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Molecular Speed Distribution
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Average Speed ($\boldsymbol{\bar{v}}$)
The average speed is the arithmetic mean of all molecular speeds, calculated by integrating $v f(v)$ over all possible speeds:
$$\bar{v} = \int0^\infty v f(v) dv = \sqrt{\frac{8kB T}{\pi m}}$$ -
Root Mean Square Speed
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The root-mean-square speed ($v_{rms}$) is a statistical measure used in physics and chemistry to describe the characteristic speed of particles (such as atoms or molecules) within a gas or liquid at a specific temperature. It is defined as the square root of the arithmetic mean of the squares of the speeds of the particles in the system. Unlike the most probable speed or …