The Kinetic Molecular Model for Gases

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Presentation transcript:

The Kinetic Molecular Model for Gases Gas consists of large number of small individual particles with negligible size Particles in constant random motion and collisions No forces exerted among each other Kinetic energy directly proportional to temperature in Kelvin

Maxwell-Boltzmann Velocity Distribution M-B Equation gives distribution of molecules in terms of: Speed/Velocity, and Energy One-dimensional Velocity Distribution in the x-direction: [ 1Du-x ]

Mcad

Maxwell-Boltzmann Distribution 3D Velocity Distribution: [ 3Du ] , Let: a = m/2kT Cartesian Coordinates:

Maxwell-Boltzmann Speed Distribution Re-shape box into sphere of same volume with radius u . V = (4/3)  u3 with u2 = ux2 + uy2 + uz2 dV = dux duy duz = 4  u2 du

3D Maxwell-Boltzmann Speed Distribution Low T High T

3D Maxwell-Boltzmann Speed Distribution Conversion of Velocity-distribution to Energy-distribution:  = ½ m u2 ; d  = mu du

Velocity Values from M-B Distribution urms = root mean square velocity uavg = average velocity ump = most probable velocity

Comparison of Velocity Values Ratio in terms of : urms uavg ump 1.73 1.60 1.41

Fraction of molecules with E > Ea : e-Ea/RT (Maxwell-Boltzmann Distribution)