JEE Main Kinetic Theory of Gases Revision Notes

Kinetic Theory of Gases JEE Revision Notes

Our faculties have prepared a brief of the Kinetic Theory of Gases JEE revision notes for your preparation. These important concepts and sub-topics are listed below.

• Kinetic Theory of Gases

The kinetic theory of gases relates the macroscopic properties of gases like temperature, and pressure to the microscopic attributes of gas molecules such as speed, and kinetic energy.

• Ideal Gas

An ideal gas is a type of gas in which the molecules are of the zero size, and there is no force of attraction between them.

• Ideal Gas Law

The relation between P, V, and T is called the ideal gas law.

PV = nRT

n = no. of moles

R = Universal Gas Constant

• Types of Gas Constants

1. R or Universal Gas Constant

\[R = \frac{P_{0}V_{0}}{T_{0}}\]

Its value = 8.314 J/K-mol.

2. R or Specific Gas Constant

\[PV = \frac{R}{M}T\]

\[\Rightarrow PV = rT\],

where, \[r = \frac{R}{M}\]

• Real Gas

The gases showing deviation from ideal gas features are real gases.

Gas Laws

1. Boyle’s Law

This law states that at a constant temperature, the volume of a given mass of the gas is inversely proportional to its pressure, i.e.,

P  ∝ 1/V ⇒ P = K/V or PV = K,

where K depends upon the nature and temperature of the gas.

2. Gay Lussac’s Law of Pressure

At constant volume, the pressure of the gas is directly proportional to its absolute temperature, i.e.,

\[\frac{P}{T} = \frac{P_{0}}{T_{0}}\]

Or, \[\frac{P - P_{0}}{P_{0}T} = \frac{1}{273}\] = γp

Here, γp = 1273is the pressure coefficient of the gas at constant volume.

3. Dalton’s Law of Partial Gases

The total pressure exerted by the gases on the walls of a container is equal to the sum of the partial pressures of the individual gases.

P = p1 + p2 + p3 +.....or

\[\frac{nRT}{V}\] =  p1 + p2 + p3 +.....

4. Graham’s Law of Diffusion

Two gases with molecules weights M1 and M2 will always have the same KE at the same temperature, then the velocity of the gas is inversely proportional to the square roots of their molecular weights. It is given as:

\[\frac{v_{1}}{v_{2}} = \sqrt{\frac{M_{2}}{M_{1}}}\]

• Speed of  a Gas

1. Mean Speed

\[C = \sqrt{\frac{8kT}{m \pi}}\]

2. RMS Speed

\[C_{RMS} = \sqrt{\frac{C_{1}^{2} + C_{2}^{2} + ... = C_{n}^{2}}{n}} = \sqrt{\frac{3kT}{m}}\]

• Pressure of a Gas

\[P = \frac{1}{3} \rho C^{2}\]

• Degree of Freedom

The degree of freedom defines the number of ways in which the configuration or position of the system may change.

1. For a monatomic gas:

The degree of freedom, i.e., n  = 3 

2. For a diatomic gas three cases are as follows. 

1. At very low temperature:

At 0 - 250 K, n = 3.

2. At medium temperature:

At 250 - 750 K, n = 5 (Translational, n = 3 and Rotational, n = 2).

3. At high temperature beyond 750 K:

n = 7

(Translational, n = 3, Rotational, n = 2, and Vibrational, n = 1).

• The relationship between specific heat capacities and the degree of freedom

γ = \[\frac{C_{p}}{C_{v}}\] = [1 + 2/n]

1. For monoatomic gas (n = 3):  γ = 5/3 or 1.67.

2. For diatomic gas:

• At medium temperature (n = 5): γ = 7/5 or 1.4.

• At high temperature (n = 7): γ = 9/7 or 1.29.

• Mean Free Path

The mean free path is the average/mean distance a particle travels to meet another particle.

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