kinetic theory of gases

<–2/”>a >Kinetic theory of gases

The kinetic theory describes a gas as a large number of submicroscopic particles (atoms or Molecules), all of which are in constant rapid motion that has randomness arising from their many collisions with each other and with the walls of the container.

According to kinetic theory of gases, the molecules of a gas are in random motion. So, the Average velocity of the molecules is zero.

Assumptions of Kinetic Theory of Gases

Every gas consists of extremely small particles known as molecules. The molecules of a given gas are all identical but are different from those of another gas. 2. The molecules of a gas are identical spherical, rigid and perfectly elastic point masses. -9 3. Their molecular size is negligible in comparison to intermolecular distance (10 m). 4. The speed of gas molecules lies between zero and infinity (very high speed). 5. The distance covered by the molecules between two successive collisions is known as free path and mean of all free path is known as mean free path. 6. The number of collision per unit volume in a gas remains constant. 7. No attractive or repulsive force acts between gas molecules. 8. Gravitational to extremely attraction among the molecules is ineffective due small masses and very high speed of molecules.

Temperature and pressure are macroscopic properties of gases. These properties are related to molecular motion, which is a microscopic phenomenon. The kinetic theory of gases correlates between macroscopic properties and microscopic phenomena. Kinetics means the study of motion, and in this case motions of gas molecules.

At the same temperature and volume, the same numbers of moles of all gases exert the same pressure on the walls of their containers. This is known as Avogadros principle. His theory implies that same numbers of moles of gas have the same number of molecules.

Common sense tells us that the pressure is proportional to the average kinetic energy of all the gas molecules. Avogadros principle also implies that the kinetic energies of various gases are the same at the same temperature. The molecular masses are different from gas to gas, and if all gases have the same average kinetic energy, the average speed of a gas is unique.

Boltzmann and Maxwell extended the theory to imply that the average kinetic energy of a gas depends on its temperature.

They let u be the average or root-mean-square speed of a gas whose molar mass is M. Since N is the Avogadro’s number, the average kinetic energy is (1/2) (M/N) u2 or

M 3R T 3

K.E. = — u2 = —- = — k T

2 N 2 N 2

Note that M / N is the mass of a single molecule. Thus,

u = (3k N T / M)1/2 = (3 R T / M)1/2.

where k (= R/N) is the Boltzmann constant. Note that u so evaluated is based on the average energy of gas molecules being the same, and it is called the root-mean-square speed; u is not the average speed of gas molecules.,

The kinetic theory of gases is a statistical theory of a fluid that explains many of the macroscopic properties of gases, such as pressure, temperature, and viscosity, by considering the motions of a large number of microscopic particles (molecules or atoms).

The theory is based on the following assumptions:

The molecules of a gas are in constant random motion.
The molecules of a gas are much smaller than the distances between them.
The molecules of a gas interact with each other only through elastic collisions.
The average kinetic energy of the molecules of a gas is proportional to the absolute temperature of the gas.

The kinetic theory of gases can be used to explain a wide range of phenomena, including pressure, temperature, internal energy, entropy, diffusion, viscosity, heat capacity, Sound waves, and Brownian motion.

Pressure is the force exerted by a gas per unit area. It can be explained by the kinetic theory of gases as the result of the collisions of gas molecules with the walls of a container. The more rapidly the molecules are moving, the greater the pressure they exert.
Temperature is a measure of the average kinetic energy of the molecules of a gas. The higher the temperature, the greater the average kinetic energy of the molecules and the faster they are moving.
Internal energy is the total energy of a system. It can be divided into two parts: kinetic energy and potential energy. The kinetic energy of a system is the energy of motion of its components. The potential energy of a system is the energy stored in its components due to their positions or arrangement. The internal energy of a gas is due to the kinetic energy of its molecules.
Entropy is a measure of the disorder of a system. The higher the entropy, the greater the disorder. The kinetic theory of gases predicts that the entropy of a gas will always increase over time. This is because the molecules of a gas are constantly moving and colliding with each other. These collisions cause the molecules to spread out and become more disordered.
Diffusion is the movement of molecules from an area of high concentration to an area of low concentration. The kinetic theory of gases predicts that diffusion will occur because the molecules of a gas are constantly moving. The molecules in an area of high concentration will have a higher average kinetic energy than the molecules in an area of low concentration. This means that the molecules in an area of high concentration will be moving faster than the molecules in an area of low concentration. The faster-moving molecules will tend to move into the area of low concentration, causing the molecules to spread out.
Viscosity is a measure of the resistance of a fluid to flow. The kinetic theory of gases predicts that viscosity will occur because the molecules of a gas are constantly colliding with each other. These collisions cause the molecules to stick together, which makes it difficult for the fluid to flow.
Heat capacity is the amount of heat required to raise the temperature of a substance by one degree Celsius. The kinetic theory of gases predicts that the heat capacity of a gas will be proportional to the average kinetic energy of its molecules. This is because the molecules of a gas need to be moving faster in order to have a higher temperature.
Sound waves are waves of pressure that travel through a medium. The kinetic theory of gases predicts that sound waves can travel through a gas because the molecules of a gas are constantly moving. The collisions of these molecules with each other can transfer energy from one molecule to another, causing the sound wave to travel through the gas.
Brownian motion is the random movement of particles suspended in a fluid. The kinetic theory of gases predicts that Brownian motion will occur because the molecules of a fluid are constantly moving. These collisions cause the particles to move randomly.

The kinetic theory of gases is a powerful tool that can be used to explain a wide range of phenomena. It is a fundamental theory in physics and chemistry, and it has many applications in engineering and other fields.

What is the kinetic theory of gases?

The kinetic theory of gases is a model of a gas that explains many of its properties. It assumes that the gas is made up of tiny particles called molecules that are in constant motion. The molecules are constantly colliding with each other and with the walls of the container. The collisions with the walls of the container are what cause the pressure of the gas.

What are the assumptions of the kinetic theory of gases?

The assumptions of the kinetic theory of gases are as follows:

The molecules of a gas are very small compared to the distances between them.
The molecules of a gas are in constant motion.
The molecules of a gas are not attracted to each other or to the walls of the container.
The collisions between molecules are elastic, meaning that there is no loss of energy in the collisions.

What are the properties of gases that can be explained by the kinetic theory of gases?

The properties of gases that can be explained by the kinetic theory of gases are as follows:

Pressure: The pressure of a gas is caused by the collisions of the molecules with the walls of the container. The more molecules there are in a given volume, the more collisions there will be, and the higher the pressure will be.
Temperature: The temperature of a gas is a measure of the average kinetic energy of the molecules. The higher the temperature, the faster the molecules are moving, and the higher the average kinetic energy.
Volume: The volume of a gas is determined by the amount of space that the molecules take up. The more molecules there are, the more space they will take up.
Density: The density of a gas is determined by the mass of the molecules and the volume that they take up. The more mass the molecules have, or the less space they take up, the higher the density will be.

What are some applications of the kinetic theory of gases?

Some applications of the kinetic theory of gases are as follows:

Refrigerators: Refrigerators work by using the kinetic theory of gases. The refrigerant gas is compressed, which raises its temperature. The hot gas is then passed through a coil that is located outside of the refrigerator. The heat from the gas is transferred to the outside air, and the gas cools down. The cool gas is then passed through a coil that is located inside of the refrigerator. The heat from the inside of the refrigerator is transferred to the gas, and the gas warms up. The warm gas is then compressed again, and the cycle repeats.
Air conditioners: Air conditioners work in a similar way to refrigerators. The refrigerant gas is compressed, which raises its temperature. The hot gas is then passed through a coil that is located outside of the air conditioner. The heat from the gas is transferred to the outside air, and the gas cools down. The cool gas is then passed through a coil that is located inside of the air conditioner. The heat from the inside of the air conditioner is transferred to the gas, and the gas warms up. The warm gas is then compressed again, and the cycle repeats.
Engines: Engines work by using the kinetic theory of gases. The fuel-air mixture is compressed, which raises its temperature. The hot gas is then ignited, which causes it to expand rapidly. The expansion of the gas pushes on the piston, which turns the crankshaft. The crankshaft turns the wheels, which makes the car move.

What are some limitations of the kinetic theory of gases?

Some limitations of the kinetic theory of gases are as follows:

The molecules of a gas are not perfectly elastic. There is some loss of energy in the collisions between molecules.
The molecules of a gas are attracted to each other. This attraction is very weak, but it can have an effect on the properties of the gas.
The molecules of a gas are not always in constant motion. They can sometimes be in a state of equilibrium.

What are some future directions for research in the kinetic theory of gases?

Some future directions for research in the kinetic theory of gases are as follows:

Developing more accurate models of the collisions between molecules.
Studying the effects of intermolecular forces on the properties of gases.
Investigating the behavior of gases in extreme conditions, such as very high or low temperatures or very high pressures.

Sure, here are some MCQs without mentioning the topic of kinetic theory of gases:

Which of the following is not a property of gases?
(A) Gases have low density.
(B) Gases have high compressibility.
(C) Gases have high thermal conductivity.
(D) Gases have low viscosity.
Which of the following is the correct equation of state for an ideal gas?
(A) PV = nRT
(B) PV = nRT/P
(C) PV = nRT/V
(D) PV = nRT/T
The average kinetic energy of a gas molecule is proportional to
(A) the square root of the temperature.
(B) the temperature.
(C) the square of the temperature.
(D) the cube of the temperature.
The root mean square speed of a gas molecule is proportional to
(A) the square root of the temperature.
(B) the temperature.
(C) the square of the temperature.
(D) the cube of the temperature.
The pressure of a gas is due to
(A) the collisions of gas molecules with the walls of the container.
(B) the attractive forces between gas molecules.
(C) the repulsive forces between gas molecules.
(D) the kinetic energy of gas molecules.
The volume of a gas is due to
(A) the collisions of gas molecules with the walls of the container.
(B) the attractive forces between gas molecules.
(C) the repulsive forces between gas molecules.
(D) the kinetic energy of gas molecules.
The temperature of a gas is a measure of
(A) the average kinetic energy of gas molecules.
(B) the average speed of gas molecules.
(C) the average momentum of gas molecules.
(D) the average energy of gas molecules.
The number of moles of a gas is a measure of
(A) the amount of gas.
(B) the mass of gas.
(C) the volume of gas.
(D) the density of gas.
The ideal gas law is a mathematical relationship between
(A) pressure, volume, and temperature.
(B) pressure, volume, and number of moles.
(C) pressure, temperature, and number of moles.
(D) volume, temperature, and number of moles.
The kinetic theory of gases is a theory that explains the behavior of gases in terms of
(A) the motion of gas molecules.
(B) the collisions of gas molecules with each other and with the walls of the container.
(C) the energy of gas molecules.
(D) all of the above.