Your IP: 38.107.179.234 United States Near: United States

Lookup IP Information

1 2 3 4 5 6 7 8 Next

Below is the list of all allocated IP address in 33.249.0.0 - 33.249.255.255 network range, sorted by latency.

Thermodynamics Branches Classical · Statistical · Chemical Equilibrium / Non-equilibrium Thermofluids Laws Zeroth · First · Second · Third Systems State: Equation of state Ideal gas · Real gas Phase of matter · Equilibrium Control volume · Instruments Processes: Isobaric · Isochoric · Isothermal Adiabatic · Isentropic · Isenthalpic Quasistatic · Polytropic Free expansion Reversibility · Irreversibility Endoreversibility Cycles: Heat engines · Heat pumps Thermal efficiency System properties Property diagrams Intensive and extensive properties State functions: Temperature / Entropy (intro.) † Pressure / Volume † Chemical potential / Particle no. † († Conjugate variables) Vapor quality Reduced properties Process functions: Work · Heat Material properties Specific heat capacity  c = T N Compressibility  β = − 1 V Thermal expansion  α = 1 V Property database Equations Carnot's theorem Clausius theorem Fundamental relation Ideal gas law Maxwell relations Table of thermodynamic equations Potentials Free energy · Free entropy Internal energy U(S,V) Enthalpy H(S,p) = U + pV Helmholtz free energy A(T,V) = U − TS Gibbs free energy G(T,p) = H − TS History and Culture Philosophy: Entropy and time · Entropy and life Brownian ratchet Maxwell's demon Heat death paradox Loschmidt's paradox Synergetics History: General · Heat · Entropy · Gas laws Perpetual motion Theories: Caloric theory · Vis viva Theory of heat Mechanical equivalent of heat Motive power Publications: "An Experimental Enquiry Concerning ... Heat" "On the Equilibrium of Heterogeneous Substances" "Reflections on the Motive Power of Fire" Timelines of: Thermodynamics · Heat engines Art: Maxwell's thermodynamic surface Education: Entropy as energy dispersal Scientists Daniel Bernoulli Sadi Carnot Benoît Paul Émile Clapeyron Rudolf Clausius Hermann von Helmholtz Julius Robert von Mayer William Rankine John Smeaton Georg Ernst Stahl Benjamin Thompson William Thomson John James Waterston v • d • e A thermodynamic free entropy is an entropic thermodynamic potential analogous to the free energy. Also known as a Massieu, Planck, or Massieu-Planck potentials (or functions), or (rarely) free information. In statistical mechanics, free entropies frequently appear as the logarithm of a partition function. In mathematics, free entropy is the generalization of entropy defined in free probability. A free entropy is generated by a Legendre transform of the entropy. The different potentials correspond to different constraints to which the system may be subjected. Contents 1 Examples 2 Dependence of the potentials on the natural variables 2.1 Entropy 2.2 Massieu potential \ Helmholtz free entropy 2.3 Planck potential \ Gibbs free entropy 3 References 4 Bibliography // Examples See also: List of thermodynamic properties The most common examples are: Name Function Alt. function Natural variables Entropy Massieu potential \ Helmholtz free entropy Planck potential \ Gibbs free entropy where S is entropy Φ is the Massieu potential[1][2] Ξ is the Planck potential[1] U is internal energy T is temperature P is pressure V is volume A is Helmholtz free energy G is Gibbs free energy Ni is number of particles (or number of moles) composing the i-th chemical component μi is the chemical potential of the i-th chemical component s is the total number of components i is the ith components. Note that the use of the terms "Massieu" and "Planck" for explicit Massieu-Planck potentials are somewhat obscure and ambiguous. In particular "Planck potential" has alternative meanings. The most standard notation for an entropic potential is ψ, used by both Planck and Schrödinger. (Note that Gibbs used ψ to denote the free energy.) Free entropies where invented by French engineer Francois Massieu in 1869, and actually predate Gibb's free energy (1875). Dependence of the potentials on the natural variables Entropy S = S(U,V,{Ni}) By the definition of a total differential, . From the equations of state, . The differentials in the above equation are all of extensive variables, so they may be integrated to yield . Massieu potential \ Helmholtz free entropy Starting over at the definition of Φ and taking the total differential, we have via a Legendre transform (and the chain rule) , , . The above differentials are not all of extensive variables, so the equation may not be directly integrated. From dΦ we see that . If reciprocal variables are not desired,[3]:222 , , , , Φ = Φ(T,V,{Ni}). Planck potential \ Gibbs free entropy Starting over at the definition of Ξ and taking the total differential, we have via a Legendre transform (and the chain rule) . The above differentials are not all of extensive variables, so the equation may not be directly integrated. From dΞ we see that . If reciprocal variables are not desired,[3]:222 , , , , Ξ = Ξ(T,P,{Ni}). References ^ a b Antoni Planes; Eduard Vives (2000-10-24). "Entropic variables and Massieu-Planck functions". Entropic Formulation of Statistical Mechanics. Universitat de Barcelona. http://www.ecm.ub.es/condensed/eduard/papers/massieu/node2.html. Retrieved 2007-09-18.  ^ T. Wada; A.M. Scarfone (12 2004). "Connections between Tsallis’ formalisms employing the standard linear average energy and ones employing the normalized q-average energy". Physics Letters, Section A: General, Atomic and Solid State Physics 335 (5-6): 351–362. doi:10.1016/j.physleta.2004.12.054. http://arxiv.org/abs/cond-mat/0410527v1. Retrieved 2007-09-18.  ^ a b The Collected Papers of Peter J. W. Debye. New York, New York: Interscience Publishers, Inc.. 1954.  Bibliography Massieu, M.F. (1869). Compt. Rend.. 69. pp. 1057.  Callen, Herbert B. (1985). Thermodynamics and an Introduction to Themostatistics (2nd ed.). New York: John Wiley & Sons. ISBN 0-471-86256-8.