Coopersmith 2010 Oxford Univ Press

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Coopersmith J (2010) Energy, the subtle concept. The discovery of Feynman’s blocks from Leibnitz to Einstein. Oxford Univ Press:400 pp.


Coopersmith J (2010) Oxford Univ Press


Some citations

  • Also the historical sequence of events is surprising. The steam age was well under way - steam locomotives pulling trains and steam engines powering industry - decades before 'energy' had been discovered and its conservation stated as the First Law of Thermodynamics. Also, the Second Law trumped the First Law by being discovered first, then came the Third Law, and the Zeroth Law was last of all.
  • Peripatetic school around 300 BC: .. when the motive force is further from the lever, it will cause a greater movement.
  • The idea of a perpetually acting device appears to have originated in India, where a perpetually rotating wheel had religious significance, symbolizing eternal cycles such as the cycle of reincarnation (wheel symbols often appear in Indian temples).
  • Descartes' measure for action is identical to our measure for work (against gravity) and as such is the very start of our quest for the concept of energy.
  • Newton's Second Law of Motion: The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. - 'Alteration of motion' was ambiguous. It meant 'rate of alteration of motion' - or acceleration.
  • Leibniz: ' .. active forces are preserved in the world.' .. The equivalence of this active force to our concept of energy is striking, especially when we realize that Leibniz's concept of force is not Newton's, but is given by the quantity m·v2.
  • Otto von Guericke: Pressure would turn out to be a concept almost - but not quite - as intimately linked to heat and to energy as was temperature.
  • Daniel Bernoulli: The pressure of the air is due to the impacts made by these corpuscles with the walls and piston of the cylinder.
  • .. geometers (applied mathematicians) had been using Newton's definition of force (as in F = ma) for years. .. More surprising, no one had attributed this relationship to Newton - least of all Newton himself (he attributed it to Galilieo!). More surprising, still, both m·v and m·v2 were regularly coming out of the mathematics. Clearly, the geometers and the natural philosophers weren't talking to each other, even when these roles were combined into one person.
  • Just as happens today, it was one thing to do the mathematics and another thing to take on board the full meaning and implications of that mathematics.
  • In the Newtonian [force] view, and isolated body is the centre of attention and we track its twists and turns, its accelerations and decelerations, as it moves along its path and encounters the slings and arrows (the external forces) of fortune. In the energy view to come, a system is examined in its entirety and we look at the interplay between the various bodies within this system and within a certain time interval or cycle.
  • .. new concepts in physics are only forged when experiment, mathematics, and the ideas themselves all move forward together. Now we see that yet another factor that is important - technology.
  • Lazare Carnot: This new concept, work, justified its existence by its utility to the engineers and by its universality, being applicable whatever the force and whatever the machine.
  • Something 'actual', such as motion, is easier to understand than something latent. Also, vis viva and foce are more intuitively obvious concepts as they both relate to an individual body. Potential energy relates instead to the relative positions of bodies or parts of a body within a system - it should more properly be called the energy of relative position or of configuration.
  • Daniel Bernoulli: One can sometimes substitute the modern word 'energy' for the old term 'live force' in his work without disturbing the meaning.
  • Johann Bernoulli: 'In every case of equilibrium of forces, in whatever way they are applied, and in whatever directions they act on [one] another, either mediately or immediately, the sum of the positive energies will be equal to the sum of th eneative energies, taken as positive.' It is noteworthy that Johann coined a new term for this virtual work - he called it the energy. This is the first time that the word 'energy' is used in physics.
  • d'Alembert: .. he refers to 'velocities' and 'motions' when he should be talking about accelerations and forces.
  • Lagrange introduces some terminology: T and V stand for the kinetic and potential energies, respectively. (Needless to say, he doesn't spell this out - the symbols T and V just sort of arise. ..)
  • As a change involves a comparison of motions, then this change can be determined absolutely even while the individual motions themselves are relative.
  • Watt introduced a new measure for the rate of doing work, the horsepower., .. Owners of a Watt steam engine had free installation and servicing, but had to pay a 'royalty' equal to a third of the savings on their previous fuel bills, for example, the cost of hay for horses.
  • Fourier: .. defining the 'flux' - the amount of heat crossing unit area per unit time.
  • Mayer: .. he wanted to understand and promote his new idea of 'force' (energy).
  • Faraday: 'The highest law in physical sciences which our faculties permit us to perceive - [is] the Conservation of Force.'
  • Thus Faraday, like Newton, missed 'energy'. We now turn to our last scientific personage, von Helmholtz, who, when he wrote 'force', really did mean 'energy' (most of the time).
  • In the birth of a new concept, as with the birth of a child, there is usually an interim period during which an appropriate name must be found. In the memoir Helmholtz used only the term 'force', sometimes in the old Newtonian way but usually in the new way, meaning 'energy'. It is invariably clear from the context which meaning is intended; thus 'forces of attraction and repulsion (force means force) and 'the principle of the conservation of force' and 'force equivalent' (force means energy). The term 'energy' was introduced by Thomson in 1852 and Helmholtz very much approved.


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  • Joule [J]; 1 J = 1 N·m = 1 V·C; 1 cal = 4.184 J
Fundamental relationships
» Energy
» Exergy
» Extensive quantity
» Force
» Pressure
» Intensive quantity
Forms of energy
» Internal-energy, dU
» Enthalpy, dH
» Heat, deQ
» Bound energy, dB
Forms of exergy
» Helmholtz energy, dA
» Gibbs energy, dG
» Work, deW
» Dissipated energy, diD

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Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2:112 pp. doi:10.26124/bec:2020-0002
Gnaiger Erich et al ― MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1.

Gnaiger E et al ― MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1. doi:10.26124/bec:2020-0001.v1.


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