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National Bird Day: Why Birds Matter to Us

National Bird Day is celebrated every year on 5 January . This day is observed to spread awareness about birds, their importance in nature, and the need to protect them. Birds are beautiful living beings and play a very important role in keeping our environment healthy. Origin of National Bird Day National Bird Day was first celebrated in the year 2002 . It was started by bird lovers and environmental groups to protect birds from dangers like deforestation, pollution, and illegal hunting. The main aim of this day is to teach people, especially students, why birds are important and how we can help save them. Why Is National Bird Day Celebrated Every Year? National Bird Day is celebrated every year because many bird species are disappearing due to human activities. Cutting trees, using plastic, pollution, and climate change are harming birds and their homes. This day reminds us that: Birds need protection Nature should be respected Everyone has a responsibil...
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Postulates of classical statistical mechanics | Statistical mechanics

Postulates of classical statistical mechanics

  • It is based on the following postulates

Postulates of equal a priori probability

  • According to this postulate the probability of finding the phase point for given system in any region of the Γ-space is identical with that for any other region of equal extension or volume.
  • Or For a system in equilibrium, all accessible microstates corresponding to a given macro-state are equally probable.
  • Thus in thermodynamic equilibrium the system under consideration is a member of an ensemble (micro-canonical ensemble) with a density function ρ (p, q) and the value of density function is given according to the following rule.
  • If E < H (p, q) < E + ΔE, ρ (p, q) = constant, otherwise ρ (p, q) = 0
  • Thus all members of the ensemble have the same number of particles N and same volume V.
  • Let f (p, q) represents any measurable property of the system.
  • If the postulate of equal a priori probability is useful, then the average value of f (p, q) from different methods have the same results.

(i) Most probable value of f (p, q)

  • It is that value of f (p, q) which is possessed by the largest number of systems in the ensemble.

(ii) Ensemble average of f (p, q)

  • The ensemble average of f (p, q) i.e, < f > is given by

  • Both the values of f (p, q) i.e., the most probable value and the ensemble average are nearly equal, if the mean square fluctuation (MSF) is small i.e.,

                 
  • In all physical cases, MSF is of the order of 1/N
  • Since N → ∞ and therefore MSF << 1
  • Thus the most probable value of f (p, q) and ensemble average of f (p, q) both have identical values.


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