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Diff for: physics/speeds_of_gas_molecules.py

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speeds of particles in an ideal gas.
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The distribution is given by the following equation:
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.. math:: f(v) = \left(\frac{M}{2 \pi RT}\right)^{\frac{3}{2}} \cdot 4 \pi v^2 \cdot e^{-\frac{Mv^2}{2RT}}
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.. math:: f(v) = \left(\frac{M}{2 \pi RT}\right)^{\frac{3}{2}} \cdot 4 \pi v^2
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\cdot e^{-\frac{Mv^2}{2RT}}
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where:
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* :math:`f(v)` is the fraction of molecules with a speed :math:`v`
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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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distribution with respect to :math:`v` and setting the result equal to zero.
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The result is:
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.. math:: v_{mp} = \sqrt{\frac{2RT}{M}}
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