SklogWiki - User contributions [en]

Biographies

2007-05-24T11:09:47Z

161.111.27.10:

==People==
*[[Berni J. Alder]]
*[[Daniel Bernoulli]]
*[[Ludwig Eduard Boltzmann]]
*[[Robert Boyle]]
*[[Nicolas Léonard Sadi Carnot]]
*[[Jacques Alexandre César Charles]]
*[[Rudolf Julius Emanuel Clausius]]
*[[A. F. Devonshire]]
*[[Paul J. Flory]]
*[[Sir Ralph Howard Fowler FRS]]
*[[Joseph Louis Gay-Lussac]]
*[[Pierre-Gilles de Gennes]]
*[[Josiah Willard Gibbs]]
*[[Hermann Ludwig Ferdinand von Helmholtz]]
*[[James Prescott Joule]]
*[[Walter Kauzmann]]
*[[John G. Kirkwood]]
*[[Sir John Edward Lennard-Jones KBE, FRS]]
*[[Johann Josef Loschmidt]]
*[[James Clerk Maxwell]]
*[[Nicholas Metropolis]]
*[[Lars Onsager]]
*[[J. S. Rowlinson]]
*[[Benjamin Thompson]]
*[[William Thomson]] 1st Baron Kelvin
*[[Stanislaw Ulam]]
*[[Loup Verlet]]
*[[Johannes Diderik van der Waals]]
*[[T. E. Wainwright]]
*[[Kenneth G. Wilson]]
*[[Ernst Friedrich Ferdinand Zermelo]]

Biographies

2007-05-24T11:08:35Z

161.111.27.10:

Jacques Alexandre César Charles

2007-05-24T10:29:32Z

161.111.27.10: New page: Jacques Alexandre César Charles, french chemist, physicist, and aeronaut, was born November 12, 1746, in Beaugency, Loiret, France. Beginning as a clerk in the finance ministry, Charles t...

Jacques Alexandre César Charles, french chemist, physicist, and
aeronaut, was born November 12, 1746, in Beaugency, Loiret, France. Beginning as a clerk in the finance ministry, Charles turned to science and experimented with electricity. He developed several inventions, including a hydrometer and reflecting goniometer, and improved the Gravesand heliostat and Fahrenheit's aerometer. He is best known for his formulation in 1787 of one of the basic gas laws, known as Charles's law, which states that, at constant pressure, the volume occupied by a fixed weight of gas is directly proportional to the absolute temperature. However, during his lifetime, Charles was better known for inventing the hydrogen balloon.

Loup Verlet

2007-05-24T10:11:04Z

161.111.27.10:

Loup Verlet (1931-) is a French physicist who pioneered the computer simulation of molecular dynamics models. In a famous 1967 paper he developed what is now known as Verlet integration (a method for the numerical integration of equations of motion) and the Verlet list (a data structure that keeps track of each molecule's immediate neighbors in order to speed computer calculations of molecule to molecule interactions).

== External links ==

Loup Verlet

2007-05-24T10:10:35Z

161.111.27.10:

Loup Verlet (1931-) is a French physicist who pioneered the computer simulation of molecular dynamics models. In a famous 1967 paper he developed what is now known as [[Media:Verlet integration]] (a method for the numerical integration of equations of motion) and the Verlet list (a data structure that keeps track of each molecule's immediate neighbors in order to speed computer calculations of molecule to molecule interactions).

== External links ==

Loup Verlet

2007-05-24T10:09:59Z

161.111.27.10:

Loup Verlet

2007-05-24T10:09:40Z

161.111.27.10: New page: Loup Verlet (1931-) is a French physicist who pioneered the computer simulation of molecular dynamics models. In a famous 1967 paper he developed what is now known as Verlet integration (a...

William Thomson

2007-05-24T10:07:23Z

161.111.27.10: /* External links */

William Thomson, 1st Baron Kelvin, OM, GCVO, PC, PRS, FRSE, (Belfast, Ireland: 26 June 1824 – Largs, Ayrshire, Scotland: 17 December 1907) was a mathematical physicist, engineer, and outstanding leader in the physical sciences of the 19th century.

== External links ==
*[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Thomson.html BIBLIOGRAPHY OF William Thompson]

William Thomson

2007-05-24T10:05:33Z

161.111.27.10:

William Thomson

2007-05-24T10:03:34Z

161.111.27.10: New page: William Thomson, 1st Baron Kelvin, OM, GCVO, PC, PRS, FRSE, (Belfast, Ireland: 26 June 1824 – Largs, Ayrshire, Scotland: 17 December 1907) was a mathematical physicist, engineer, and out...

Nicholas Metropolis

2007-05-24T09:54:42Z

161.111.27.10: New page: Nicholas Constantine Metropolis (June 11, 1915 – Los Alamos, Nuevo Mexico, October 17, 1999) was an American mathematician, physicist, and computer scientist.

Nicholas Constantine Metropolis (June 11, 1915 – Los
Alamos, Nuevo Mexico, October 17, 1999) was an American mathematician, physicist, and computer scientist.

Hermann Ludwig Ferdinand von Helmholtz

2007-05-24T09:19:57Z

161.111.27.10: /* External links */

Hermann Ludwig Ferdinand von Helmholtz (Postdam, August 31, 1821
– Berlín, September 8, 1894)

== External links ==
*[http://www.1911encyclopedia.org/Hermann_Ludwig_Ferdinand_Von_Helmholtz BIBLIOGRAPHY OF Hermann Ludwig Ferdinand von Helmholtz]

Hermann Ludwig Ferdinand von Helmholtz

2007-05-24T09:19:35Z

161.111.27.10:

Hermann Ludwig Ferdinand von Helmholtz (Postdam, August 31, 1821
– Berlín, September 8, 1894)

== External links ==

Hermann Ludwig Ferdinand von Helmholtz

2007-05-24T09:19:12Z

161.111.27.10: New page: Hermann Ludwig Ferdinand von Helmholtz (Postdam, August 31, 1821 – Berlín, September 8, 1894)

Hermann Ludwig Ferdinand von Helmholtz (Postdam, August 31, 1821
– Berlín, September 8, 1894)

Joseph Louis Gay-Lussac

2007-05-24T09:08:17Z

161.111.27.10: /* External links */

Joseph Louis Gay-Lussac (December 6, 1778 – May 9, 1850) was a French chemist and physicist. He is known mostly for two laws related to gases, and for his work on alcohol-water mixtures, which led to the degrees Gay-Lussac used to measure alcoholic beverages in many countries.

== External links ==
*[http://en.wikipedia.org/wiki/Joseph_Louis_Gay-Lussac BIBLIOGRAPHY OF Joseph Louis Gay-Lussac]

*[http://en.wikipedia.org/wiki/Gay-Lussac's_law Gay-Lussac's law]

Joseph Louis Gay-Lussac

2007-05-24T09:07:36Z

161.111.27.10:

Joseph Louis Gay-Lussac

2007-05-24T09:07:04Z

161.111.27.10: New page: Joseph Louis Gay-Lussac (December 6, 1778 – May 9, 1850) was a French chemist and physicist. He is known mostly for two laws related to gases, and for his work on alcohol-water mixtures,...

Nicolas Léonard Sadi Carnot

2007-05-24T09:00:23Z

161.111.27.10: /* External links */

'''Nicolas Léonard Sadi Carnot''' (Nicolas Léonard Sadi Carnot (June 1, 1796 - August 24, 1832) was a
French physicist and military engineer who gave the first successful
theoretical account of heat engines, now known as the Carnot cycle,
thereby laying the foundations of the second law of
thermodynamics. Technically, he is the world's first thermodynamicist,
being responsible for such concepts as Carnot efficiency, Carnot
theorem, Carnot heat engine, [[Carnot cycle]] and others.

[[Category:Person]]

== External links ==
*[http://www-history.mcs.st-andrews.ac.uk/Biographies/Carnot_Sadi.html BIBLIOGRAPHY OF Nicolas Léonard Sadi Carnot ]

Nicolas Léonard Sadi Carnot

2007-05-24T08:59:07Z

161.111.27.10:

Nicolas Léonard Sadi Carnot

2007-05-24T08:58:34Z

161.111.27.10:

Nicolas Léonard Sadi Carnot

2007-05-24T08:57:17Z

161.111.27.10:

'''Nicolas Léonard Sadi Carnot''' (Nicolas Léonard Sadi Carnot (June 1, 1796 - August 24, 1832) was a
French physicist and military engineer who gave the first successful
theoretical account of heat engines, now known as the Carnot cycle,
thereby laying the foundations of the second law of
thermodynamics. Technically, he is the world's first thermodynamicist,
being responsible for such concepts as Carnot efficiency, Carnot
theorem, Carnot heat engine, and others.

June 1, 1796 - August 24, 1832)
Inventor of the [[Carnot cycle]].

[[Category:Person]]

Robert Boyle

2007-05-24T08:49:45Z

161.111.27.10: /* External links */

'''Robert Boyle''' (Lismore Castle, province of Munster, Ireland : 25 January 1627 - 30 December 1691)
is famous for [[Boyle's law]].
[[Category:Person]]
== External links ==
*[http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Boyle.html BIOGRAPHY OF Robert Boyle]

Robert Boyle

2007-05-24T08:44:11Z

161.111.27.10:

'''Robert Boyle''' (Lismore Castle, province of Munster, Ireland : 25 January 1627 - 30 December 1691)
is famous for [[Boyle's law]].
[[Category:Person]]
== External links ==

Robert Boyle

2007-05-24T08:14:23Z

161.111.27.10:

Robert Boyle (Lismore Castle, province of Munster, Ireland : 25 January 1627 - 30 December 1691)
[[Category:Person]]

Robert Boyle

2007-05-24T08:12:47Z

161.111.27.10:

Robert Boyle (Lirmore Castle, province of 25 January 1627 - 30 December 1691)
[[Category:Person]]

Robert Boyle

2007-05-24T08:09:44Z

161.111.27.10:

Robert Boyle (25 January 1627 - 30 December 1691)
[[Category:Person]]

Robert Boyle

2007-05-24T08:08:45Z

161.111.27.10:

(25 January 1627 - 30 December 1691)
[[Category:Person]]

Ideal gas partition function

2007-03-28T12:59:24Z

161.111.27.10:

[[Canonical ensemble]] partition function, ''Q'',
for a system of ''N'' identical particles each of mass ''m''

:<math>Q_{NVT}=\frac{1}{N!}\frac{1}{h^{3N}}\int\int dp^N dr^N \exp \left[ - \frac{H(p^N, r^N)}{k_B T}\right]</math>

When the particles are distinguishable then the factor ''N!'' disappears. <math>H(p^N, r^N)</math> is the [[Hamiltonian]]
(Sir William Rowan Hamilton 1805-1865 Ireland)
corresponding to the total energy of the system.
''H'' is a function of the ''3N'' positions and ''3N'' momenta of the particles in the system.
The Hamiltonian can be written as the sum of the kinetic and the potential energies of the system as follows

:<math>H(p^N, r^N)= \sum_{i=1}^N \frac{|p_i |^2}{2m} + V(r^N)</math>

Thus we have

:<math>Q_{NVT}=\frac{1}{N!}\frac{1}{h^{3N}}\int dp^N \exp \left[ - \frac{|p_i |^2}{2mk_B T}\right]
\int dr^N \exp \left[ - \frac{V(r^N)} {k_B T}\right]</math>

This separation is only possible if <math>V(r^N)</math> is independent of velocity (as is generally the case).
The momentum integral can be solved analytically:

:<math>\int dp^N \exp \left[ - \frac{|p |^2}{2mk_B T}\right]=(2 \pi m k_b T)^{3N/2}</math>

Thus we have

:<math>Q_{NVT}=\frac{1}{N!} \frac{1}{h^{3N}} \left( 2 \pi m k_B T\right)^{3N/2}
\int dr^N \exp \left[ - \frac{V(r^N)} {k_B T}\right]</math>

The integral over positions is known as the ''configuration integral'', <math>Z_{NVT}</math>

:<math>Z_{NVT}= \int dr^N \exp \left[ - \frac{V(r^N)} {k_B T}\right]</math>

In an ideal gas there are no interactions between particles so <math>V(r^N)=0</math>
Thus <math>\exp(-V(r^N)/k_B T)=1</math> for every gas particle.
The integral of 1 over the coordinates of each atom is equal to the volume so for ''N'' particles
the ''configuration integral'' is given by <math>V^N</math> where ''V'' is the volume.
Thus we have

:<math>Q_{NVT}=\frac{V^N}{N!}\left( \frac{2 \pi m k_B T}{h^2}\right)^{3N/2}</math>

If we define the [[de Broglie thermal wavelength]] as <math>\Lambda</math>
where

:<math>\Lambda = \sqrt{h^2 / 2 \pi m k_B T}</math>

one arrives at

:<math>Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N</math>

Thus one can now write the partition function for a real system can be built up from
the contribution of the ideal system (the momenta) and a contribution due to
particle interactions, ''i.e.''

:<math>Q_{NVT}=Q_{NVT}^{\rm ideal} ~Q_{NVT}^{\rm excess}</math>
[[Category:Ideal gas]]
[[Category:Statistical mechanics]]