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.

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.

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.

scholarly journals ANISOTROPY OF THERMODYNAMIC POTENTIALS IN MECHANICALLY STRESSED HAFNIA STRUCTURES

2020 ◽  
Author(s):  
Viacheslav Konstantinov ◽  
◽  
Aleksandr Italyantsev
Keyword(s):  
Free Energy ◽  
Ab Initio Calculations ◽  
Ab Initio ◽  
Helmholtz Free Energy ◽  
Thermodynamic Potentials

Anisotropy of Helmholtz free energy in mechanically stressed tetragonal hafnia structures is studied. Ab-initio calculations method is used for the modelling of the structures and estimation of Helmholtz free energy.

scholarly journals Fluctuation Theorem of Information Exchange within an Ensemble of Paths Conditioned at a Coupled-Microstates

2019 ◽  
Author(s):  
Lee Jinwoo
Keyword(s):  
Free Energy ◽  
Information Exchange ◽  
Thermodynamic Potential ◽  
Heat Bath ◽  
Fluctuation Theorem ◽  
State Function ◽  
Local Form ◽  
Fluctuation Theorems ◽  
Thermodynamic Potentials ◽  
Fluctuating System

Fluctuation theorems are a class of equalities each of which links a thermodynamic path functional such as heat and work to a state function such as entropy and free energy. Jinwoo and Tanaka [L. Jinwoo and H. Tanaka, Sci. Rep. 5, 7832 (2015)] have shown that each microstate of a fluctuating system can be regarded as an ensemble (or a 'macrostate') if we consider trajectories that reach each microstate. They have revealed that local forms of entropy and free energy are true thermodynamic potentials of each microstate, encoding heat, and work, respectively, within an ensemble of paths that reach each state. Here we show that information that is characterized by the local form of mutual information between two subsystems in a heat bath is also a true thermodynamic potential of each coupled state and encodes the entropy production of the subsystems and heat bath during a coupling process. To this end, we extend the fluctuation theorem of information exchange [T. Sagawa and M. Ueda, Phys. Rev. Lett. 109, 180602 (2012)] by showing that the fluctuation theorem holds even within an ensemble of paths that reach a coupled state during dynamic co-evolution of two subsystems.

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

scholarly journals Free Energy of Metals from Quasi-Harmonic Models of Thermal Disorder

Metals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 195
Author(s):  
Pavel A. Korzhavyi ◽  
Jing Zhang
Keyword(s):  
Free Energy ◽  
First Principles ◽  
Density Functional ◽  
Helmholtz Free Energy ◽  
Complex Materials ◽  
Predictive Capability ◽  
Temperature Dependent ◽  
Disordered Alloys ◽  
Thermal Disorder ◽  
Structure Calculations

A simple modeling method to extend first-principles electronic structure calculations to finite temperatures is presented. The method is applicable to crystalline solids exhibiting complex thermal disorder and employs quasi-harmonic models to represent the vibrational and magnetic free energy contributions. The main outcome is the Helmholtz free energy, calculated as a function of volume and temperature, from which the other related thermophysical properties (such as temperature-dependent lattice and elastic constants) can be derived. Our test calculations for Fe, Ni, Ti, and W metals in the paramagnetic state at temperatures of up to 1600 K show that the predictive capability of the quasi-harmonic modeling approach is mainly limited by the electron density functional approximation used and, in the second place, by the neglect of higher-order anharmonic effects. The developed methodology is equally applicable to disordered alloys and ordered compounds and can therefore be useful in modeling realistically complex materials.

Thermodynamics Energy for Both Supervised and Unsupervised Learning Neural Nets at a Constant Temperature

1999 ◽  
Vol 09 (03) ◽  
pp. 175-186 ◽  
Author(s):  
HAROLD SZU
Keyword(s):  
Free Energy ◽  
Constant Temperature ◽  
Helmholtz Free Energy ◽  
Principal Component ◽  
Neural Nets ◽  
Mixing Condition ◽  
Smart Cameras ◽  
Minimization Principle ◽  
Output Entropy ◽  
Artificial Neural Network Ann

Unified Lyaponov function is given for the first time to prove the learning methodologies convergence of artificial neural network (ANN), both supervised and unsupervised, from the viewpoint of the minimization of the Helmholtz free energy at the constant temperature. Early in 1982, Hopfield has proven the supervised learning by the energy minimization principle. Recently in 1996, Bell & Sejnowski has algorithmically demonstrated. Independent Component Analyses (ICA) generalizing the Principal Component Analyses (PCA) that the continuing reduction of early vision redundancy happens towards the "sparse edge maps" by maximization of the ANN output entropy. We explore the combination of both as Lyaponov function of which the proven convergence gives both learning methodologies. The unification is possible because of the thermodynamics Helmholtz free energy at a constant temperature. The blind de-mixing condition for more than two objects using two sensor measurement. We design two smart cameras with short term working memory to do better image de-mixing of more than two objects. We consider channel communication application that we can efficiently mix four images using matrices [AO] and [Al] to send through two channels.

Thermodynamics of Bidisperse Ferrofluids in Zero External Magnetic Field: Theory and Simulations

2015 ◽  
Vol 233-234 ◽  
pp. 331-334
Author(s):  
Anna Yu. Solovyova ◽  
Ekaterina A. Elfimova
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Free Energy ◽  
External Magnetic Field ◽  
Volume Concentration ◽  
Helmholtz Free Energy ◽  
Hard Spheres ◽  
Particle Volume ◽  
Simulation Data ◽  
Theoretical Predictions

The thermodynamic properties of a ferrofluid modeled by a bidisperse system of dipolar hard spheres in the absence of external magnetic field are investigated using theory and simulations. The theory is based on the virial expansion of the Helmholtz free energy in terms of particle volume concentration. Comparison between the theoretical predictions and simulation data shows a great agreement of the results.

scholarly journals Hamiltonian Thermodynamics

2020 ◽  
Vol 16 (4) ◽  
pp. 557-580
Author(s):  
S.A. Rashkovskiy ◽  
Keyword(s):  
Free Energy ◽  
Hamiltonian Systems ◽  
Thermal Energy ◽  
Helmholtz Free Energy ◽  
Random Processes ◽  
Carnot Cycle ◽  
Thermodynamic Process ◽  
Thermodynamic Cycles ◽  
Thermodynamic State ◽  
Laws Of Thermodynamics

It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we show that thermodynamics (or, more precisely, a thermodynamically-like description) can be constructed even for deterministic Hamiltonian systems, for example, systems with only one degree of freedom. We show that for such systems it is possible to introduce analogs of thermal energy, temperature, entropy, Helmholtz free energy, etc., which are related to each other by the usual thermodynamic relations. For the Hamiltonian systems considered, the first and second laws of thermodynamics are rigorously derived, which have the same form as in ordinary (molecular) thermodynamics. It is shown that for Hamiltonian systems it is possible to introduce the concepts of a thermodynamic state, a thermodynamic process, and thermodynamic cycles, in particular, the Carnot cycle, which are described by the same relations as their usual thermodynamic analogs.

Sign in / Sign up

Export Citation Format

Share Document