Ideal solution

In physical chemistry, ideal solution refers to []

Overview
In 1955, Kenneth Denbigh, in his Principles of Chemical Equilibrium, defined ideal solution as follows: [3]

“A solution is said to be ‘ideal’ if the chemical potential of every component is a linear function of the logarithm of its mole fraction according to the following relation:

[Untitled]

where μ*i is a function only of temperature and pressure.”

In 1978, Gurdeep Raj, in his Advanced Physical Chemistry (pg. 1420), defined ideal solution as follows:

“In an ideal solution of two components A and B, all the intermolecular forces between A and A, B and B, and A and B are alike, so that the escaping tendency of an A or B molecule would be independent of whether it is being surrounded by A molecules, B molecules or varying proportions of A and B molecules. Thus, the escaping tendency, as measured by the vapor pressure, of each component in this type of solution will remain the same as that in the pure component therefore Raoult's law is obeyed. Such a solution can only form if the components A and B are identical in structure and polarity.”

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Dark ages (Islamic golden age)
A segment from the dark ages article, showing the "Islamic golden age", wherein many middle ages geniuses, were synthesized, (c.800-1100) (Ѻ), which ended when Hamid Al-Ghazali (1058-1111) declared mathematicsevil” or the “work of the devil” (Tyson, 2011) (Ѻ).

Beg | Ideal society | Ideal solution | Ideal gas?
In 1987, Mirza Beg, in his New Dimensions in Sociology, conjectured, thematic to his overall work, that the physico-chemical term “ideal solution”, in scientific definition and meaning, is represented, in physico-chemical sociological terms, by the society formed by Muhammad in c.600; the following is one summary of this view:

““The author has suggested a universality of phenomena, the attraction and repulsive forces at atomic and molecular level, micro-cosmic and macro-cosmic level and among celestial bodies to be operative also among human beings which are an integral part of the universe and that similar forces should govern their interaction or behaviour. The author [Beg] believes, for example, that a society is comparable to a ‘physical solution’ which would be ‘ideal’ if the interaction among the components of these two systems is uniform. Such a society was present at the time of the Muhammad when interaction among Sahabah (Ѻ) and Muhajirun (Ѻ) was so congenial as to compare with the physico-chemical laws for ideal solution.”
Mumtaz Kazi (1987) “Forward by a Scientist” to Mirza Beg’s New Dimensions in Sociology (pg. ii) [2]

Firstly, in respect to areas of difficulty, is the notice here that Beg is mixing “religious history”, which more often than not tends to be invented history, with science, and secondly, that the majority of nearly all founders of national religions, tend to be fictional or rather invented characters or god-to-prophet rescripts. Such is likely the case with Muhammad (see: Muhammad never existed), as is the case with Jesus (see: Jesus never existed), Moses (see: Moses never existed), and Abraham (see: Abraham never existed).

This being the case, there was, invariably, however, a religious “recension” (see: recension theory), which beginning in c.600 gave rise to Islamic religion, and in turn the Islamic golden age (c.800-1100), as shown adjacent, a period of intellectual brightness, wherein many middle ages geniuses were produced.

It can, accordingly, be conceded that in c.600, during the so-called Muslim recension, there were two, or more, non-polar molecular species, Muhajirun (Ѻ), the first pilgrims to adhere to the new creed, which we might call molecular species A, and the Sahabah (Ѻ), the surrounding molecular species B, who first came into contact with the “religious ideas” of A, or of the newly reformulated religion, who prior to that time, had different “polarities” and would not mix, e.g. like the Christian Protestants and Catholics of the 17th century, or something along these lines, but that after the new religion was assimilated, they began to have the same polarity, and therein or thereby “equivalent intermolecular forces”, as Beg conjectures, whether between A and A, B and B, or A and B.

Quotes
The following are related quotes:

“A first important step is made by showing that no better result will be obtained by the use of any other machinery than the ordinary piston and cylinder, or by using many cylinders instead of one, provided that the steam be supplied with heat in the same way: the steam possessing during and after formation a certain definite amount of expansive energy which, if duly utilized, will do a certain definite amount of work: and it follows therefore that to obtain greater efficiency the treatment of the steam must he altered, or steam must be replaced by some other fluid. To see whether anything can be gained in this way it is necessary to consider, instead of steam, some body of more simple constitution, so that we may be able to construct a complete and exact theory of the action of heat upon it. Such a body is suggested by the properties of the permanent gases (Ѻ), all which possess certain characteristics so approximately, as to suggest to us the consideration of an ideal body [see: ideal gas; ideal perfect gas] called a perfect gas, in which they shall be precisely realized. The fourth chapter is therefore occupied with the discussion of the action of heat on a perfect gas, and the result is utilized to study the operation of the simplest forms of air engines, when it is found that although in circumstances conceivable in practice, the efficiency is more than double that of the steam engine previously considered, yet still fully one-half the heat expended will be wasted. The cause of the waste, however, is remarkably different in the two cases; in the air engine, all the heat is in the first instance employed in doing work, and the waste is caused by the necessity which exists in air engines for a compressing apparatus, which requires so much power to work it that the larger part of the energy originally exerted on the working piston is thrown away: while in the steam engine, on the other hand, although some energy is employed in compression, represented by the back pressure on the working piston, yet the greater part of the waste arises from the great amount of internal work which it is necessary to do in order to generate steam, little of which can be utilized by the process of expansion.”
— James Cotterill (1871), Steam-Engine Considered as a Heat Engine (pgs. vii-viii) [1]

References
1. Cotterill, James. (1871). Steam-Engine Considered as a Heat Engine: A Treatise on the Theory of the Steam Engine, Illustrated by Diagrams, Tables, and Examples from Practice. E. & F.N. Spon, 1878.
2. Beg, Mirza Arshad Ali. (1987). New Dimensions in Sociology: a Physico-Chemical Approach to Human Behavior (abs) (intro) (pdf, annotations by Libb Thims, 2014) (Foreword by a Scientist, pgs. i-iii). Karachi: The Hamdard Foundation.
3. Denbigh, Kenneth G. (1955). The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering (pg. 249). Cambridge University Press, 1981.

External links
Ideal solution – Wikipedia.

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