Question: Consider an ideal classical gas in equilibrium at a temperature T in the presence of a uniform gravitational field. The probability P ( z )

Consider an ideal classical gas in equilibrium at a temperature T in the presence of a uniform gravitational field. The probability P(z)dz that an atom is at a height between z and z + dz above the Earth's surface is equal to:
P left parenthesis z right parenthesis d z equals beta m g space e to the power minus beta m g z end to the power d z

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