Kinetic Theory of Gases
Kinetic Theory of Gases
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An ideal gas has the following properties:
An ideal gas has the following properties:
A gas is composed of particles (atoms & molecules) that are separated by average distances that are much greater than the sizes of the molecules themselves.
A gas is composed of particles (atoms & molecules) that are separated by average distances that are much greater than the sizes of the molecules themselves.
A gas is composed of a large number of gas particles (N) moving in random directions and a variety of speeds as shown by the Boltzmann distribution.
A gas is composed of a large number of gas particles (N) moving in random directions and a variety of speeds as shown by the Boltzmann distribution.
The particles of a gas are in constant random motion and obey laws of mechanics. They are attracted to each other & to the the sides of the container, but those forces are negligible since the speeds and KE are significantly large.
The particles of a gas are in constant random motion and obey laws of mechanics. They are attracted to each other & to the the sides of the container, but those forces are negligible since the speeds and KE are significantly large.
Describe the distribution of speeds of molecules in a gas.
Describe the distribution of speeds of molecules in a gas.
Influence of temperature on the speed distribution
Influence of temperature on the speed distribution
With increasing temperatures, the curve maximum shifts to higher and higher speeds!
With increasing temperatures, the curve maximum shifts to higher and higher speeds!
Even at very low temperatures, there are gas molecules that have very high speeds!
Even at very low temperatures, there are gas molecules that have very high speeds!
Influence of particle mass on the speed distribution
Influence of particle mass on the speed distribution
With decreasing mases, the curve maximum shifts to higher and higher speeds!
With decreasing mases, the curve maximum shifts to higher and higher speeds!
Collisions between particles & the container are presumed to be perfectly elastic; when two molecules collide, they change their directions and kinetic energies, but the total kinetic energy and momentum within the system is conserved.
Collisions between particles & the container are presumed to be perfectly elastic; when two molecules collide, they change their directions and kinetic energies, but the total kinetic energy and momentum within the system is conserved.
Describe the relationship between the temperature of a gas and the kinetic energy of atoms and molecules.
Describe the relationship between the temperature of a gas and the kinetic energy of atoms and molecules.
The average kinetic energy of the gas molecules is directly proportional to the absolute (Kelvin) temperature.
The average kinetic energy of the gas molecules is directly proportional to the absolute (Kelvin) temperature.
Kelvin (Absolute) Temperature Scale
Kelvin (Absolute) Temperature Scale
Internal energy of a Mono-atomic Gas
Internal energy of a Mono-atomic Gas
Internal Energy of an Ideal Gas
Internal Energy of an Ideal Gas
The internal energy is the total of all the energy associated with the motion of the atoms or molecules in the system. Microscopic forms of energy include those due to the rotation, vibration, translation, and interactions among the molecules of a substance
The internal energy is the total of all the energy associated with the motion of the atoms or molecules in the system. Microscopic forms of energy include those due to the rotation, vibration, translation, and interactions among the molecules of a substance
Degrees of freedom.
Degrees of freedom.
This means that each particle possess, on average, units of energy. Monatomic particles have only three translational degrees of freedom, corresponding to their motion in three dimensions. They possess no internal rotational or vibrational degrees of freedom.
This means that each particle possess, on average, units of energy. Monatomic particles have only three translational degrees of freedom, corresponding to their motion in three dimensions. They possess no internal rotational or vibrational degrees of freedom.
Monatomic Gas – Internal Energy
Monatomic Gas – Internal Energy
The internal energy of an ideal gas depends only on temperature and the number of moles of gas.
The internal energy of an ideal gas depends only on temperature and the number of moles of gas.
For a monatomic ideal gas (such as helium, neon, or argon), the only contribution to the energy comes from translational kinetic energy. The average translational kinetic energy of a single atom depends only on the gas temperature and is given by equation:
For a monatomic ideal gas (such as helium, neon, or argon), the only contribution to the energy comes from translational kinetic energy. The average translational kinetic energy of a single atom depends only on the gas temperature and is given by equation:
Ideal Gas Constants
Ideal Gas Constants
Sample problems
Sample problems
Problem #1: CALCULATING KINETIC ENERGY AND SPEED OF A GAS MOLECULE
Problem #1: CALCULATING KINETIC ENERGY AND SPEED OF A GAS MOLECULE
(a) What is the average kinetic energy of a gas molecule at 20.0ºC (room temperature)?
(a) What is the average kinetic energy of a gas molecule at 20.0ºC (room temperature)?
(b) Find the average speed of a nitrogen molecule (N2) at this temperature.
(b) Find the average speed of a nitrogen molecule (N2) at this temperature.
Problem #2: CALCULATING TEMPERATURE: ESCAPE VELOCITY OF HELIUM ATOMS
Problem #2: CALCULATING TEMPERATURE: ESCAPE VELOCITY OF HELIUM ATOMS
In order to escape Earth’s gravity, an object near the top of the atmosphere (at an altitude of 100 km) must travel away from Earth at 11.1 km/s. This speed is called the escape velocity. At what temperature would helium atoms have an average speed equal to the escape velocity?
In order to escape Earth’s gravity, an object near the top of the atmosphere (at an altitude of 100 km) must travel away from Earth at 11.1 km/s. This speed is called the escape velocity. At what temperature would helium atoms have an average speed equal to the escape velocity?
TED-Ed: Einstein's miracle year
TED-Ed: Einstein's miracle year
As the year 1905 began, Albert Einstein faced life as a “failed” academic. Yet within the next twelve months, he would publish four extraordinary papers, each on a different topic, that were destined to radically transform our understanding of the universe.
As the year 1905 began, Albert Einstein faced life as a “failed” academic. Yet within the next twelve months, he would publish four extraordinary papers, each on a different topic, that were destined to radically transform our understanding of the universe.
Random Force & Brownian Motion - Sixty Symbols
Random Force & Brownian Motion - Sixty Symbols
Professor Bowley discusses Albert Einstein, Brownian motion and whether pollen is alive.
Professor Bowley discusses Albert Einstein, Brownian motion and whether pollen is alive.
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