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The average speed can be calculated by integrating the Maxwell-Boltzmann distribution
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from 0 to infinity and dividing by the total number of molecules. The result is:
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.. math:: v_{avg} = \sqrt{\frac{8RT}{\pi M}}
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The most probable speed is the speed at which the Maxwell-Boltzmann distribution
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is at its maximum. This can be found by differentiating the Maxwell-Boltzmann
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distribution with respect to :math:`v` and setting the result equal to zero. The result is:
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.. math:: v_{mp} = \sqrt{\frac{2RT}{M}}
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The root-mean-square speed is another measure of the average speed
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of the molecules in a gas. It is calculated by taking the square root
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of the average of the squares of the speeds of the molecules. The result is:
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.. math:: v_{rms} = \sqrt{\frac{3RT}{M}}
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Here we have defined functions to calculate the average and
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