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Maxwell-Boltzmann distribution
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Describe the Maxwell-Boltzmann energy distribution curve.
Draw and explain qualitatively Maxwell-Boltzmann energy distribution curves for
different temperatures.
Recall that temperature is a measure of the average kinetic energy of the molecules in a
gas. (Statement in Kinetic Molecular Theory).
(KE)avg = 3/2 RT
Were R is the ideal gas constant and T is temperature in Kelvin
Boltzmann wanted to use statistics to explain macroscopic observations. Thus he came
up with a distribution function to describe the range of energies of molecules at a given
temperature.
Many scientists did not believe in his work and publicly stated that he was wrong. Some
did not believe that you could use mathematics to describe the motion of particles that
would ultimately lead to a prediction of macroscopic properties. Unfortunately he
committed suicide before discoveries relating to quantum mechanics “proved” his
theories correct.
Below is a picture of a Maxwell-Boltzmann distribution for a gas at various temperatures
 The graph shows the probability that a particular molecule has a given speed
(and thus kinetic energy …KE= 1/2mv2 )
 At a given temperature, molecules can have a range of speeds/kinetic energies.
 Notice that the higher the temperature, the most probable speed increases, as
expected.
 Also notice that the higher the temperature the more spread out the distribution