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What Are The Basic Postulates Of Statistical Mechanics?
Fundamental Postulates Of The Statistical Mechanics: The fundamental postulates of the statistical mechanics are:
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Assuming Maxwell-Boltzmann Distribution Of Molecular Speed, Obtain The Expression Of (i) Average Velocity (ii) r.m.s. Velocity And (iii) Most Probable Velocity.
According to Maxwell’s velocity distribution law, the number of molecules having velocity in the range and is given by, (i) Average Velocity: The average velocity is where, is the total number of molecules. by using, where, (ii) r.m.s. velocity (): The mean square velocity is, by using, Therefore, (iii) Most Probable Velocity (): The most…
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Consider A System Of ‘N’ Ideal Boltzmann Gas Of ‘N’ Molecules Of Mass ‘m’ In A Volume ‘V’. Derive The Maxwell-Boltzmann Distribution Law Of Energy Amon The Molecules. Hence Derive An Expression Of Molecular Velocity Distribution Law And Momentum Distribution Law.
Maxwell’s energy distribution law: Let us consider a system of an ideal Boltzmann gas of molecules of mass in a volume . Let us consider a continuous distribution of the molecular energies so that the energy levels are continuously distributed. The number of the molecules between the energy range and is given by, where, is…
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Write Down Maxwell’s Distribution Law And Show That It Corroborates The Equipartition Law Of Energy.
Maxwell’s distribution law: Maxwell’s distribution law is given by, where, is the number of the particles distributed in states and is the energy of each particle. is constant, is Boltzmann constant and is the absolute temperature. Corroboration of Maxwell’s distribution law with the equipartition of energy: Let us consider a continuous distribution of the molecular…
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What Do You Mean By A Classical Distribution Function? Applying The Classical Distribution Function Establish The Principle Of Equipartition of Energy.
Classical Distribution Function: The ratio of the number of particles distributed in the states to the number of states is called distribution function. It is the average number of the particles per quantum state of the system. The Classical or the Maxwell-Boltzmann distribution function is given by, where, is constant, is Boltzmann constant and is…
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Deduce Maxwell-Boltzmann Distribution Function.
Maxwell-Boltzmann Distribution Function: Let us consider a system of N distinguishable particles having total energy E which is divided into several levels. The level has states containing particles each of the energy subject to the conditions that both N and E are constants i.e. and The number of the ways in which the N particles…
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A particle moves in a plane in such a way that its distance from the origin remains constant. What is the radial component of the velocity?
We know that when a particle is moving along a curve in a plane, then the transverse component of velocity is . [To know the derivation of the radial component of velocity (CLICK HERE) ] Since the particle moves in such a way that the distance from the origin of the particle remains constant, this…
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The trajectory of a particle moving in a plane in a straight line passing through the origin. What is the transverse component of velocity?
Transverse component of velocity of a particle moving along a straight line in a plane: We know that when a particle is moving along a curve in a plane, then the transverse component of velocity is . [To know the derivation of the transverse component of velocity (CLICK HERE) ] Since, here the particle is…
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The Cartesian Co-Ordinates Of A Point Are (1, 0, 1). Find The Spherical Polar Co-Ordinates Of That Point.
Let us consider the spherical polar co-ordinate of the point are . Now given that the Cartesian co-ordinate of that point are, We know that, and, So the spherical polar co-ordinates of the given point are [ To know the relations between the cartesian co-ordinates and the spherical polar co-ordinates (CLICK HERE) ]
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The Cartesian Co-Ordinates Of A Point Are (1, 0, 0). Find The Spherical Polar Co-Ordinates Of That Point.
Let us consider the spherical polar co-ordinate of the point are . Now given that the Cartesian co-ordinate of that point are, We know that, and, So the spherical polar co-ordinates of the given point are [ To know the relations between the cartesian co-ordinates and the spherical polar co-ordinate (CLICK HERE) ]
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Calculate The Spherical Polar Co-Ordinates Of A Point Whose Cartesian Co-Ordinates Are (1, 0, √3).
Let us consider the spherical polar co-ordinate of the point are . Now given that the Cartesian co-ordinate of that point are, We know that, and, So the spherical polar co-ordinates of the given point are [ To know the relation between cartesian co-ordinates and the spherical polar co-ordinates (CLICK HERE) ]
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The motion of a particle is described by the equation, x=4sin2t, y=4cos2t and z=6t. Find the equation of velocity and acceleration of the particle.
The motion of the particle is described by the three equations, , and So the displacement of the particle can be written as, where, , and are the unit vectors in three dimensional Cartesian co-ordinate system along the X-axis, Y-axis and Z-axis respectively. Again the velocity is the time derivative of the displacement vector, so…
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