A Mnemonic Scheme for Thermodynamics

MRS Bulletin ◽  
2009 ◽  
Vol 34 (2) ◽  
pp. 92-94 ◽  
Author(s):  
J.-C. Zhao
Keyword(s):  
Free Energy ◽  
Internal Energy ◽  
Gibbs Free Energy ◽  
Maxwell Equations ◽  
Helmholtz Free Energy ◽  
State Variables ◽  
Max Born ◽  
Thermodynamic Potentials ◽  
Classical Thermodynamics ◽  
Thermodynamic Equations

AbstractA mnemonic scheme is presented to help recall the equations in classical thermodynamics that connect the four state variables (temperature, pressure, volume, and entropy) to the four thermodynamic potentials (internal energy, Helmholtz free energy, enthalpy, and Gibbs free energy). Max Born created a square to help recall the thermodynamic equations. The new scheme here separates the Max Born square into two squares, resulting in easier recalling of several sets of equations, including the Maxwell equations, without complicated rules to remember the positive or negative signs.

scholarly journals Fishing with Scissors: A Mnemonic for Thermodynamic Formula

2021 ◽  
Vol 37 (3) ◽  
pp. 700-703
Author(s):  
Gami Girishkumar Bhagavanbhai ◽  
Juan J. Bravo-Suárez ◽  
Rawesh Kumar
Keyword(s):  
Free Energy ◽  
Thermodynamic Potential ◽  
Helmholtz Free Energy ◽  
Large Range ◽  
State Variables ◽  
Quick Method ◽  
Practical Applications ◽  
Simple Set ◽  
Thermodynamic Potentials ◽  
Thermodynamic Equations

Most of the branches of engineering and basic science require,to a different extent,the use of basic thermodynamic formulas relating state variables (temperature, T; pressure, P; volume, V; entropy, S) and thermodynamic potentials (internal energy, U; Helmholtz free energy, A; enthalpy, H; Gibbs free energy, G). The different interrelations among variables, their constrains, and dependencies make them particularly difficult to remember and understand. For students learning and for chemists and engineers needing to rapidly recall these thermodynamic relationships for problem solving and practical applications, a quick method to easily remember them would be most welcome. Herein, Fishing with scissors mnemonic is presented. The mnemonic is seen as Sun with rays. Thermodynamic potential terms (A, G, H, U) as alphabetic doubles are aligned in sun rays regions where as state variables (T, P, S, V) are at sun body. Following a simple set of rules in this mnemonic, a large range of thermodynamic equations can be easily recalled without direction or sign difficulties present in previously reported methods.

Thermodynamic Potentials

2019 ◽  
pp. 148-158
Author(s):  
Robert H. Swendsen
Keyword(s):  
Free Energy ◽  
Problem Solving ◽  
Gibbs Free Energy ◽  
Helmholtz Free Energy ◽  
Independent Predictor ◽  
Predictor Variable ◽  
Fundamental Relation ◽  
Thermodynamic Potentials ◽  
Negative Temperatures ◽  
Legendre Transforms

Thermodynamics specifies the relation between an independent, predictor variable, and what is predicted. It is often the case that changing the variables regarded as independent can greatly simplify problem solving. The chapter shows how using an intensive variable (like temperature or pressure) as the predictor loses information that can be retained if it is expressed by a different function. It shows the importance of Legendre transforms, which contain the same information about the system as is available by using extensive variables. Legendre transforms exploiting the fundamental relation are shown to yield the Helmholtz free energy, the enthalpy, and the Gibbs free energy. Massieu functions are introduced as an alternative that is particularly important for models exhibiting negative temperatures.

Free energy

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Helmholtz Free Energy ◽  
Chemical Potential ◽  
Free Energies ◽  
Central Concept ◽  
Mathematical Properties ◽  
Closed Systems ◽  
Coupled Reactions ◽  
Enthalpy And Entropy

A critical chapter, explaining how the principles of thermodynamics can be applied to real systems. The central concept is the Gibbs free energy, which is explored in depth, with many examples. Specific topics addressed are: Spontaneous changes in closed systems. Definitions and mathematical properties of Gibbs free energy and Helmholtz free energy. Enthalpy- and entropy-driven reactions. Maximum available work. Coupled reactions, and how to make non-spontaneous changes happen, with examples such as tidying a room, life, and global warming. Standard Gibbs free energies. Mixtures, partial molar quantities and the chemical potential.

Theoretical study of thermodynamic properties for SmAlO3 under the effects of pressure and temperature

2018 ◽  
Vol 32 (23) ◽  
pp. 1850247 ◽  
Author(s):  
Ghulam Mustafa ◽  
Ahmad Afaq ◽  
Najm Ul Aarifeen ◽  
Muhammad Asif ◽  
Jamil Ahmad ◽  
...  
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Bulk Modulus ◽  
Internal Energy ◽  
Debye Temperature ◽  
Density Functional ◽  
Helmholtz Free Energy ◽  
Coefficient Of Thermal Expansion ◽  
Temperature Limit ◽  
Debye Model

In the present paper, we have investigated SmAlO3 for their thermodynamic properties under effect of pressure and temperature by employing density functional theory (DFT) and quasi-harmonic Debye model. The various thermodynamic properties like Bulk Modulus, entropy, internal energy, Helmholtz free energy, Debye temperature, coefficient of thermal expansion, Grüneisen parameter and heat capacities of the ternary alloy are calculated. We found that Bulk Modulus, Debye temperature and Helmholtz free energy have decreasing trend with rise of temperature while their values have increasing behavior with rise of pressure. The internal energy of the system almost remains same with variation in pressure but temperature effectively increasing it. Our results are in good agreement with available data at low-temperature limit.

Chemical Potential

1993 ◽  
Author(s):  
Brian Bayly
Keyword(s):  
Free Energy ◽  
Total Energy ◽  
Internal Energy ◽  
Gibbs Free Energy ◽  
Chemical Potential ◽  
Extensive Literature ◽  
External Energy ◽  
Free Standing ◽  
Energy Bound ◽  
The Masses

The purpose of the first chapter was to give an overview of the book’s contents: the topics covered, results gained, limitations, and so on. The next seven chapters, starting with this one, give the groundwork on which the main conclusions are based. The intention is to assemble the needed ideas, taking advantage of the fact that an extensive literature exists in which the ideas are established, discussed, restricted, etc. What follows is thus an extract of selected essentials from other documents, rather than being a free-standing and self-contained development of the ideas. The reader is asked to relate the ideas as summarized here to the longer discussions in which they appear elsewhere. The total energy in a portion of material can be split in either of two ways: . . . Total energy = internal energy + external energy, or . . . . . . Total energy = free energy + bound energy . . . In symbols, . . . U + PV = total = G + TS . . . where U = internal energy of the portion; G = free energy of the portion, specifically the Gibbs free energy or enthalpy; P = pressure; V = volume of the portion; T = temperature; S = entropy of the portion. All the terms except the free energy, G, have independent definitions, so the equations just given define that quantity: . . . G = U + PV – TS (2.1) . . . The equation relates to whatever portion of material one has in view. We now suppose that the material has n components and that, in the portion considered, the masses of each are m1, m2, . . . , mn. Then we imagine increasing m1 by a small amount δm1 while keeping P, T, and m2, m3, . . , ,mn constant. Let the consequent change in G be δG: then the limit of the ratio δG/δm1 as δm1 → 0 is the quantity of interest, henceforth written μ1; it is the chemical potential of component 1 in the material at its current pressure, temperature, and composition.

Ab initio study of thermodynamic properties of bulk zinc-blende CdS: Comparing the LDA and GGA

2018 ◽  
Vol 32 (20) ◽  
pp. 1850207 ◽  
Author(s):  
Fatemeh Badieian Baghsiyahi ◽  
Arsalan Akhtar ◽  
Mahboubeh Yeganeh
Keyword(s):  
Free Energy ◽  
Thermal Expansion ◽  
Thermodynamic Properties ◽  
Bulk Modulus ◽  
Internal Energy ◽  
Density Functional ◽  
Helmholtz Free Energy ◽  
Constant Volume ◽  
Grüneisen Parameter ◽  
Zinc Blende

In the present study, we have investigated the phonon and thermodynamic properties of bulk zinc-blende CdS by first-principle calculations within the density functional theory (DFT) and the density functional perturbation theory (DFPT) method using the quasi harmonic approximation (QHA). We calculated the phonon dispersion at several high symmetry directions, density of phonon state, temperature dependence feature of Helmholtz free energy (F), internal energy, bulk modulus, constant-volume specific heat, entropy, coefficient of the volume thermal expansion and Grüneisen parameter estimated with the local density approximation (LDA) and generalized gradient approximation (GGA) for the exchange-correlation potential and compared them with each other. For internal energy, Helmholtz free energy, constant volume heat capacity and phonon entropy the LDA and GGA results are very similar. But, the LDA gives lattice constants that are smaller than GGA while phonon frequencies, bulk modulus and cohesive energies are larger. On the other hand, the results obtained through the GGA approximation for the coefficient of the volume thermal expansion and Grüneisen parameter are larger than those obtained from LDA.

scholarly journals Finding Exact Forms on a Thermodynamic Manifold

2018 ◽  
Author(s):  
Chao Ju ◽  
Mark Stalzer
Keyword(s):  
Maxwell Equations ◽  
Stokes Equations ◽  
Differential Forms ◽  
Thermodynamic System ◽  
Navier Stokes ◽  
State Variables ◽  
Navier Stokes Equations ◽  
Vector Calculus ◽  
Cotangent Space ◽  
Classical Thermodynamics

Because only two variables are needed to characterize a simple thermodynamic system in equilibrium, any such system is constrained on a 2D manifold. Of particular interest are the exact 1-forms on the cotangent space of that manifold, since the integral of exact 1-forms is path-independent, a crucial property satisfied by state variables such as internal energy dE and entropy dS. Our prior work [1] shows that given an appropriate language of vector calculus, a machine can re-discover the Maxwell equations and the incompressible Navier-Stokes equations from data. In this paper, We enhance this language by including differential forms and show that machines can re-discover the equation for entropy dS given data. Since entropy appears in various fields of science in different guises, a potential extension of this work is to use the machinery developed in this paper to let machines discover the expressions for entropy from data in fields other than classical thermodynamics.

Nonequilibrium Thermodynamic State Variables of Human Self-Paced Rhythmic Motions: Canonical-Dissipative Approach, Augmented Langevin Equation, and Entropy Maximization

2015 ◽  
Vol 22 (01) ◽  
pp. 1550007 ◽  
Author(s):  
S. Kim ◽  
J. M. Gordon ◽  
T. D. Frank
Keyword(s):  
Free Energy ◽  
Internal Energy ◽  
Limit Cycle ◽  
Langevin Equation ◽  
Oscillation Frequency ◽  
Nonequilibrium Thermodynamic ◽  
State Variables ◽  
Thermodynamic State ◽  
Stochastic Limit ◽  
Limit Cycle Oscillator

Nonequilibrium thermodynamic state variables are derived for a stochastic limit-cycle oscillator model that has been used in motor control research to describe human rhythmic limb movements. The nonequilibrium thermodynamic state variables are regarded as counterparts to the thermodynamic state variables entropy, internal energy, and free energy of equilibrium systems. The derivation of the state variables is based on maximum entropy distributions of the Hamiltonian energy of the stochastic limit-cycle oscillators. The limit-cycle oscillator model belongs to the class of canonical-dissipative systems, on the one hand, and, on the other hand, can be cast into the form of an augmented Langevin equation. Both concepts are known as physical models for open systems. Experimental data from paced and self-paced pendulum swinging experiments are presented and estimates for the nonequilibrium thermodynamic state variables are given. Entropy and internal energy increased with increasing oscillation frequency both for the paced and self-paced conditions. Interestingly, the nonequilibrium free energy decayed when oscillation frequency was increased, which is akin to the decay of the Landau free energy when the control parameter is scaled further away from its critical value.

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