Maxwell's Speed Distribution - Kinetic Theory of Gases (Chapter 25): IIT JEE Class 11 Physics
Here we describe the topic as, Maxwell’s speed distribution from the kinetic theory of gases of IIT JEE class 11 physics.
Kinetic theory of gases, a theory based on a simplified molecular or particle description of a gas, from which many gross properties of the gas can be derived.
The British scientist James Clerk Maxwell and the Austrian physicist Ludwig Boltzmann, in the 19th century, led in establishing the theory, which became one of the most important concepts in modern science.
The simplest kinetic model is based on the assumptions that:
(1) The gas is composed of a large number of identical molecules moving in random directions, separated by distances that are large compared with their size.
(2) The molecules undergo perfectly elastic collisions (no energy loss) with each other and with the walls of the container, but otherwise, do not interact.
(3) The transfer of kinetic energy between molecules is heat. These simplifying assumptions bring the characteristics of gases within the range of mathematical treatment.
Maxwell-Boltzmann distribution:
The kinetic molecular theory is used to determine the motion of a molecule of an ideal gas under a certain set of conditions.
However, when looking at a mole of an ideal gas, it is impossible to measure the velocity of each molecule at every instant of time.
Therefore, the Maxwell-Boltzmann distribution is used to determine how many molecules are moving between velocities v and v + DV.
Assuming that the one-dimensional distributions are independent of one another, that the velocity in the y and z directions does not affect the x velocity.
The Maxwell-Boltzmann distribution can be used to determine the distribution of the kinetic energy of for a set of molecules.
The distribution of the kinetic energy is identical to the distribution of the speeds for a certain gas at any temperature.
Three-speed expressions can be derived from the Maxwell-Boltzmann distribution:
The most probable speed, the average speed, and the root-mean-square speed.
All the above-mentioned topics are described in an interactive and efficient manner so that the students could easily understand them.
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