Use a Lagrange multiplier technique to show that for a system characterized by the following modified Maxwell-Boltzmann

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Use a Lagrange multiplier technique to show that for a system characterized by the following modified Maxwell-Boltzmann distribution function

where Tis constant, the entropy S, defined by

is a maximum when the density n is constant, independent of r. Consider that the system has a total of N particles in a fixed volume V at a temperature T.

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