Already a member?
Sign in
Welcome! Wikis are websites that everyone can build together. It's easy!
- EasyEdit
- Edit tags
- Email page
-
(what's this?What are these tools?
People just like you can add or edit the content on this site. If you want to try editing, but aren't ready to add to this site, try our demo area.
Read more about editing pages at Wetpaint Central.
)
Mechanical equivalent of heat
In thermodynamics, the mechanical equivalent of heat is 778.26 ft-lb a value which represents the amount of mechanical work needed to raise the temperature of one pound of water by one degree Fahrenheit. In modern terms, the mechanical equivalent of heat, symbol J, is the ratio of a unit of mechanical energy to the equivalent unit of thermal energy (W/Q), when a system of units is used in which then differ. [10] The value of J is 4.186 10E7 ergs per calorie. The concept loses its usefulness in SI units in which all forms of energy are expressed in joules and J therefore has a value of 1.
The value, in its original sense, means that the work energy released when a one pound weight falls through a height of 778 feet can affect a temperature increase of one degree in a pound of water, through a number of means of energy conversion. The standardized SI value is 4.186 J/cal. Mathematically, using terminology developed by German physicist Rudolf Clausius in the 1850s, the mechanical equivalent of heat A is a proportionality constant relating the equivalence of heat Q and work W: [1]
Q = A∙W
The calculation of A was determined by a number of individuals, including: Benjamin Thomson (1798), Marc Séguin (1839), Robert Mayer (1842), Ludwig Colding (1843), James Joule (1843 to 1849), Carl Holtzmann (1845), and Gustave-Adolphe Hirn (1856). [2] The best known calculation was that performed by James Joule in 1843 wherein the falling weight was attached to wound rope to a wooden paddlewheel immersed in a tub of water. When the weight fell, the paddle wheel turned, causing agitation in the water and as a result a temperature increase. [3] The depiction shown adjacent is an engraving of Joule's apparatus for measuring the mechanical equivalent of heat from the August 1869 issue of Harper's New Monthly Magazine, No. 231.
History
The earliest experiments showing that mechanical work could produce heat in a fixed ratio were the cannon boring experiments done by American-born English physicist Benjamin Thomson which showed that by continuously boring a cannon barrel with a dull drill bit, a seemingly unlimited supply of heat could be produced. Rumford published his results in a paper titled "An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction" presented to the Royal Society in 1798. Thomson found that the work of one horse during two and a half hours is sufficient to raise through 180° Fahrenheit 26.58 pounds of water. From this he calculated that one pound heated one degree is equivalent to 940 British units of work. [2]
In 1799, British chemist and physicist Humphry Davy conducted “ice-rubbing experiments”, where in a room colder than the freezing point of water, he generated heat or made ice melt by the mechanical rubbing of cubes together. By doing this, Davy demonstrated the conversion of work into heat and that indefinite amounts of heat could be generated from a body, this being contrary to caloric theory, which limits the amount. [4]
In the early 1840s, English physicist James Joule repeated Davy’s ice-rubbing experiments and began to extrapolate this principle to various other work-producing experiments, such as chemical, mechanical, and electrical. In Joule's famous 1843 paper, entitled "The Mechanical Equivalent of Heat", he published the value A for the amount of work W required to produce a unit of heat Q. Joule contended that motion and heat were mutually interchangeable and that in every case, a given amount of work would generate the same amount of heat, regardless of the process. [3] In 1843, Joule summarized his overall objective and theory by stating that:
“I shall lose no time in repeating and extending these experiments, being satisfied that the grand agents of nature are … indestructible; and that wherever mechanical force is expended, an exact equivalent of heat is always obtained.”
In 1842, German physician Robert Mayer outlined a similar take on the mechanical equivalent of heat in living bodies in his paper entitled “Remarks on the Forces of Inorganic Nature”. [5]
In 1839, Danish civil engineer and physicist Ludwig Colding conducting experiments on the compressibility of water; later summarized with a review of other data on compression and friction of various materials. In this work, published in 1843, he went on to state that "the quantities of heat evolved are, in every case, proportional to the lost moving forces" though he did not calculate a mechanical equivalent of heat. [6]
In the years to follow, in a series of quantitative experiments sponsored by the Royal Danish Academy of Sciences and Letters, Colding was able to obtain various values for the mechanical equivalent of heat. By 1850, Colding had obtained a value for the mechanical equivalent of heat, some 14% lower than the modern value (4.1860 J/cal) at a time when Joule had measured 4.159 J·cal-1. [7] A subsequent calculation by Colding in 1852 yielded a value only 3% below modern values.
In 1845, C. von Holtzmann began to assign the letter "a" to the mechanical equivalent of heat and calculated values using methods similar to those of Mayer. [8] In his paper, he stated that "I call the unit of heat the heat which by its entrance into a gas can do the mechanical work a—that is, to use definite units, which can lift a kilograms through one meter." German physicist Rudolf Clausius would later, in 1850, begin to adopt this symbol use and terminology in his Mechanical Theory of Heat.
In 1856, French physicist Gustave-Adolphe Hirn’s conducted experiments in the determination of the mechanical equivalent of heat of a human being in working action. In particular, Hirn calculated a value for the mechanical equivalent of heat for a man doing work, i.e. running on a paddle-wheel like stair-climber treadmill, in a sealed chamber. To achieve this end, a man was placed in a hermetically closed chamber, and made to turn a wheel which could, at choice, revolve with or without doing work. The heat given out in the chamber was then ascertained by the ordinary calorimetric process. From these experiments, Hirn deduced a valuation of the mechanical equivalent of heat for animated motors; but the number which he obtained differed considerably from the standard obtained by Joule via physico-mechanical methods. [9]
In 1850, and over the next fifteen years, German physicist Rudolf Clausius began to use the mechanical equivalent of heat as a basis of his Mechanical Theory of Heat, which is considered the core book of modern thermodynamics. In his first article "On the Motive Power of Heat and on the Laws which can be Deduced from it for the Theory of Heat", Clausius begins by citing the mechanical equivalent of heat results of Holtzmann, Mayer, and Joule, but then then applies its logic to the heat-generating working action of the "working body" and the likely changes that result in the condition of the working body in a Carnot cycle. In this direction, by 1854 Clausius had enunciated what he called the theorem of the equivalence of heat and work as such: [1]
“Mechanical work may be transformed into heat, and conversely heat into work, the magnitude of the one being always proportional to that of the other.”
This logic was then molded, via a number of arguments, into the (a) the conservation of energy and (b) the equivalence-value of all uncompensated transformations (entropy); or what are commonly known as the first and second laws of thermodynamics, respectively.
References
1. (a) Clausius, Rudolf. (1850). "On the Motive Power of Heat, and on the Laws which may be deduced from it for the Theory of Heat", Poggendorff's Annalen der Physick, LXXIX, 368, 500.
(b) Clausius, Rudolf. (1865). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
2. McCulloch, Richard S. (1876). Treatise on the Mechanical Theory of Heat - and its Applications to the Steam-Engine, etc. New York: D. Van Nostrand Publishers.
3. Joule, James P. (1845). "On the Mechanical Equivalent of Heat", Brit. Assoc. Rep., trans. Chemical Sect, p.31, read before the British Association at Cambridge, June.
4. Milestones in Thermodynamics – Thermal Physics, University of Notre Dame.
5. (a) Mayer, J. Robert. (1842). “Remarks on the Forces of Inorganic Nature”. Annalender Chemie und Pharmacie, Justin von Liebigs’ journal.
(b) Caneva, Kenneth L. (1993). Robert Mayer and the Conservation of Energy, (index: “heat: mechanical equivalence of, pgs. 25, 27-28, 37-38, 194, 233-34, 252, 261-62). Princeton, New Jersey: Princeton University Press.
6. Colding, Ludwig A. (1843). "Nogle saetninger om kraefterne" ("Theses concerning force"), read at the Royal Danish Academy of Sciences and Letters, published as Colding (1856).
7. (a) Dahl, P.F. (1981). "Colding, Ludwig August" in Gillespie, C.C. (ed.) (1981). Dictionary of Scientific Biography, Supplement I, New York: Charles Screibner's Sons, 84-87.
(b) Joule, James P. (1850). Philosophical Transactions of the Royal Society of London 140(1): 61-82.
8. Holtzmann, Carl von. (1845). “Ueber die Warme und Elaslicitat der gase und Dampfe” (“On the Heat and elasticity of Gases and Vapours”), Mannheim: Taylor’s Scientific Memoirs, iv. 189; also Pogg. Ann., vol. 72a.
9. Marey, Étienne-Jules. (1973). La Machine Animale (Animal Mechanism: A Treatise on Terrestrial and Aërial Locomotion), (pg. 13-18). D. Appleton and Co.
10. Daintith, John: Editor. (2005). Oxford Dictionary of Science, 5th ed. New York: Oxford University Press.
Latest page update: made by Sadi-Carnot
, Apr 16 2008, 10:33 PM EDT
(about this update
About This Update
Moved from: Key terms
- Sadi-Carnot
No content added or deleted.
- complete history)
Moved from: Key terms
- Sadi-Carnot
No content added or deleted.
- complete history)
More Info: links to this page