MICROSTATE & MACROSTATE
In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations. In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density.
A macrostate is characterized by a probability distribution of possible states across a certain statistical ensemble of all microstates. This distribution describes the probability of finding the system in a certain microstate. In the thermodynamic limit, the microstates visited by a macroscopic system during its fluctuations all have the same macroscopic properties.
2 COINS-
Macrostate= { HH,HT,TT }
Microstate= {HH,HT,TH,TT }
number of microstates= (basis)^N=2^2=4
FOR N COINS,
NO. OF MACROSTATE=N+1
NO. OF MICROSTATE=2^N
For N DICE,
NO. OF MACROSTATE= 5N+1
NO. OF. MICROSTATE=6^N
ENSEMBLE-
A large number of non-interacting and independent systems together is called Ensemble. The member of ensemble is called element.
Different elements may have same macrostates but different microstates.
TYPES OF ENSEMBLE-
1. Micro-canonical Ensemble
2. Canonical ensemble
3. Grand-Canonical Ensemble
Micro-canonical Ensemble-
Microcanonical ensemble is a collection of essentially independent ensembles having the same energy, volume and number of systems. The individual ensembles are separated by rigid and well insulated walls such that the values of E,V & N are not affected by the presence of other systems.
Canonical Ensemble-
The canonical ensemble is a collection of an essentially independent ensembles having the same temperature, volume and number of identical particles. The individual ensemble is separated by rigid,impermeable but diathermic walls. Since energy can be exchanged between the ensembles, they will reach a common temperature. Hence, In canonical ensemble, system can exchange energy but not particles.
Grand-Canonical Ensemble-
The grand canonical ensemble is a collection of essentially independent ensembles having the same temperature, volume and a chemical potential. In grand canonical ensemble we have a collection of ensembles, each occupying a separate volume but an exchange energy and molecules with each other.
In this case, the individual ensembles are separated by rigid,permeable, diathermic walls. The grand canonical ensemble will correspond to a situation when we know both the average energy and the average number of particles in the ensemble.
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