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**ideal gas law**is an equation of state describing the behavior of a body of ideal or perfect gas, defined by the expression:

where

*P*is the pressure of the body of gas,

*V*the volume,

*n*as the number of mols,

*R*the gas constant, and

*T*the temperature.

History

The first verbalized statement of the ideal gas law seems to have been made in parts in 1738 by Dutch-born Swiss mathematician Daniel Bernoulli.

In 1834, French engineer Emile Clapyron was defining the gas law as such:

which he says is Mariotte’s law (PV = k, at constant temperature) combined with that of Gay-Lussac's law (P = kT, at constant volume). [5]

In 1850, German physicist Rudolf Clausius, in his "On the Moving Force of Heat", was defining the gas law as such:

which he says is "the combined laws of Mariotte and Gay-Lussac" and in which he derives a value for the constant

*a*of:

with

*t*the temperature in degrees centigrade. In reference to this gas law, Clausius introduces the notion of dependent variables and independent variables, to the effect that in a three variable equation, i.e. p, v, and t, one can treat any one of these three magnitudes, which then is called the "dependent variable", as a function of the other two, which are then called the "independent variables".

Classical version | Molar version | Avogadro's law

The first statement of the modern version of the gas law, with the particle count measure 'n' in the formula, seems to have been done in the 1893

*Theoretical Chemistry*

*from the Standpoint of Avogadro’s Rule and Thermodynamics*by German chemist Walther Nernst, in which he integrated of Avogadro's rule (1811) into modern chemical thermodynamics, to the result that he states that if

*n*

__g-mol__of different gases are under the pressure

*P*, filling a volume

*V*, at an absolute temperature

*T*, then in the sense of

__Dalton's law__: [1][8]

In 1897, German physicist Max Planck was also using the same modern-version formula in his chapter on "Molecular Weight". [2] This expression became commonplace with its use in the classic 1923 textbook

*Thermodynamics and the Free Energy of Chemical Substances*by American physical chemists Gilbert Lewis and Merle Randall. [3]

Statistical version | Molecular version | Boltzmann's constant

If n, the number of g-moles, gram moles, or moles, of gas, is set equal to: [9]

where

*N*is the actual number of molecules and

*NA*is Avogadro's number, and one defines the commonly used ratio of the gas constant

*R*to Avogadro's number to be equal to a new so-called constant of nature:

where the subscript "B" is in honor of Austrian physicist Ludwig Boltzmann, via substitution, the classical "molar-based" ideal gas law can also be written in the alternative so-called "molecular" or statistical mechanical form:

or

with the subscript "B" (for Boltzmann) assumed, where

*kB*is called the Boltzmann constant, a constant that was first calculated in the 1900 work of German physicist Max Planck.

Other

In 1936, Italian-born American physicist Enrico Fermi was defining what he called the "equation of state for the ideal gas or perfect gas" as follows: [6]

where

*m*is grams of a gas, and

*M*is molecular weight, and expression which Fermi says includes Boyle's law, Gay-Lussac's law, and

__Avogadro's law__. [7] If, according to Fermi, the number of grams of the gas equals the molecular weight of the gas, then:

which he says is the condition for what is called the "gram-molecule" amount of a gas. Hence, the gram molecule ideal gas law becomes:

Of note, the inconsistency with which authors upper or lower case letters for pressure volume and temperature is a bit puzzling, as there seems to be some type of unwritten rule practiced, albeit inconsistently.

See also

● Social ideal gas law

References

1. Nernst, Walther. (1893).

*Theoretical Chemistry*

*: from the Standpoint of Avogadro’s Rule and Thermodynamics*(PV=nRT, pgs. 32, 41)

*.*MacMillan and Co.

2. Planck, Max. (1897).

*Treatise on Thermodynamics*(ch. 2: Molecular Weight, pgs. 23-33)

*.*Longmans, Green and Co.

3. Lewis, Gilbert N. and Randall, Merle. (1923).

*Thermodynamics and the Free Energy of Chemical Substances*(pg. 63)

*.*McGraw-Hill Book Co., Inc.

4. Ideal gas law (T-shirt) – Zazzle.com.

5. Clapeyron, Émile. (1834). “Memoir on the Motive Power of Heat”,

*Journal de l’Ecole Polytechnique.*XIV, 153 (and Poggendorff's

*Annalender Physick,*LIX, [1843] 446, 566).

6. Fermi, Enrico. (1936).

*Thermodynamics*(pg. 8)

*.*Prentice Hall.

7. Avogadro’s law – Wikipedia.

8. Dalton’s law – Wikipedia.

9. (a) Basavaraju, G. and Ghosh, Dipan. (1984).

*Mechanics and Thermodynamics*(pgs. 349-50). Tata McGraw-Hill.

(b) Wolf, Jonathan S. (2003).

*How to Prepare for the Advanced Placement Exam*:

*Physics B*(pg. 212). Barron’s Educational Series.

External links

● Ideal gas law – Wikipedia.