Title page to the English translation of the first edition (1865) of by Rudolf Clausius, translated by Thomas Hirst, with an introduction by John Tyndall.The Mechanical Theory of Heat |

**The Mechanical Theory of Heat***: with its Applications to the Steam Engine and to Physical Properties of Bodies*, or

*Die Mechanische Wärmetheorie*(German), is a 376-page 1867 book written by German physicist Rudolf Clausius, that is the founding publication and linchpin of the entire edifice of the science of thermodynamics, in which the ten fundamental equations of thermodynamics were penned. [1]

The book, a collection of nine memoirs (papers) of Clausius, is the result of a prolonged investigative correction of French physicist Sadi Carnot's 1824 paper "On the Motive Power of Fire", in which Clausius modified Carnot's caloric theory based postulates on the nature of the relationship between heat and work, in particular the assumption that no change occurs in the working body during one heat cycle, with the recent experimental discoveries contained in the theory of heat and mechanical equivalent of heat, to result in the modern mathematical formulation of the first and second laws of thermodynamics.

First edition | 1865

The first edition of Clausius'

*The Mechanical Theory of Heat*, consist of a mathematical introduction, his collection of nine memoirs on the mechanical theory of heat, published in the fifteen years prior in various journals (principally in Poggendorff’s

*Annalen*), along with an attachment of notes and appendices:

- Mathematical Introduction (1858): On the Treatment of Differential Equations which are not Directly Integrable, pp. 1-13.
- First Memoir (1850): On the Moving Force of Heat and the Laws of Heat Which May be Deduced Therefrom, pp. 14-69
- Second Memoir (1851): On the Deportment of Vapour During its Expansion Under Different Circumstances, pp. 90-100
- Third Memoir (1851): On the Theoretic Connexion of Two Empirical Laws Relating to the Tensions and the Latent Heat of Different Vapours, pp. 104-110
- Fourth Memoir (1854): On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat, pp. 111-135
- Fifth Memoir (1856): On the Application of the Mechanical theory of Heat to the Steam-Engine, pp. 136-207
- Sixth Memoir (1862): On the Application of the Theorem of the Equivalence of Transformations to Interior Work, pp. 215-250
- Seventh Memoir (1863): On an Axiom in the Mechanical Theory of Heat, pp. 267-289.
- Eighth Memoir (1863): On the Concentration of Rays of Heat and Light, and on the Limits of its Action, pp. 290-326.
- Ninth Memoir (1865): On Several Convenient Forms of the Fundamental Equations of the Mechanical Theory of Heat, pp. 327-365.

Second edition | 1875

After having taught the subject for a number of years, in 1875 Clausius finished rewriting the book so as to take it from a collection of papers to a "text-book of the subject". It was published in 1876 and later as an English translation edition in 1879. The opening paragraph of page one of this last and final English edition is shown below: [2]

“Every force tends to give motion to the body on which it acts; but it may be prevented from doing so by other opposing forces, so that equilibrium results, and the body remains at rest. In this case the force performs no work. But as soon as the body moves under the influence of the force, work is performed.”

In the preface to the second edition, he states that his long experience as a lecturer on the subject at the Polytechnic School and at several universities over the last ten years, since the publication of the first edition, has taught him how the subject matter should be arranged to make this “somewhat difficult theory” more readily intelligible. The chapters to the second edition are listed below:

# | Chapter Title | Pgs. |

Translator's Preface (by Walter Browne) | v-vi | |

Author's Preface (by Rudolf Clausius) | vii-viii | |

Table of Contents | ix-xvi | |

Mathematical Introduction: on Mechanical Work, On Energy, and on the Treatment of Non-Integrable Differential Equations | 1-20 | |

I | First Main Principle of the Mechanical Theory of Heat: or Principle of the Equivalence of Heat and Work | 21-38 |

II | On Perfect Gases | 39-68 |

III | Second Main Principle of the Mechanical Theory of Heat | 69-90 |

IV | The Second Main Principle Under Another Form: or Principle of the Equivalence of Transformations | 91-109 |

V | Formation of the Two Fundamental Equations | 110-125 |

VI | Application of the Mechanical Theory of Heat to Saturated Vapour | 126-162 |

VII | Fusion and Vaporization of Solid Bodies | 163-174 |

VIII | On Homogeneous Bodies | 175-194 |

IX | Determination of Energy and Entropy | 195-211 |

X | On Non-Reversible Processes | 212-234 |

XI | Application of the Mechanical Theory of Heat to the Steam-Engine | 235-294 |

XIII | On the Concentration of Rays of Light and Heat on the Limits of its Operation | 295-331 |

XIII | Discussions on the Mechanical Theory of Heat as Here Developed, and on its Foundations | 332-362 |

Appendix I: On the Thermo-Elastic Properties of Solids (by Walter Browne) | 363-368 | |

Appendix II: On the Continuity of the Liquid and and Gaseous States of Matter (by Walter Browne) | 369-371 | |

Appendix III: On Capillarity (by Walter Browne) | 372-376 |

Overviews of the chapters are slowly being written as subfiled wikipages to this page (as linked to above).

References

1. (a) Clausius, Rudolph. (1865).

*The Mechanical Theory of Heat*

*: with its Applications to the Steam Engine and to Physical Properties of Bodies*. London: John van Voorst.

(b) Clausius, Rudolf. (1867).

*Abhandlungen Uber die Mechanische Wärmetheorie*(

*Treatises on the Mechanical Theory of Heat*)

*.*Braunschweig: Druck und Verlag von Friedrich vieweg und Sohn.

(c)

*The Mechanical Theory of Heat*(20 online synopsis pages) - HumanThermodynamics.com.

2. (a) Clausius, Rudolf. (1879).

*The Mechanical Theory of Heat*.

*London: Macmillan & Co.*

(d) Clausius, Rudolf. (1879).

*Die Mechanische Wärmetheorie*. Braunschweig: Druck und Verlag von Friedrich vieweg und Sohn.

Videos

● Thims, Libb. (2008). “Good News: Clausius’ Mechanical Theory of Heat is Available!” (V), HumanChemistry101, Oct 22.