The Mayer-Joule Principle: The Foundation of the First Law of Thermodynamics

M.

 

Bailyn

, (, , ), pp. –.

D.

 

Roller

, (, , ), pp. –, 61–81.

, 3rd ed. (, , ), p. .

E.

Mach

, (, , ), pp. –, 224–250.

(, , ). Translated by T. J. McCormack from the German.

In thermodynamics and statistical physics, temperature subtly enters equations via Boltzmann's constant $k=1.38×10−23J/K$⁠. A relevant discussion can be found in

H. S.

 

Leff

, “”  , – ().

R. H.

 

Fowler

and

E. A.

 

Guggenheim

, (, , ), p. .

A.

 

Sommerfeld

, (, , ), p. , edited by

F.

 

Bopp

,

J.

 

Meixner

; translated by J. Kestin.

C. J. T.

 

Lewis

, (, , ), pp. –.

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Black

, , Vol. , edited by

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Black

, “,”  , ().

The first published reference to the calorie appeared anonymously (presumably by a student of Clement) in Le Producteur,  , – (). For a full discussion of Clement's related work on the calorimetric properties of gases, see Mach (Ref. 5, pp. 182–190).

B.

 

Thompson

, “,”  , – ().

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Tisza

, (, , ), pp. , 23–24.

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Brush

, , Vol. (, , ), pp. –.

S.

 

Carnot

, , edited by

E.

 

Mendoza

(, , ). Translated by R. H. Thurston from the French Reflexions Sur la Puissance Motrice du Feu (Bachelier, Paris, 1824).

R.

 

Newburgh

, “,”  , – ().

In 1841, Mayer wrote that the fall of a weight m*g from a height of 365 m corresponds to the heating of an equal mass of water by 1°C. Although he did not give a value for J explicitly, his result implies (9.8 m/s²)(365 m)(m*kg) = (J)(m*kg)(l kcal/kg/°C)(1°)C, or $J=3.58J/cal$⁠. This value was low primarily because Mayer used early and flawed specific heat values for air. He did not publish the derivation outlined in the text until 1845, in a paper entitled, “The motions of organisms and their relation to metabolism — An essay in natural science.” Mayer's failure to provide supporting details in 1841 exacerbated a controversy about whether he or Joule was first to arrive at the “mechanical equivalent ofheat.” In 1851 Mayer published a corrected result using improved specific heat data, which implied $J=4.165J/cal$⁠, close to Joule's value, 4.18 J/cal. English translations of the 1841 and 1845 papers are in

R. B.

 

Lindsay

, (, , ), pp. –, 84.

The value of J depends upon the specific definition of calorie, among several that are common. For example, the thermo-chemical calorie is defined as 4.184 J exactly, while the International Table calorie = 4.1868 J. See

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Thompson

,

B. N.

 

Taylor

, (SI) (), available online at http://physics.nist.gov/cuu/pdf/sp811.pdf.

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Lloyd

, “,”  , – ().

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Clausius

, “,”  , –, 500–524 ().

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Zemansky

, “,”  , ().

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Romer

, “,”  , – ().

J. W.

 

Jewett

, “,”  , – ().

H. S.

 

Leff

, “,”  , – ().

W. T.

 

Grandy

, (, , ), p. .