The isotherms of an imperfect gas

ABSTRACTThe liquid drop model of an imperfect gas in the form introduced by Wergeland is discussed by using the method of the grand ensembles and the equation of state of the system is derived. This equation of state is of the same general type as the one derived by Mayer for a more general model. It is shown that in both cases the isotherms consist of two analytically different parts in the limit where the number of particles in the system, N, goes to infinity.

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The perfect Bose-Einstein gas in the theory of the quantum-mechanical grand canonical ensembles

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1952.0102 ◽

1952 ◽

Vol 212 (1111) ◽

pp. 552-558 ◽

Cited By ~ 2

Keyword(s):

Equation Of State ◽

Energy Levels ◽

Einstein Condensation ◽

Quantum Mechanical ◽

Condensation Phenomenon ◽

Bose Einstein ◽

Canonical Ensembles ◽

Grand Canonical ◽

Different Parts ◽

Number Of Particles

The theory of quantum-mechanical grand canonical ensembles is used to derive for the case of a perfect Bose-Einstein gas the average number of particles in the different energy levels, the fluctuations in these numbers and the equation of state. The Einstein condensation phenomenon is then discussed, and it is shown that in a p-v diagram (v being the specific volume) the isotherm consists of two analytically different parts in the limit where the number of particles in the system, JV, goes to infinity. It is also shown that for finite N at the critical volume ∂ n p/∂v n is of the order N1/3 (n-2) in accordance with a result obtained by Wergeland & Hove-Storhoug.

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METAL-SURFACE CORRELATION ENERGY FROM THE LIQUID DROP MODEL: A BACK-OF-THE-ENVELOPE ESTIMATE

Modern Physics Letters B ◽

10.1142/s0217984991001325 ◽

1991 ◽

Vol 05 (16) ◽

pp. 1081-1085 ◽

Cited By ~ 1

Author(s):

JOHN P. PERDEW ◽

G. ROSENSTEEL

Keyword(s):

Surface Density ◽

Random Phase Approximation ◽

Liquid Drop ◽

Correlation Energy ◽

Local Density ◽

Strong Dependence ◽

Random Phase ◽

Liquid Drop Model ◽

Elementary Estimate ◽

The One

The liquid drop model applied to the one-electron problem provides an elementary estimate of the correlation contribution to the surface and curvature energies of jellium, in terms of bulk electron density and bulk correlation energy. Within the random phase approximation (RPA), this estimate correctly predicts the size of the surface correlation energy, its strong dependence upon bulk density, and its weak dependence upon surface density profile. The local density approximation (LDA) to RPA predicts surface correlation energies that are far too small, as a consequence of the LDA self-interaction error. Possible implications beyond RPA are discussed. The power and limitations of the liquid drop expansion are illustrated by the example of one-electron jellium spheroids.

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A NEW PHENOMENOLOGICAL FORMULA FOR GROUND-STATE BINDING ENERGIES

International Journal of Modern Physics E ◽

10.1142/s0218301311017417 ◽

2011 ◽

Vol 20 (01) ◽

pp. 179-190 ◽

Cited By ~ 7

Author(s):

G. GANGOPADHYAY

Keyword(s):

Binding Energy ◽

Single Particle ◽

Ground State ◽

Liquid Drop ◽

Alpha Decay ◽

Binding Energies ◽

Present Calculation ◽

Mean Square ◽

Liquid Drop Model ◽

The One

A phenomenological formula based on liquid drop model has been proposed for ground-state binding energies of nuclei. The effect due to bunching of single particle levels has been incorporated through a term resembling the one-body Hamiltonian. The effect of n–p interaction has been included through a function of valence nucleons. A total of 50 parameters has been used in the present calculation. The root mean square (r.m.s.) deviation for the binding energy values for 2140 nuclei comes out to be 0.376 MeV, and that for 1091 alpha decay energies is 0.284 MeV. The correspondence with the conventional liquid drop model is discussed.

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Open-source nuclear equation of state framework based on the liquid-drop model with Skyrme interaction

Physical Review C ◽

10.1103/physrevc.96.065802 ◽

2017 ◽

Vol 96 (6) ◽

Cited By ~ 34

Author(s):

A. S. Schneider ◽

L. F. Roberts ◽

C. D. Ott

Keyword(s):

Equation Of State ◽

Open Source ◽

Liquid Drop ◽

Liquid Drop Model ◽

Skyrme Interaction ◽

Nuclear Equation Of State

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SIMULASI ENERGI IKAT DAN ENERGI DISINTEGRASI PELURUHAN UNSUR RADIOAKTIF DERET AKTINIUM BERDASARKAN MODEL INTI TETESAN CAIRAN (TELAAH KLASIK)

JURNAL PEMBELAJARAN FISIKA ◽

10.19184/jpf.v10i1.23583 ◽

2021 ◽

Vol 10 (1) ◽

pp. 22

Author(s):

Maharani Karunia Putri ◽

Albertus Djoko Lesmono ◽

Alex Harijanto

Keyword(s):

Binding Energy ◽

Beta Decay ◽

Liquid Drop ◽

Alpha Decay ◽

Liquid Drop Model ◽

Research Results ◽

Key Word ◽

Calculation Results ◽

Number Of Particles ◽

Model Approach

The purpose of this research is to make simulation with Matlab application to calculate the binding energy and disintegration energy of Actinium series based of liquid drop model approach. This research is experimental description. The steps: 1) prepare literature studies of elements in the radioactive process; 2) reviewing some literatures; 3) do calculation simulation; 4) analyze and discuss the results of calculations; 5) conclude the research results. The calculation results show that the binding energy value of the Actinium Series based of liquid drop model approach is in accordance with the theory where the binding energy is directly proportional to the mass and the number of particles, so that the binding energy decreases in linear graph. The largest binding energy owned by 92U235 element is 1786,751 MeV. While the smallest binding energy owned by the 81Tl20 element is 1616,311 MeV. The disintegration energy found in the radioactive actinium series has a positive value, so this is in accordance with the conditions for the occurrence of decay, which is Q> 0. The largest disintegration energy produced from alpha decay by element 91Pa231 is 4.9335 MeV and the smallest binding energy generated from beta decay by the element 90Th231 is 0,0018 MeV. Key Word: Disintegration Energy, Binding Energy, Liquid Drop Model Approach.

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Liquid Drop Model for Investigating the Outer Crust of Neutron Star

Proceeding International Conference on Science and Engineering ◽

10.14421/icse.v2.60 ◽

2019 ◽

Vol 2 ◽

pp. 87-91

Author(s):

Feni Fitrishia ◽

Eko Tri Sulistyani ◽

Romy Hanang Setya Budhi

Keyword(s):

Neutron Star ◽

Equation Of State ◽

Total Energy ◽

Liquid Drop ◽

Liquid Drop Model ◽

Model Approximation ◽

Mass Model ◽

System Equation ◽

Long Time ◽

Outer Crust

The properties of outer crust of cooling neutron star by using Liquid Drop Model approximation has been studied. Th is mass model is used to derive the properties of outer crust of neutron star matter such as total energy of system, equation of state (relationship between pressure and density), and composition of the outer crust. The properties of the outer crust are studied under the assumption that neutron star has created for long time and the matter in neutron star is in its ground state. The composition of the outer crust consists of ions Z arranged in a lattice and free electrons e, so that the total energy of the system consists of three contributions: the mass-energy of the nuclear, the energy of electrons and lattice. The equation of state (the relationship between pressure and density) shows that the pressure increases with increasing density in the outer crust layer. With a simple model based on liquid drop model, it is known that the outer crust is composed of nuclei which are at Z ≈ 20-50, with 56Fe core at the upper layer, and 154Cd core at the lowermost layer of the outer crust.

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Solidaritas Sebagai Norma Dasar Dalam Etika Paulus

DISKURSUS - JURNAL FILSAFAT DAN TEOLOGI STF DRIYARKARA ◽

10.36383/diskursus.v11i1.159 ◽

1970 ◽

Vol 11 (1) ◽

pp. 79-100

Author(s):

Martin Harun

Keyword(s):

Community Building ◽

Lord's Supper ◽

Body Of Christ ◽

The Poor ◽

Central Elements ◽

The New Testament ◽

Unity In Diversity ◽

The One ◽

The Church ◽

Different Parts

Abstract: Solidarity, a modern word and concept, has old roots in the concept of koinonia (fellowship) as it is understood in the New Testament. David G. Horrell even maintains that what we now call solidarity, functions as a meta norm in Paul’s ethics, since phenomena of solidarity are clearly present in the central elements of Paul’s community building. Reference is made to the two basic rituals, Baptism and the Lord’s Supper, which build unity in diversity; to the most frequently used form of address, adelphoi/brothers, which asks for familial treatment of one another; also to the special way in which Paul often tries to restore unity in the middle of conflicts; and especially to his metaphor of the Church as the one body of Christ with many different parts that need and support one another. When speaking about the collections as a sign of the Greek community’s solidarity with the poor community in Jerusalem, Paul refers to Christ’s solidarity as the source of solidarity within and among communities. Keywords: Solidarity, fellowship, David Horrell, Paul, Ethics, baptism, the Lord’s Supper, brothers, Body of Christ, Christ’s solidarity. Abstrak: Solidaritas, sebuah kata dan paham modern, memiliki akar yang lama, antara lain dalam paham koinonia (persekutuan), sebagaimana digunakan dalam Alkitab Perjanjian Baru. David G. Horrell mempertahankan bahwa apa yang sekarang kita sebut solidaritas, merupakan norma dasar (meta norm) dalam etika Paulus, sebab fenomen-fenomen solidaritas tampak dalam unsur-unsur sentral pembinaan jemaatnya, antara lain dalam kedua ritual paling dasar, baptisan dan perjamuan Tuhan, yang membina kesatuan dalam perbedaan. Solidaritas juga muncul dalam sebutan paling frekuen, saudara-saudara (adelphoi), yang menuntut suatu etos kekeluargaan. Solidaritas juga tampak dalam banyak seruan Paulus untuk memulihkan kesatuan apabila ia berhadapan dengan perpecahan, dan teristimewa dalam menggambarkan jemaat sebagai satu tubuh Kristus dengan banyak anggota yang berbeda dan saling membutuhkan serta memberi. Dalam konteks kolekte-kolekte sebagai tanda solidaritas antarjemaat, Paulus secara eksplisit menunjuk kepada solidaritas Kristus dengan kita sebagai dasar terdalam dari solidaritas antarumat. Kata-kata kunci: Solidaritas, persekutuan, David Horrell, Paulus, etika, baptisan, Perjamuan Tuhan, saudara-saudara, Tubuh Kristus, solidaritas Kristus.

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Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-021-01954-2 ◽

2021 ◽

Vol 60 (3) ◽

Author(s):

Phan Thành Nam ◽

Marcin Napiórkowski

Keyword(s):

Density Matrix ◽

Ground State ◽

Mean Field ◽

Interaction Strength ◽

Bose Gas ◽

Body Density ◽

The Mean ◽

The One ◽

Mean Field Regime ◽

Number Of Particles

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.

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