Kinetic theory of gases Flashcards
What is the kinetic theory of gases?
The kinetic theory describes the behaviour of gases at a molecular level. An understanding of how gases behave at a molecular level may then be used to explain certain macroscopic properties, such as temperature and pressure
The kinetic theory of gases is a model of gas behaviour that describes the characteristics of an imaginary, ideal gas.
The model arises from four simple postulates
What are the four postulates of the kinetic theory of gases
1) Gases consist of a large number of particles - either atoms or molecules
(note - the particles are very far apart, so the space between each particle is much larger than the particle itself, and therefore the volume of particles of a gas is negligible compared to the total volume of a gas)
2) Individual particles are moving in random directions and at random speeds
(i.e. There is no general pattern governing the magnitude or direction of speed of the particles in a gas. As such, at any one time, they are moving in several different directions at different speeds.)
3) Individual particles travel in straight lines between abrupt collisions
(collisions are perfectly elastic, which means that the total kinetic energy does not change during the collision)
4) There are no attractive or repulsive forces between the particles
(If there were to be attractive forces, the particles would stick together and change phase, e.g. from a gas to a liquid, or liquid to solid. This would involve a breach of Postulate 3, since it would involve a loss of kinetic energy.)
History of the kinetic theory: list four key dates and progress
1739 - Daniel Bernoulli
Gases consist of a large number of molecules moving in all directions
Their impact on surfaces causes the pressure that is felt
What is felt as heat is the kinetic energy of their motion
1857 - Rudolph Clausius
Developed a more elabourate version of the Bernoulli theory
1859 - James Clerk Maxwell
Described the distribution of molecular velocities within a gas
1868 - Ludwig Boltzmann
Further modified Maxwell’s description to explain heat conduction.
Do real gases behave like the ideal gas in the kinetic theory?
2 main points. When are these most important?
Real gases deviate slightly from the behavior of the ideal gas because
- Real gas particles occupy a small but finite volume (whereas in an ideal gas, the particles have a negligible volume)
- The gas particles exhibit attractive forces for one another (and therefore may stick together or change phase)
These properties become increasingly important when particles are close together, for example at low temperatures or at high pressures.
Therefore they may behave (more or less) approximately to the imaginary ideal gas, depending upon conditions of temperature and pressure. In extreme conditions this behaviour will be very different, e.g. liquefaction.
What is Brownian motion
Discovery, history, examples
Brownian motion provides a demonstration that fluids are really made up of fast moving particles.
1828: Robert Brown observed with a microscope that pollen molecules floating in water exhibit constant chaotic movements
1905: Einstein combined ideas from the kinetic theory of gases and classical fluid dynamics. He showed conclusively that this motion was caused by the bombardment of the pollen particles by invisible water molecules.
Similar phenomena can be observed when dust particles are seen to dance in a sunbeam, or smoke particles are released from a burning cord into a small glass container.
What is the Maxwell-Boltzmann distribution?
A distribution of the probability that any random particle will have a given speed.
X axis = speed, y axis = fraction of particles moving at speed s
At any moment in time, the particles of a gas are moving at random speeds. Maxwell (1849) produced the first mathematical description of speeds of gas particles, Bolzman (1868) modified this.
What is the effect of increasing temperature on the Maxwell-Bolzmann distribution?
Heat energy added to a gas manifests as in increase in the kinetic energy of the gas particles -> the average speed to the molecules of the gas increases.
The peak of the Maxwell-Bolzmann distribution shifts to the RIGHT.
The area under the curve remains constant as this is a probability distribution and the total therefore always sums to one.
What is the relationship between temperature and average kinetic energy of gas particles?
What is formula for kinetic energy?
Do all gases have the same speed at the same kinetic energy?
**Temperature is a reflection of the average kinetic energy of the particles of a gas. At a given temperature, the average kinetic energy of particles of different gases is the same.
If heat energy is added to a gas, this manifests as an increase in the kinetic energy of the gas particles, and the average speed of the gas particles increases.
Kinetic energy = 1/2 mv^2
(m = mass, v = velocity)
Thus, gases with a higher molecular weight, and therefore mass, will have a slower average speed for.a given kinetic energy?
What is the effect of gas molecular weight on the max-bolzmann distribution?
At a given temperature, the average kinetic energy of particles of different gases will be the same.
Kinetic energy = 1/2 * mass * velocity^2
Thus gases with a higher molecular weight, and therefore mass, will have a slower average speed for a given kinetic energy –> at a given temperature, gases with a higher molecular weight have a distribution of speeds that is shifted towards the left.
