CBSE Class 11th Kinetic Theory

CBSE Class 11th Kinetic Theory
Boltzman, Maxwell, and others established the kinetic theory in the nineteenth century. Gas behavior is explained by kinetic theory, which is predicated on the notion that gases are made up of fast-moving atoms or molecules.

Ideal Gas - A perfect or ideal gas is one that strictly abides by gas laws, such as Gay Lussac's law, Boyle's law, and Charle's law.
The following qualities characterize an ideal gas:
(i) An ideal gas molecule is a point mass devoid of geometric dimensions.
(ii) The gas's molecules do not exhibit any forces of attraction or repulsion.

Kinetic Theory and Gas Pressure - A gas's pressure arises from the constant barrage of gas molecules against the container walls. The kinetic theory states that the pressure P that an ideal gas exerts is given by

Boyle’s Law - 
This law states that, under constant gas temperature conditions, the volume (V) of a fixed mass of a gas is inversely proportional to the gas's pressure (P).

Charle’s Law - 
This equation states that, under the assumption that the gas's pressure stays constant, the volume (V) of a given mass of the gas is precisely proportional to its temperature.

Gay Lussac’s Law (or Pressure Law) -
 According to this law, the pressure P of a given mass of a gas is directly proportional to its absolute temperature T, provided the volume V of the gas remains constant.

Equation of State of an Ideal Gas - 
An equation of state describes the relationship between a gas's pressure (P), volume (V), and absolute temperature (T). An ideal gas's equation of state is PV = nRT, where n is the contained gas's moles and R is the molar gas constant, which has the same value for all gases: R = 8.315 JK-1 mob-1.

Avagadro’s Law - 
Equal volumes of all gases under S.T.P. contain the same number of molecules, equaling 6.023 x 1023.

Graham’s Law of Diffusion of Gases - 
It states that rate of diffusion of a gas is inversely proportional to the square root of the density of the gas.

Hence, denser the gas, the slower is the rate of diffusion.

Dalton’s Law of Partial Pressures -
This law states that the total of the separate pressures of a mixture of non-interacting gases equals the resulting pressure that the mixture exerts.
P = P1 + P2 + ————-Pn, for example. The arithmetic mean of the gas molecules' speeds is what is known as the mean (or average) speed of the molecules in a gas.

Kinetic Interpretation of Temperature - 
The absolute temperature (T) of a gas determines the total average kinetic energy of all of its molecules. As a result, the average kinetic energy, or IT, of a gas's molecules is determined by its temperature.
U =  3/2 RT.
This interpretation of temperature states that when T = 0, the average kinetic energy U is zero, meaning that at absolute zero, molecular motion completely stops.

Degrees of Freedom - 
The total number of independent co-ordinates required to specify the position of a molecule or the number of independent modes of motion possible with any molecule is called degree of freedom.
Mono-, di-, and polyatomic (N) molecules have, 3,5 or (3 N-K) number of degrees of freedom, where K is the number of constraints [restrictions associated with the structure].

Law of Equipartition of Energy:
The energy of a dynamic system in thermal equilibrium is distributed evenly among its degrees of freedom, and the energy of each degree of freedom per molecule is equal to 1/2 kT, where k is the Boltzmann constant.

Mean Free Path - 
The mean free path of a molecule in a gas is the average distance travelled by the molecule between two successive collisions.
(i) A greater mean free path results from fewer molecules per unit volume of the gas.
(ii) The mean free path is larger, the smaller the diameter.
(iii) A bigger mean free path corresponds to a smaller density. When vacuum is present, ρ = 0, λ —>∞
(iv) A gas's mean free path increases with decreasing gas pressure.
(v) A gas's mean free path increases with temperature.

FAQ-  

Q.1 What is kinetic theory in physics?
Ans. Kinetic theory is a fundamental concept in physics that describes the behavior of gases by considering them as a collection of particles in constant random motion. It provides insights into the relationships between temperature, pressure, volume, and the motion of gas particles.
Q.2 What are the key principles of kinetic theory?
Ans. The key principles of Kinetic Theory include the assumption that gases consist of particles (atoms or molecules) in constant random motion, collisions between particles and container walls lead to pressure, and the average kinetic energy of gas particles is directly proportional to temperature.
Q.3 How does kinetic theory explain the behavior of gases?
Ans. Kinetic Theory explains various macroscopic properties of gases, such as pressure, temperature, and volume, in terms of the microscopic behavior of gas particles. It describes how the kinetic energy of gas particles and their collisions with the walls of the container result in observable properties.
Q.4 What is the relationship between temperature and kinetic energy according to kinetic theory?
Ans. According to kinetic theory, temperature is directly proportional to the average kinetic energy of gas particles. As temperature increases, the average speed of gas particles increases, leading to higher kinetic energy.
Q.5 What is the ideal gas law, and how is it derived from kinetic theory?
Ans. The Ideal Gas Law, PV = nRT, relates the pressure (P), volume (V), temperature (T), and the number of moles of gas (n) with the gas constant (R). It is derived from Kinetic Theory by considering the relationship between the average kinetic energy of gas particles and pressure, volume, and temperature.