Skip to main content

भारतीय रसायन के पिता आचार्य प्रफुल्ल चंद्र रे की जयंती पर व्याख्यान का आयोजन

भारतीय रसायन के पिता आचार्य प्रफुल्ल चंद्र रे की जयंती पर व्याख्यान का आयोजन विज्ञान भारती उदयपुर इकाई एवं बीएन कॉलेज ऑफ फार्मेसी, बीएन विश्वविद्यालय के संयुक्त तत्वावधान में कार्यक्रम सम्पन्न उदयपुर, 2 अगस्त। भारतीय रसायन के पिता आचार्य प्रफुल्ल चंद्र रे की जयंती के अवसर पर विज्ञान भारती उदयपुर इकाई (चित्तौड़ प्रांत) एवं बीएन कॉलेज ऑफ फार्मेसी, बीएन विश्वविद्यालय के संयुक्त तत्वावधान में एक विशेष व्याख्यान का आयोजन किया गया। कार्यक्रम का उद्देश्य आचार्य पी.सी. रे के वैज्ञानिक योगदान एवं उनके देशभक्ति से ओतप्रोत जीवन पर प्रकाश डालना था। ज्ञातव्य है कि भारत की पहली फार्मा कंपनी आचार्य रे ने ही बंगाल केमिकल एंड फार्मास्यूटिकल्स लिमिटेड, कोलकाता में 1901 में प्रारंभ की थी। कार्यक्रम में विज्ञान भारती के उद्देश्य एवं गतिविधियों की जानकारी डॉ. अमित गुप्ता द्वारा दी गई। आचार्य पी.सी. रे के जीवन और कार्यों पर मुख्य व्याख्यान डॉ. लोकेश अग्रवाल द्वारा प्रस्तुत किया गया। उन्होंने बताया कि कैसे आचार्य रे ने विज्ञान को समाज की सेवा का माध्यम बनाया और रसायन विज्ञान में भारत को आत्मनिर्भर बनान...
Post a Comment

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
Labels:

Comments

Post a Comment

Popular posts from this blog

Calculus | Mathematics | BSc

Calculus Differential Calculus, Integral Calculus and Differential Equation Authors: Dr. Vimal Saraswat, Dr. Anil Kumar Menaria, Dr. Chandrapal Singh Chouhan ISBN : 978-93-94954-67-0 Price: Rs. 395.00  Publisher: Himanshu Publications, Hiran Magri Udaipur; Himanshu Publications Prakash House, Ansari Road, New Delhi E-mail : info@sacademy.co.in Phone:  +91 9664392614 To buy this book click on Calculus by Saraswat This book includes the following topics  Pedal Equations and Derivative of the Length of an Arc Polar co-ordinates Relation between cartesian and polar co-ordinates Angle between radius vector and tangent Angle of intersection of two polar curves Polar tangent, subtangent, normal, subnormal and their lengths Perpendicular from pole to tangent and its length Pedal equation Differential coefficient of length of the arc When the equation of curve is in cartesian form (x, y); When the equation of curve is in ...
Post a Comment
Read more

Advanced Calculus | Mathematics | BSc

Advanced Calculus Advanced Differential Calculus, Integral Calculus and Vector Calculus Authors: Dr. Vimal Saraswat, Dr. Anil Kumar Menaria ISBN : 978-81-7906-950-9 Price: Rs. 375.00 Publisher: Himanshu Publications, Hiran Magri Udaipur; Himanshu Publications Prakash House, Ansari Road, New Delhi E-mail :  info@sacademy.co.in Phone:  +91 9664392614 To buy this book click on the link Advanced Calculus by Saraswat This book includes the following topics  Continuity Introduction Limit Left and right limit To find the R.H.L. and L.H.L. of a function Existence of limit)/li> Distinction between the value and limit of a function Some theorems based on limits Methods of finding the limit of functions Some standard limits Cauchy’s definition of continuity Continuity from left and right Continuity of a function in an interval Continuity in the open interval); Continuity in the closed in...
Post a Comment
Read more

B.N.U. First Semester Physics Syllabus

B.N. UNIVERSITY, UDAIPUR B.Sc. I Semester Physics PHYS MJ 111T: MECHANICS UNIT-I Laws of motion and Frame of reference: Laws of motion, conservation of momentum and energy, Co-ordinate frames, inertial and non-inertial frame of reference, Galilean transformation and invariance, fictitious force, centrifugal force, transformation of coordinate, velocity, acceleration and displacement in a rotating frame of reference, uniformly rotating frame of reference, Coriolis force, effect of centrifugal and Coriolis force due to earth’s rotation, Foucault’s pendulum. UNIT-II Gravitational Field and Potential: Newton’s universal law of gravitation, gravitational field intensity, gravitational potential due to spherical shell and solid sphere, gravitational potential energy, Laplace and Poisson’s equations, Gauss’s law, gravitational self-energy of a uniform sphere. Dynamics of System of Particles: Centre of mass, calculation of centre of mass of regular rigid bodies ...
Post a Comment
Read more