- #1

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- Summary:
- My textbook defined chemical potential in two different ways. How can same thing have 2 definitions?

I am trying to learn statistical physics. While learning MB statistics, my textbook defined chemical potential as ##\mu = (\frac{\partial F}{\partial N})_{V,T}##. That's nice.

Later when I started on Quantum statistics, my textbook described all three distribution functions via:

##n_i = \frac{g_i}{e^{\alpha + \beta E_i} + \kappa}##

We had already found out the value of beta from MB statistics (using MB distr. function. Why would that apply here is another mystery altogether)

Then suddenly book said:

##n_i = \frac{g_i}{e^{\frac{E_i - \mu}{K_B T}} + \kappa}##

Where we define chemical potential via the relation ##\alpha = -\mu/kT## (and its exponential is called fugacity)

How and why did the book define the same thing twice!?

Later when I started on Quantum statistics, my textbook described all three distribution functions via:

##n_i = \frac{g_i}{e^{\alpha + \beta E_i} + \kappa}##

We had already found out the value of beta from MB statistics (using MB distr. function. Why would that apply here is another mystery altogether)

Then suddenly book said:

##n_i = \frac{g_i}{e^{\frac{E_i - \mu}{K_B T}} + \kappa}##

Where we define chemical potential via the relation ##\alpha = -\mu/kT## (and its exponential is called fugacity)

How and why did the book define the same thing twice!?