Question

Are grand canonical ensemble and macrocanonical ensemble same ?

Answer 1

ensemble represents the system which has the same number of particles, volume and energy. As per the first postulate we can assume that all the microstates of this ensemble will have same probability of occurrence. Let the number of energy levels for the state of microcanonical ensemble be .So the occurrence or the probability of any microstate will be:



 

Before we derive the thermodynamics properties let us first connect entropy with the probability of occurrence. This is given via Gibb’s Entropy equation.

Gibb’s Entropy Equation  
We can write the canonical partition function without β i.e to write explicitly in terms of temperature T. Thus we have