I understand that the Boltzmann constant is used as a bridge between the macrosc

Question

I understand that the Boltzmann constant is used as a bridge between the macroscopic and microscopic aspects of entropy, since a thermodynamic system can be described a summation of all the particles that make up the system, but I don't understand how to describe this quantitatively. How do I relate the macroscopic entropy as described by Boltzmann S = k * ln(w).

The hint I was left with by my professor is : "Observe the
derivation of the equation of state for a dilute gas, prove that with this choice the thermodynamic
and empirical temperatures are the same"

Explanation / Answer

Boltzmann constant k has an empirical relation with universal gas constant. k=R/N N=avogadro's number so k is used for microscopic entities

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