JEE Main Kinetic Theory of Gases Revision Notes
JEE Main Kinetic Theory of Gases Revision Notes - PDF Download
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List of Important Subtopics in the Kinetic Theory of Gases
Subtopics |
Kinetic theory of gases and gas laws |
Speed, Pressure, and Kinetic Energy of gases |
Degree of Freedom |
Specific Heat Capacities of Gases |
Mean Free Path |
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
R or Universal Gas Constant
\[R = \frac{P_{0}V_{0}}{T_{0}}\]
Its value = 8.314 J/K-mol.
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
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.
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.
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 +.....
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
Mean Speed
\[C = \sqrt{\frac{8kT}{m \pi}}\]
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.
For a monatomic gas:
The degree of freedom, i.e., n = 3
For a diatomic gas three cases are as follows.
At very low temperature:
At 0 - 250 K, n = 3.
At medium temperature:
At 250 - 750 K, n = 5 (Translational, n = 3 and Rotational, n = 2).
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]
For monoatomic gas (n = 3): γ = 5/3 or 1.67.
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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Q1: What are the Assumptions of the Kinetic Theory of Gases?
Ans: The assumptions of the kinetic theory of gases are as follows:
A gas comprises several molecules that are perfectly elastic spheres with zero force of attraction between them.
The distance between these molecules is so small that their volume is assumed negligible as compared to the gas volume.
Q2: Two non-reacting monatomic ideal gases have their atomic masses in the ratio of 5: 3. The ratio of their partial pressures, when enclosed in a container is 3:4, then the ratio of their densities will be?
Ans: Here, M_{1}: M_{2} = 5: 3, P_{1}: P_{2} = 3:4, ρ_{1}: ρ_{2} = ?
We know that:
⍴_{1}/⍴_{2} = P_{1}/P_{2} * M_{1}/M_{2}
= ¾ * 5/3
After calculating, we get the ratio of densities of the mixture as:
⍴_{1}/⍴_{2} = 5/4 |
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