# Fluctuation in particle numbers for an ideal gas

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Using the expression for the ideal gas chemical potential, obtain Eq.(84). Please refer to the attached file to know what Eq.(84) is.

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##### Solution Summary

We explain the relevant thermodynamics of the chemical potential and we derive the expression for the chemical potential of an ideal gas from first principles using statistical mechanics. We then solve the problem.

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You need to compute the chemical potential of an ideal gas (or use the formula from your book, but then make sure you understand how it is derived) and then, after going through the derivation of the fluctuation in N given in your attached file, you can plug that into Eq. 83 to obtain Eq. 84. Before we start, let us see if we can guess how Eq. 84 will arise without going through all of the details. You may know that the chemical potential mu for an ideal gas is a logarithmic function of the density of the gas. But this means that N will be an exponential function of mu, so in Eq. ...

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