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[2003SM/LNP-16] Lecture-16--Open Systems —Grand Canonical EnsembleNode id: 5541page |
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22-07-07 07:07:09 |
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[2003SM/LNP-15] Lecture-15--Quantum Effects in Statistical MechanicsNode id: 5540pageQuantum effects in macroscopic systems appear in two ways. The first the energy levels are quantized. The quantization of energy levels does not need any modification in the framework. Secondly identical nature of particles constituting the system. This requires a new approach to enumerating the microstates. The microstates are not labeled by coordinates and momenta as is the case in classical theory. In quantum theory the microstates are specified by giving the number of particles for different levels. |
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22-07-07 07:07:53 |
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[2003SM/LNP-14] Lecture-14--Equipartition of EnergyNode id: 5539pageIn this lecture we derive law of equipartition of energy under the assumption that the energy is quadratic function of some variable such as coordinates and momenta. The classical theory of specific heat of gases is given and the Einstein model of taking quantum corrections is briefly discussed. A comparison of the classical and quantum model with experiments is given. |
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22-07-07 07:07:20 |
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[2003SM/LNP-13] Lecture-13--The Imperfect GasNode id: 5538pageA scheme of virial expansion to derive equation of state for imperfect gases is set up. As an application the van der Waals form of the equation of state for an imperfect gas is derived. |
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22-07-07 07:07:23 |
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[2003SM/LNP-12] Lecture-12--Applications of canonical ensembleNode id: 5537pageThe canonical partition function for an ideal gas is computed and ideal gas equation is derived. A measurement of the Boltzmann constant k is discussed using effusion of gas molecules through a hole. Distribution function of molecules in presence of gravity is as function of height is derived. |
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22-07-07 07:07:20 |
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[2003SM/LNP-11] Lecture-11-- Applications of Canonical EnsembleNode id: 5536pageIn this lecture the method of canonical ensemble is applied to paramagnetism and ideal gases. For a paramagnetic substance the variation of paramagnetic susceptibility with temperature is derived. For an ideal gas Maxwell’s distribution of velocities is obtained using canonical |
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22-07-07 07:07:41 |
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[2003SM/LNP-10] Lecture-10--Internal Energy of a System in Contact with Heat ReservoirNode id: 5535pageIn this lecture we continue our discussion of canonical partition function. An expression for internal energy is obtained in terms of the partition function. The parameter β is identified with 1/kT by noting that the parameter β in the partition function depends only on the heat bath and not on the system in equilibrium with the heat bath. The partition function is used to compute the energy of an ideal gas and comparing the same with the expression given by the equipartition theorem. The expression for other thermodynamic functions, entropy, free energy, enthalpy and variance of energy are derived in terms of the canonical partition function. Comparing the average energy with its variance gives a criterion so that the average energy may approximately represent the state of the system. |
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22-07-07 07:07:18 |
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[2003SM/LNP-09] Lecture-09--Canonical EnsembleNode id: 5534pageIn this lecture canonical ensemble and canonical partition function are introduced. This topic has a central place in equilibrium statistical mechanics. This ensemble describes the microstates of a system in equilibrium with a heat bath at temperature T . The probability of a microstate having energy E is proportional to $exp(−βE)$ where $ β = kT $ and k is Boltzmann constant. |
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22-07-07 07:07:26 |
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[2003SM/LNP-08] Lecture-08--Basic assumptions of statistical mechanicsNode id: 5533pageStatistical mechanics is based on the fundamental assumption that all microstates of an isolated system are equally |
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22-07-06 07:07:13 |
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[2003SM/LNP-07] Lecture-07--Energy of Macroscopic Systems Classical and Quantum TheoriesNode id: 5532pageEnergy of Macroscopic Systems Classical and Quantum Theories |
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22-07-06 07:07:54 |
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[2003SM/LNP-06] Lecture-06--What is Thermodynamics and Statistical MechanicsNode id: 5531pageWe begin with scope of thermodynamics and emphasize wide range of its applications. Thermodynamics takes a macroscopic view of a physical system. It laws are based on experience. Statistical mechanics is a microscopic view of physical systems and is based on established laws of classical and quantum mechanics. |
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22-07-06 07:07:01 |
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[2003SM/LNP-05] Lecture-05--Gaussian DistributionNode id: 5530pageIn this lecture the Gaussian distribution its important properties are discussed. One of its important properties is that it is completely fixed by mean and standard deviation. |
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22-07-06 07:07:54 |
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[2003SM/LNP-04] Lecture-04--Binomial DistributionNode id: 5529pageIn this lecture the binomial distribution, the random walk problem and the Poisson distributions are introduced and their interconnections and important properties are discussed. |
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22-07-06 07:07:08 |
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[Arch-Courses] Resources from Proofs Archived Courses Node id: 5514page |
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22-07-04 13:07:50 |
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[1998TH/LNP-01] Lecture -1 Thermodynamics --- Overview of the CourseNode id: 5527page |
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22-07-04 13:07:27 |
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[2003SM/LNP-20] Lecture -20 -- Specific Heat of GasesNode id: 5519page |
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22-07-04 10:07:20 |
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[2003SM/LNP-23] Lecture 23 --- Ideal Bose GasNode id: 5522page |
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22-07-04 10:07:38 |
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[2003SM/LNP-22] Lecture 22 -- Perfect Fermi GasNode id: 5521page |
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22-07-04 10:07:32 |
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[2003SM/LNP-21] Lecture 21 -- Heat Capacities of SolidsNode id: 5520page |
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22-07-04 10:07:24 |
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[2003SM/LNP-19] Lecture 19 -- Degenerate and Non-degenerate GasesNode id: 5518page |
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22-07-04 10:07:14 |
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