TAILIEUCHUNG - Basic Theoretical Physics: A Concise Overview P35

Basic Theoretical Physics: A Concise Overview P35. This concise treatment embraces, in four parts, all the main aspects of theoretical physics (I . Mechanics and Basic Relativity, II. Electrodynamics and Aspects of Optics, III. Non-relativistic Quantum Mechanics, IV. Thermodynamics and Statistical Physics). It summarizes the material that every graduate student, physicist working in industry, or physics teacher should master during his or her degree course. It thus serves both as an excellent revision and preparation tool, and as a convenient reference source, covering the whole of theoretical physics. It may also be successfully employed to deepen its readers’ insight and. | 354 46 Advanced Discussion of the Second Law By transforming from an extensive expression for the work done for example SA . Hdm h . to the corresponding intensive quantity . SA SA d llmH . m HdH . one obtains instead of the Helmholtz free energy F T V mH N the Gibbs free energy Fg T V H N F T V mH T V H N N - mHH 1 2 with dFg -pdV pdN - mH dH - SdT and the corresponding relations dFg dH mH dFg dT S etc. The second law is now dFg SA SdT . The Gibbs free energy Fg T V H N and not Helmholtz free energy F T V mH N is appropriate for Hamiltonians with a Zeeman term . the Ising Hamiltonian because the magnetic field is already taken into account in the energy values. Whereas for non-magnetic systems one can show that F T V N -kBT ln Z T V N for magnetic systems Fg T V H N kB T ln Z T V H N with Z T V H N e ßE VHN .2 i On the Impossibility of Perpetual Motion of the Second Kind The following six statements can be regarded as equivalent formulations of the second law of thermodynamics 1 Similarly for magnetic systems one may also distinguish . between a Helmholtz enthalpy IHe mho tz T p mH N and a Gibbs enthalpy Icibbs T p H N . 2 Here the prime is usually omitted. On the Impossibility of Perpetual Motion of the Second Kind 355 1 It is not possible to construct an ideal heat pump in which heat can flow from a colder body to a warmer body without any work being done to accomplish this flow. This formulation is due to Robert Clausius 1857 . In other words energy will not flow spontaneously from a low temperature object to a higher temperature object. 2 An alternative statement due to William Thomson later Lord Kelvin is essentially that you cannot create an ideal heat engine which extracts heat and converts it all to useful work. Thus a perpetual motion machine of the second kind which is a hypothetical device undergoing a cyclic process that does nothing more than convert heat into mechanical or other work clearly does not exist since it would .

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