝑦 2 𝑣 𝑦 2 𝑣 𝑦 𝑣𝑣 𝑣 𝑦 𝑦𝑦 𝑣 𝑦 𝑣 𝑦 2 2 𝑣 𝑦 2 𝑣 𝑦 2 + 𝑣 𝑧 2 𝑣 𝑧 2 𝑣 𝑧 𝑣𝑣 𝑣 𝑧 𝑧𝑧 𝑣 𝑧 𝑣 𝑧 2 2 𝑣 𝑧 2 𝑣 𝑧 2
𝑣 2 𝑣 2 𝑣𝑣 𝑣 2 2 𝑣 2 𝑣 2 =3 𝑣 𝑥 2 𝑣 𝑥 2 𝑣 𝑥 𝑣𝑣 𝑣 𝑥 𝑥𝑥 𝑣 𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 𝑣 𝑥 2
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Pressure of an IDEAL particle
p= 𝐹 𝑆 𝐹𝐹 𝐹 𝑆 𝑆𝑆 𝐹 𝑆
p= 𝑁 𝑚 0 𝑣 𝑥 2 𝑑 3 𝑁𝑁 𝑚 0 𝑚𝑚 𝑚 0 0 𝑚 0 𝑣 𝑥 2 𝑣𝑣 𝑣 𝑥 2 𝑥𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 𝑁 𝑚 0 𝑣 𝑥 2 𝑑 3 𝑑 3 𝑑𝑑 𝑑 3 3 𝑑 3 𝑁 𝑚 0 𝑣 𝑥 2 𝑑 3
𝑝𝑝= 𝑁 𝑚 0 𝑣 𝑥 2 𝑉 𝑁𝑁 𝑚 0 𝑚𝑚 𝑚 0 0 𝑚 0 𝑣 𝑥 2 𝑣𝑣 𝑣 𝑥 2 𝑥𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 𝑁 𝑚 0 𝑣 𝑥 2 𝑉 𝑉𝑉 𝑁 𝑚 0 𝑣 𝑥 2 𝑉
𝑝𝑝= 1 3 1 1 3 3 1 3 𝑁 𝑚 0 𝑣 𝑥 2 𝑉 𝑁𝑁 𝑚 0 𝑚𝑚 𝑚 0 0 𝑚 0 𝑣 𝑥 2 𝑣𝑣 𝑣 𝑥 2 𝑥𝑥 𝑣 𝑥 2 2 𝑣 𝑥 2 𝑁 𝑚 0 𝑣 𝑥 2 𝑉 𝑉𝑉 𝑁 𝑚 0 𝑣 𝑥 2 𝑉
𝑝= 1 3 ρ 𝑣 2
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PRESSURE on Microscopic Level
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Together
Dependence of kinetic energy on temperature
List numbers 1 to 8 on the paper provided to you.
For every question, write the corresponding letter of your choice.
Test Your Knowledge
Which has a fixed volume but indefinite shape?
wood
water
nitrogen
platinum
1
Which one is NOT a characteristic of a SOLID?
fixed volume
definite shape
highly compressible
strong molecular attraction
2
Which reason best explains increase of temperature in matters?
increase in number of molecules
decrease in number of molecules
higher speed of molecules
slower speed of molecules
3
Which phase or phases of matter can flow?
Liquid
Solid and Gas
Liquid and Gas
Solid, Liquid and Gas
4
In which phase can heat be transferred the fastest?
Solid
Liquid
Gas
5
6
The diagram represents molecules in a liquid.
A and C are molecules with a high amount of energy.
B and D are molecules with a low amount of energy.
Which molecule is most likely to be leaving the liquid by evaporation?
7
The graph shows the temperature of an ice as it is heated steadily. In which part of the graph is the ice melting?
8
The diagram shows how the atoms in a substance rearrange themselves during a change of state.
Which change of state is shown?
A. gas to liquid
B. liquid to gas
C. liquid to solid
D. solid to liquid
Problem solving
Решение 8:
(a) Средняя скорость = 1,44 × 10 3 мс -1
{Средняя скорость = (1,32 + 1,50 + 1,46 + 1,28 + 1,64) × 10 3 /5 = 1,44 × 10 3 мс -1 }
(б) Нам нужно суммировать индивидуальные квадратные скорости
Средняя квадратная скорость = 2,09 × 10 6 м 2 с -2
{Среднеквадратичное скорость = (1,32 2 + 1,50 2 + 1,46 2 + 1,28 2 + 1,64 2 ) × (10 3 ) 2 /5 = 2,09 × 10 6 м 2 сек -2 }
(c) Корневая среднеквадратическая скорость = 1,45 × 10 3 мс -1
{Это квадратный корень средней квадратичной скорости.}
Did we “hit” the objectives?
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