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Kinetic Energy and Molecular Speed of Gas - JEE Important Topic

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Last updated date: 23rd Apr 2024
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A Brief Introduction to Kinetic Theory of Gases

Kinetic theory of gases is a branch of Physics that studies the behaviour of gases. It is one of the most important theories in Modern Physics and has helped to develop our understanding of gas dynamics, thermodynamics, and chemical reactions. The kinetic theory of gases explains the random movement of molecules in a gas. The kinetic theory of gases depicts how gases act by accepting that the gas is composed of rapidly moving particles or atoms. In this article, we will introduce you to the basics of the kinetic theory of gases and discuss some key applications.


What Is Kinetic Energy?

The kinetic energy of an object is the measure of the work an object can do by virtue of its motion. In simple words, kinetic energy is the energy an object has because of its motion. Kinetic energy is proportional to the speed of molecules. As the speed of the colliding molecules increases, the total kinetic energy of all the gas molecules also increases. In the kinetic theory of gases, kinetic energy is the energy that a gas molecule has due to its motion. It is related to the temperature of the gas by the equation:


\[\mathbf{KE}=\frac{3}{2}\mathbf{kT}\]

where

KE is the kinetic energy,

k is Boltzmann's constant, and

T is the absolute temperature.


The average kinetic energy of a gas molecule can be thought of as its "energy of motion". At higher temperatures, molecules move faster and have more kinetic energy. At lower temperatures, they move slower and have less kinetic energy. The average kinetic energy of a molecule depends on its mass: heavier molecules have less KE per unit mass than lighter molecules.


Postulates of Kinetic Theory of Gases

  • Gases are composed of tiny particles (atoms or molecules) in constant, random motion.

  • The collisions between these particles are elastic (i.e., they conserve energy).

  • The total kinetic energy of the gas is proportional to its absolute temperature.

  • The pressure exerted by a gas is due to the collisions of its particles with the walls of the container.


Molecular Speeds

The speed related to a gathering of atoms is normal. In an ideal gas, the particles don’t interface with one another.


There are 3 types of molecular speeds, they are listed below:

  • RMS velocity

  • Average velocity

  • Most probable velocity


R.M.S Velocity: The root mean square speed of gas molecules is a measure of the average speed of the molecules in a gas. It is defined as the square root of the mean of the squares of the speeds of the molecules. The root mean square speed is a useful quantity because it allows us to predict the behaviour of gases under various conditions. For example, it can be used to calculate the pressure exerted by a gas on its container (see Ideal Gas Law).

\[{{\mathbf{V}}_{rms}}=\text{ }\sqrt{\frac{3RT}{M}}\text{ }\mathbf{or}\text{ }\sqrt{\frac{3P}{d}}\]

Average Velocity: Average speed is the arithmetic mean of the speeds of the molecules.


The average velocity of gas molecules is the speed at which they move around in a space. This can be affected by various factors such as temperature, pressure, and the type of gas. The average velocity is important because it determines how fast a gas will expand or contract in response to changes in these conditions. It also affects the rate at which chemical reactions occur.

\[{{\mathbf{V}}_{avg}}=\text{ }\sqrt{\frac{8RT}{\pi M}}\text{ }\mathbf{or}\text{ }\sqrt{\frac{8P}{\pi d}}\]

The Most Probable Velocity: The speed that corresponds to the peak of the curve is called the most probable velocity.

\[{{\mathbf{V}}_{mp}}=\text{ }\sqrt{\frac{2RT}{M}}\text{ }\mathbf{or}\text{ }\sqrt{\frac{2P}{d}}\]


Ratio of \[{{V}_{mp}}:\text{ }{{V}_{avg}}:\text{ }{{V}_{rms}}=\text{ }1:1.128:1.224\]


Summary

In this article, we discussed kinetic energy and molecular speed. Let us summarise the whole article with key points. The kinetic theory of gases is one of the most important theories in modern Physics. It has helped to develop our understanding of gas dynamics, thermodynamics, and chemical reactions. The average kinetic energy of a gas molecule can be thought of as its "energy of motion". The average velocity of gas molecules is the speed at which they move around in a space. There are three types of molecular speeds, they are RMS velocity, Average velocity, and Most probable velocity. The average velocity determines how fast a gas will expand or contract in response to changes in these conditions.

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FAQs on Kinetic Energy and Molecular Speed of Gas - JEE Important Topic

1. Why do smaller gas particles move faster?

Smaller gas particles move faster because of the molecular motion of molecules. They possess kinetic energy at all temperatures above absolute zero. Temperature is directly proportional to the average kinetic energy of gas molecules. Also, lighter gases will have higher velocities than heavier gases, at the same temperature and pressure.

2. What is kinetic energy, and how does it work?

Kinetic energy is the energy created by an object as a result of its motion. When an object is set to accelerate, it is imperative that specific forces be applied. Work is required to apply force, and once the work is completed, the energy is transmitted to the object, causing it to move at a constant velocity. The energy transported is known as kinetic energy, and it is determined by the speed and mass of the object being moved.

3. What are the limitations of the kinetic theory of gases?

The kinetic theory of gases has a number of limitations. 

  • Firstly, it assumes that the gas particles are point-like and have no size or volume. 

  • Secondly, it assumes that the particles are perfectly elastic and do not interact with each other except during collisions. 

  • Thirdly, it assumes that the collisions between particles are perfectly elastic and do not result in any energy loss.  

  • Fourthly, it only applies to ideal gases, which are hypothetical gases that do not exist in nature. 

  • Fifth, it only applies to ideal gases and does not take into account the effects of intermolecular forces. 

  • Finally, the theory is only valid at very high temperatures where the gas particles have a lot of kinetic energy. The theory does not apply to solid or liquid phases of matter.