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महाराणा प्रताप ट्रेल सज्जनगढ़ उदयपुर

महाराणा प्रताप ट्रेल सज्जनगढ़ उदयपुर में इको ट्रेल 30 नवम्बर को राजस्थान वन विभाग उदयपुर डिविजन तथा WWF-India उदयपुर डिविजन के सानिध्य में महाराणा प्रताप ट्रेल सज्जनगढ़ उदयपुर में इको ट्रेल की गई, जिसमें WWF-India के स्टेट काॅर्डिनेटर श्रीमान अरूण सोनी तथा वन विभाग कीे ओर से डाॅ. सतीश कुमार शर्मा, सेवानिवृत्त अधिकारी मौजूद थे। मुझे भी इस इको ट्रेल में जाने का सुअवसर प्राप्त हुआ, जो गोरीला व्यू पाॅइंट से बड़ी-लेक व्यू पाॅइंट तक की गई इसमें मुझे विज्ञान की एक नई शाखा के बारे में पता चला, जिसे टट्टी विज्ञान कहा जाता है। सुनने में आपको थोड़ा अजीब लगेगा, मुझे भी सुनकर हैरानी हुई, परन्तु वास्तव में एक ऐसा भी विज्ञान है, जिसके बारे में डाॅ. सतीश शर्मा ने बड़े ही विस्तार पूर्वक बताया कि किस प्रकार वनों में जानवरों की टट्टी देखकर यह पता लगाया जा सकता है कि यहां कौनसा जानवर आया था। जानवरों की टट्टी कितनी पुरानी है, वह गीली है या सूखी है। इसी के आधार पर उस विशेष जंगल में कौन-कौनसे जानवर विचरण करते हैं, उसके बारे में वन विज्ञान के कर्मचारी पता लगा लेते हैं। जानवरों की टट्टी का विश्लेषण करके यह पता लगा...
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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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