Dlí Charles

Is é Dlí Charles ceann de dhlíthe na teirmidinimice, arb ionann é agus Dlí an Gháis Idéalaigh.

Is dlí turgnamhach gáis é (ar a dtugtar 'Dlí na dToirteanna' freisin) a chuireann síos ar an gcaoi a mbíonn claonadh ag gáis forbairt nuair a théitear iad. Is é atá i ráiteas nua-aimseartha ar dhlí Charles ná:

"Tá toirt aon ghás i gcomhréir dhíreach leis an teocht i gCailviní ag brú seasmhach."

Mar sin, méadaíonn toirt gáis de mhéid 1/273 dá thoirt ag 0 °C, in aghaidh gach céime a ardaítear an teocht, má bhíonn an brú tairseach; agus mar an gcéanna, crapfaidh sé de mhéid 1/273 dá thoirt ag 0 °C in aghaidh gach céime a íslítear an teocht.

Díorthú

Seo a leanas an fhoirmle de réir Dlí Charles:

{\frac {V}{T}}=k

inarb ionann:

V = toirt an gháis

T = teocht an gháis i gCeilviní

k = Luach tairisigh

Déantar cur síos sa dlí seo ar an gcaoi a fhorbraíonn gás de réir mar a mhéadaíonn an teocht; os a choinne sin, beidh laghdú ar an toirt mar thoradh ar laghdú teochta. Chun an tsubstaint chéanna a chur i gcomparáid faoi dhá shraith coinníollacha éagsúla, is féidir an dlí a scríobh mar seo a leanas:

${\frac {V_{1}}{T_{1}}}={\frac {V_{2}}{T_{2}}}\qquad {\text{nó}}\qquad {\frac {V_{2}}{V_{1}}}={\frac {T_{2}}{T_{1}}}\qquad {\text{nó}}\qquad V_{1}T_{2}=V_{2}T_{1}.$

Taispeánann an chothromóid gur de réir mar a mhéadaíonn an dearbhtheocht, méadaítear toirt an gháis i gcomhréir freisin.

Stair

Ainmníodh an dlí i ndiaidh an eolaí Jacques Charles, a chuir an dlí bunaidh le chéile ina shaothar neamhfhoilsithe ó na 1780idí.

In dhá cheann de shraith de cheithre aiste a cuireadh i láthair idir 2 agus 30 Deireadh Fómhair 1801,^[1] léirigh John Dalton trí thurgnamh gur fhorbair na gáis agus na gaile go léir a ndearna sé staidéar orthu an méid céanna idir dhá phointe teochta seasta. Dheimhnigh an fealsamh nádúrtha Francach Joseph Louis Gay-Lussac an fhionnachtain i gcur i láthair d’Institiúid Náisiúnta na Fraince an 31 Eanáir 1802,^[2] cé gur chuir sé an fionnachtain síos do shaothar neamhfhoilsithe ó na 1780idí le Jacques Charles. Rinne Guillaume Amontons ^[3] agus Francis Hauksbee cur síos ar na bunphrionsabail ^[4] céad bliain roimhe sin.

Ba é Dalton an chéad duine a léirigh go raibh feidhm ag an dlí go forleathan maidir le gach gás, agus maidir le gaile leachtanna so-ghalaithe má bhí an teocht i bhfad os cionn an fhiuchphointe. D’aontaigh Gay-Lussac leis.^[5] Ach le dhá thomhas amháin ag dhá phointe seasta teirmileictreach an uisce. ní raibh Gay-Lussac in ann a thaispeáint gur feidhm líneach í an chothromóid a bhaineann le toirt maidir le teocht. Ar fhorais mhatamaiticiúla amháin, ní cheadaíonn páipéar Gay-Lussac aon dlí ina luaitear an gaol líneach a shannadh. Is féidir príomhchonclúidí Dalton agus Gay-Lussac araon a chur in iúl go matamaiticiúil mar:

$V_{100}-V_{0}=kV_{0}\,$

i gcás gurb é V100 an toirt a áitíonn sampla áirithe gáis ag 100 ° C; Is é V0 an toirt a áitíonn an sampla céanna gáis ag 0 ° C; agus is tairiseach é k atá mar an gcéanna do gach gás ag brú seasmhach. Níl an teocht sa chothromóid seo agus mar sin níl aon bhaint aici leis an rud ar a tugadh Dlí Charles. Bhí luach Gay-Lussac do k (1⁄2.6666) comhionann le luach níos luaithe Dalton ar ghal agus thar a bheith gar do luach an lae inniu de 1⁄2.7315. Thug Gay-Lussac creidmheas don chothromóid seo do ráitis neamhfhoilsithe ag a chomhshaoránach Poblachtach J. Charles i 1787. Cheal taifead daingean, ní féidir an dlí gáis a bhaineann toirt le teocht a ainmniú i ndiaidh Charles. Bhí i bhfad níos mó scóipe ag tomhais Dalton maidir le teocht ná Gay-Lussac, ní amháin ag tomhas an toirt ag na pointí seasta uisce ach ag dhá phointe idirmheánacha freisin. Gan a bheith ar an eolas faoi mhíchruinneas teirmiméadar mearcair ag an am, a roinneadh ina chodanna comhionanna idir na pointí seasta, Dalton, tar éis teacht ar an tuairim in Aiste II, i gcás gaile, “leathnaíonn aon sreabhán leaisteach beagnach ar bhealach aonfhoirmeach go 1370 nó 1380 páirteanna faoi 180 céim (Fahrenheit) teasa ”, ní raibh sé in ann é a dhearbhú le haghaidh na ngás.

An gaol le dearbhnialas

Is cosúil go dtugann dlí Charles le tuiscint go dtitfidh toirt gáis go dearbhnialas ag teocht áirithe (−266.66 ° C de réir fhigiúirí Gay-Lussac) nó −273.15 ° C. Ba léir ina thuairisc gur thug Gay-Lussac le fios nach raibh an dlí infheidhmithe ag teochtaí ísle:

ach is féidir liom a lua nach féidir an chonclúid dheireanach seo a bheith fíor ach amháin fad a fhanfaidh na gaile comhbhrúite go hiomlán sa staid leaisteach; agus éilíonn sé seo go n-ardófar a dteocht go leor chun go mbeidh siad in ann an brú a sheasamh a fhágann go nglacfaidh siad leis an stát leachtach.^[6]

Ag teocht dearbhnialas, níl fuinneamh ar bith ag an ngás agus dá bhrí sin cuireann na móilíní srian ar ghluaiseacht. Ní raibh aon taithí ag Gay-Lussac ar aer leachtach (a ullmhaíodh den chéad uair i 1877), cé gur cosúil gur chreid sé (mar a rinne Dalton) go bhféadfaí na “gáis bhuana” mar aer agus hidrigin a leachtú. D'oibrigh Gay-Lussac freisin le gaile leachtanna so-ghalaithe chun dlí Charles a thaispeáint, agus bhí a fhios aige nach bhfuil feidhm ag an dlí díreach os cionn fiuchphointe an leachta:

Is féidir liom a rá, áfach, nuair nach bhfuil teocht an éitear ach beagán os cionn a fiuchphointe, go bhfuil a comhdhlúthú rud beag níos gasta ná aer atmaisféaraigh. Tá baint ag an bhfíric seo le feiniméan a thaispeánann go leor corp agus iad ag dul ón leacht go dtí an staid sholadach, ach nach bhfuil ábhartha a thuilleadh ag teochtaí cúpla céim os cionn an phointe a tharlaíonn an t-aistriú.^[6]

Ba é William Thomson (ar a tugadh an Tiarna Kelvin ina dhiaidh sin) an chéad duine a thug le fios teocht ag a bhféadfadh toirt an gháis teacht go dearbhnialas in 1848: ^[7]

Seo a mbeimis ag súil leis nuair a léirímid go gcaithfidh fuacht gan teorainn freagairt do líon teoranta céimeanna den aer-teirmiméadar faoi bhun an nialais; ós rud é má bhrúimid prionsabal docht na céime, a luaitear thuas, sách fada, ba cheart dúinn pointe a fhreagraíonn do mhéid an aeir a laghdú go dtí an neamhní, a bheadh marcáilte mar −273 ° den scála (−100 / .366, más .366 an chomhéifeacht forbartha); agus dá bhrí sin is pointe é −273 ° den aer-teirmiméadar nach féidir a bhaint amach ag aon teocht theoranta, cé chomh híseal.

Mar sin féin, sainmhíníodh an “dearbhnialas” ar scála teochta Ceilvin ar dtús i dtéarmaí Dara Dlí na Teirmidinimice, a ndearna Thomson féin cur síos air i 1852.^[8] Níor ghlac Thomson leis go raibh sé seo cothrom le “ pointe náid-toirte” de dhlí Charles, ach gur sholáthair dlí Charles an íosteocht a d’fhéadfaí a bhaint amach. Is féidir a thaispeáint go bhfuil an dá rud comhionann le dearcadh staidrimh Ludwig Boltzmann ar eantrópacht (1870).

Dúirt Charles freisin, áfach:

Méadaíonn nó laghdaíonn méid maise seasta de ghás tirim 1⁄273 uair an toirt ag 0 ° C in aghaidh gach ardú 1 ° C nó titim sa teocht. Mar seo:

V_{T}=V_{0}+({\tfrac {1}{273}}\times V_{0})\times T

V_{T}=V_{0}(1+{\tfrac {T}{273}})

i gcás gurb é V_T toirt an gháis ag teocht T, V₀ an toirt ag 0 °C.

An gaol le teoiric chinéiteach

Féach freisin

Tagairtí

↑ J. Dalton (1802), "Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air" and Essay IV. "On the expansion of elastic fluids by heat," Memoirs of the Literary and Philosophical Society of Manchester, vol. 8, pt. 2, pp. 550–74, 595–602.
↑ J. Dalton (1802), "Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air" and Essay IV. "On the expansion of elastic fluids by heat," Memoirs of the Literary and Philosophical Society of Manchester, vol. 8, pt. 2, pp. 550–74, 595–602.
↑
See:
- Amontons, G. (presented 1699, published 1732) "Moyens de substituer commodément l'action du feu à la force des hommes et des chevaux pour mouvoir les machines" (Ways to conveniently substitute the action of fire for the force of men and horses to power machines), Mémoires de l’Académie des sciences de Paris (presented 1699, published 1732), 112–26; see especially pp. 113–17.
- Amontons, G. (presented 1702, published 1743) "Discours sur quelques propriétés de l'Air, & le moyen d'en connoître la température dans tous les climats de la Terre" (Discourse on some properties of air and on the means of knowing the temperature in all climates of the Earth), Mémoires de l’Académie des sciences de Paris, 155–74.
- Review of Amontons' findings: "Sur une nouvelle proprieté de l'air, et une nouvelle construction de Thermométre" (On a new property of the air and a new construction of thermometer), Histoire de l'Academie royale des sciences, 1–8 (submitted: 1702 ; published: 1743).
↑ * Englishman Francis Hauksbee (1660–1713) independently also discovered Charles's law: Francis Hauksbee (1708) "An account of an experiment touching the different densities of air, from the greatest natural heat to the greatest natural cold in this climate," Curtha i gcartlann 2015-12-14 ar an Wayback Machine Philosophical Transactions of the Royal Society of London 26(315): 93–96.
↑ Gay-Lussac (1802), from p. 166:
"Si l'on divise l'augmentation totale de volume par le nombre de degrés qui l'ont produite ou par 80, on trouvera, en faisant le volume à la température 0 égal à l'unité, que l'augmentation de volume pour chaque degré est de 1 / 223.33 ou bien de 1 / 266.66 pour chaque degré du thermomètre centrigrade."
If one divides the total increase in volume by the number of degrees that produce it or by 80, one will find, by making the volume at the temperature 0 equal to unity (1), that the increase in volume for each degree is 1 / 223.33 or 1 / 266.66 for each degree of the centigrade thermometer.
From p. 174:
" … elle nous porte, par conséquent, à conclure que tous les gaz et toutes les vapeurs se dilatent également par les mêmes degrés de chaleur."
… it leads us, consequently, to conclude that all gases and all vapors expand equally [when subjected to] the same degrees of heat.
↑ ^6.0 ^6.1 Earráid leis an lua: Invalid <ref> tag; no text was provided for refs named GL02
↑ Thomson, William (1848), "On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations", Philosophical Magazine: 100–06.
↑ Thomson, William (1852), "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam", Philosophical Magazine, 4. Extract.

[1] J. Dalton (1802), "Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air" and Essay IV. "On the expansion of elastic fluids by heat," Memoirs of the Literary and Philosophical Society of Manchester, vol. 8, pt. 2, pp. 550–74, 595–602.

[2] J. Dalton (1802), "Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air" and Essay IV. "On the expansion of elastic fluids by heat," Memoirs of the Literary and Philosophical Society of Manchester, vol. 8, pt. 2, pp. 550–74, 595–602.

[Amontons-3] See:
Amontons, G. (presented 1699, published 1732) "Moyens de substituer commodément l'action du feu à la force des hommes et des chevaux pour mouvoir les machines" (Ways to conveniently substitute the action of fire for the force of men and horses to power machines), Mémoires de l’Académie des sciences de Paris (presented 1699, published 1732), 112–26; see especially pp. 113–17.

Amontons, G. (presented 1702, published 1743) "Discours sur quelques propriétés de l'Air, & le moyen d'en connoître la température dans tous les climats de la Terre" (Discourse on some properties of air and on the means of knowing the temperature in all climates of the Earth), Mémoires de l’Académie des sciences de Paris, 155–74.

Review of Amontons' findings: "Sur une nouvelle proprieté de l'air, et une nouvelle construction de Thermométre" (On a new property of the air and a new construction of thermometer), Histoire de l'Academie royale des sciences, 1–8 (submitted: 1702 ; published: 1743).

[4] Amontons, G. (presented 1699, published 1732) "Moyens de substituer commodément l'action du feu à la force des hommes et des chevaux pour mouvoir les machines" (Ways to conveniently substitute the action of fire for the force of men and horses to power machines), Mémoires de l’Académie des sciences de Paris (presented 1699, published 1732), 112–26; see especially pp. 113–17.

[5] Amontons, G. (presented 1702, published 1743) "Discours sur quelques propriétés de l'Air, & le moyen d'en connoître la température dans tous les climats de la Terre" (Discourse on some properties of air and on the means of knowing the temperature in all climates of the Earth), Mémoires de l’Académie des sciences de Paris, 155–74.

[6] Review of Amontons' findings: "Sur une nouvelle proprieté de l'air, et une nouvelle construction de Thermométre" (On a new property of the air and a new construction of thermometer), Histoire de l'Academie royale des sciences, 1–8 (submitted: 1702 ; published: 1743).

[Hauksbee-4] * Englishman Francis Hauksbee (1660–1713) independently also discovered Charles's law: Francis Hauksbee (1708) "An account of an experiment touching the different densities of air, from the greatest natural heat to the greatest natural cold in this climate," Curtha i gcartlann 2015-12-14 ar an Wayback Machine Philosophical Transactions of the Royal Society of London 26(315): 93–96.

[5] Gay-Lussac (1802), from p. 166:
"Si l'on divise l'augmentation totale de volume par le nombre de degrés qui l'ont produite ou par 80, on trouvera, en faisant le volume à la température 0 égal à l'unité, que l'augmentation de volume pour chaque degré est de 1 / 223.33 ou bien de 1 / 266.66 pour chaque degré du thermomètre centrigrade."
If one divides the total increase in volume by the number of degrees that produce it or by 80, one will find, by making the volume at the temperature 0 equal to unity (1), that the increase in volume for each degree is 1 / 223.33 or 1 / 266.66 for each degree of the centigrade thermometer.
From p. 174:
" … elle nous porte, par conséquent, à conclure que tous les gaz et toutes les vapeurs se dilatent également par les mêmes degrés de chaleur."
… it leads us, consequently, to conclude that all gases and all vapors expand equally [when subjected to] the same degrees of heat.

[GL02-6] 6.0 ^6.1 Earráid leis an lua: Invalid <ref> tag; no text was provided for refs named GL02

[Kelvin48-7] Thomson, William (1848), "On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations", Philosophical Magazine: 100–06.

[8] Thomson, William (1852), "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam", Philosophical Magazine, 4. Extract.

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