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चार महीने का बच्चा कैसे बना अरब़पति

चार महीने का बच्चा कैसे बना अरब़पति? जन्म के सिर्फ चार माह बाद यदि कोई बच्चा अरबपति बन जाए तो इसे उसकी किस्मत ही कहेंगे। भारत के एकाग्रह रोहन मूर्ति नाम के बच्चे की किस्मत कुछ इसी प्रकार चमकी है। देश की दूसरी सबसे बड़ी आइटी कम्पनी इंफोसिस के फाउंडर नारायण मूर्ति ने सोमवार अपने चार महीने के पोते एकाग्रह मूर्ति को 240 करोड़ रूपए के शेयरों की हिस्सेदारी का तोहफा देकर उसे शायद देश का सबसे कम उम्र का अरबपति बना दिया है। BSE की फाइलिंग के अनुसार इंफोसिस में अब एकाग्रह रोहन की 15 लाख शेयरों की हिस्सेदारी हो गई है। इसका मतलब अब एकाग्रह रोहन इंफोसिस का 0.04% का हिस्सेदार है। शेयरों के स्थानान्तरण के बाद नारायण मूर्ति के पास कम्पनी के कुल शेयरों का 0.36% हिस्सा बचा है। जिस समय नारायण मूर्ति द्वारा अपने पोते को शेयर देने की खबर बाई उस समय इंफोसिस के शेयरों में गिरावट देखने को मिल रही थी। एकाग्रह रोहन, नारायण मूर्ति तथा सुधा मूर्ति के बेट रोहन मूर्ति और उनकी पत्नि अर्पणा कृष्णन का बेटा है। आपको यह पता होगा कि नोरायण मूर्ति ने अपनी पत्नि सुधा मूर्ति से 10 हजार रूपए उधार लेकर 1981 में इंफोसिस क
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Grand canonical ensemble | Statistical mechanics | L-9

Grand canonical ensemble

Grand canonical ensemble

  • Microcanonical ensemble is a collection of independent assemblies in which energy (E), volume (V), and number of particles (N) remain constant.
  • Canonical ensemble is a collection of independent assemblies in which temperature (T), volume (V), and number of particles (N) remain constant.
  • It mean a microcanonical ensemble ⟶ Canonical ensemble, if we ignore the condition E = constant.
  • Therefore the energy exchange takes place in this ensemble.
  • Actually in chemical process, the number of particles N varies and it is very difficult to keep the number of particles constant in various phenomenon like radioactive decay process.
  • Thus grand canonical ensemble is an ensemble in which the exchange of energy as well as the number of particles takes place with the heat reservoir.
  • The grand canonical ensemble is a collection of essentially independent assemblies having the same temperature T, volume V, and a chemical potential µ.

  • Thus grand canonical ensemble is a situation in which we know both the average energy and the average number of particles in assembly, otherwise we don’t know the state of the system.
  • The density function in Гspace for grand canonical ensemble = ρ (p, q, N)
  • Here p is momenta, q is coordinate and N is number of particles.
  • To find ρ (p, q, N), we consider the canonical ensemble for a system with particles N, volume V and temperature T.
  • Here we can not take exactly V = constant, so our focus is on a small sub-volume V1 of the system.
  • Let N1 particles be in volume V1, and N2 particles be in volume V2
  • N1 + N2 = N   ⇒   N2 = N - N1    and    V1 + V2 = V   ⇒   V2 = V - V1
  • Also we assume that V2 >> V1 and N2 >> N1
  • If H1 and H2 be the Hamiltonian of the system then
  • The total Hamiltonian of the composite system
  • H (p, q, N) = H1 (p1, q1, N1) + H2 (p2, q2, N2)

Partition function of the system

  • The partition function of the total system
  • Here A (N, V, T) is the Helmholtz free energy.
  • In the last term we consider that the system under consideration to become infinite in size or 0 ≤ N < ∞.
  • For thermodynamic function, we define grand partition function

Average number of particle

  • By ensemble average, the average number of particles

Internal energy

To know more about this topic please click the link https://youtu.be/1dpbmImt8UE
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