In thermodynamics,

Overview

In 1904, James Jeans, in his

In 1920, Jeans, in a latter edition of his

one, the first part of the above equation, entropy depending on the velocities of the molecules, the other, the second part above, on the positional coordinates of the molecules. [3]

Entropy and life debate

On

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Quotes

The following are related quotes:

References

1. (a) Jeans, James. (1904).

(b) Jeans, James. (1905). “The Kinematics of a Granular Medium in Normal Piling” (Ѻ),

(c) Jeans, James. (1920).

2. Jeans, James. (1905). “The Kinematics of a Granular Medium in Normal Piling” (Ѻ),

3. Jeans, James. (1920).

4. Jeans, James. (1934). “Letter | Activities of Life and the Second Law of Thermodynamics” (abs),

**positional entropy**is []Overview

In 1904, James Jeans, in his

*The Dynamical Theory of Gases*(§194), was referring to “positional entropy”, based on what seems to be, his own peculiar derivation, based on his concept of “positional coordinates” of molecules in a gas body, framed around Max Planck's 1901 entropy formula*S = k log W*. [1] He began citing this term the following year:“We may perhaps summarize the question by saying that the‘positional entropy’of the system is a maximum when the system is in the normal and anti-normal piling.”— James Jeans (1905), “The Kinematics of a Granular Medium in Normal Piling” [2]

In 1920, Jeans, in a latter edition of his

*The Dynamical Theory of Gases*(pgs. 178-180), gives his own peculiar derivation of a gas system that yields an entropy equation, entropy symbolized by phi φ, consisting of two parts:one, the first part of the above equation, entropy depending on the velocities of the molecules, the other, the second part above, on the positional coordinates of the molecules. [3]

Entropy and life debate

On

**21 Apr**1934, Jeans, amid the Jeans, Donnan, Guggenheim debate, referred to the “normal” formula for positional entropy (an invention which seems to be his own), as follows: [4]“I am anxious to treat Prof. Donnan's views with all courtesy, but think his last letter, written in conjunction with Prof. Guggenheim, is entirely invalidated, like his previous letter, by a technical error in thermodynamics. The ordinary formula for theof a large number of particles is:positional entropypositional entropy =k∫∫∫ ν log νdxdydz

where v is the number of particles per unit volume. Thus, moving N particles from a place of density ν to one of higher density ν' decreases the entropy bykN(log ν’ – log ν)

Surely Profs. Donnan and Guggenheim haveoverlooked the factorN.Owing to its presence, moving a single molecule does not, as they contend, have the same effect as moving a truckload ofNmolecules, but only 1/Nth of this effect. The same error, I think, invalidates their second paragraph.”

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“Typical views in the 1930's on this subject were expressed in anexchange of lettersto the journalNaturebetween F. G. Donnan, a professor of physical and inorganic chemistry, and the physicist James Jeans. Donnan [1934] challenged the view expressed by Jeans in his bookThe New Background of Sciencethat organisms must have some means for evading the second law of thermodynamics. Jeans [1934] replied that a person steering a large steamship adds little entropy in the activities of steering, but the ‘positional entropy’ of the cargo is changed considerably. This is due to moving the cargo from a location where it has a high density υ1 to a location where it has a low density υ2, thereby changing the positional entropy byΔS = kBN[ln υ1 – ln υ2]. In this case, the intervention of anintelligent beingis incidental to the entropy calculation. In spite of the entry of the physicist E. A. Guggenheim on Donnan's side, and the exchange of several more letters, this controversy died without being resolved and without, apparently, leaving any further trace. Jeans' positional entropy is only one example of the types of entropy proposed during this period.”— Paul McEvoy (2002),Classical Theory(pg. 175)

References

1. (a) Jeans, James. (1904).

*The Dynamical Theory of Gases*(§194). Publisher.(b) Jeans, James. (1905). “The Kinematics of a Granular Medium in Normal Piling” (Ѻ),

*Proceedings of the London Mathematical Society*(pg. 136), Jan 12.(c) Jeans, James. (1920).

*The Dynamical Theory of Gases*(entropy, pgs. 78, 178, 180; of radiation, pgs. 367, 397; positional, 15+ pgs). Publisher.2. Jeans, James. (1905). “The Kinematics of a Granular Medium in Normal Piling” (Ѻ),

*Proceedings of the London Mathematical Society*(pg. 136), Jan 12.3. Jeans, James. (1920).

*The Dynamical Theory of Gases*(entropy, pgs. 78, 178, 180; of radiation, pgs. 367, 397; positional, 15+ pgs). Publisher.4. Jeans, James. (1934). “Letter | Activities of Life and the Second Law of Thermodynamics” (abs),

*Nature*, Apr 21, 133:612.