Apskatīt Ideālas gāzes likums izejas kodu

[[File:Ideal gas isotherms.svg|thumb|Ideālās gāzes izotermas]]
'''Ideālas gāzes likums''' ir hipotētiskās [[ideāla gāze|ideālās gāzes]] stāvokļa vienādojums. To var izmantot arī [[reāla gāze|reālām gāzēm]] zemā [[spiediens|spiedienā]] un augstā [[temperatūra|temperatūrā]], lai noteiktu sakarību starp temperatūru, spiedienu un tilpumu. Tas ir [[Boila—Mariota likums|Boila—Mariota]], [[Šarla likums|Šarla]] un [[Gē-Lisaka likums|Gē-Lisaka likumu]] apvienojums ar [[Avogadro likums|Avogadro likumu]].

Pirmais to izteica francūzis [[Benuā Klapeirons]] (''Benoît Émile Clapeyron'') 1834. gadā.<ref>{{Cite journal | author = Clapeyron, E. | authorlink = Benoît Paul Émile Clapeyron | year = 1834 | title = Mémoire sur la puissance motrice de la chaleur | journal = [[Journal de l'École Polytechnique]] | volume = XIV | pages = 153–90}} {{Fr icon}} [http://gallica.bnf.fr/ark:/12148/bpt6k4336791/f157.table Facsimile at the Bibliothèque nationale de France (pp.&nbsp;153–90).]</ref> 1874. gadā krievs [[Dmitrijs Mendeļejevs]] likumā ieviesa universālo [[Gāzu konstante|gāzu konstanti]] ''R'', tā aizvietojot lielo daudzumu specifisko gāzu konstanšu.<ref>{{Cite journal | author = Mendeleev, D. I. | authorlink = Dmitri Mendeleev | year = 1874 | title = О сжимаемости газов (On the compressibility of gases) | journal = [[Russian Journal of Chemical Society and the Physical Society]] | volume = 6 | pages = 309–352 }}  {{Ru icon}}  (From the Laboratory of the University of St. Petersburg).</ref><ref>{{Cite journal | author = Mendeleev, D. I. | authorlink = Dmitri Mendeleev | year = 1875 | title = Об упругости газов (On the elasticity of gases) }}  {{Ru icon}} [http://gallica.bnf.fr/ark:/12148/bpt6k95208b.r=mendeleev.langEN Facsimile at the Bibliothèque nationale de France]</ref><ref>{{Cite journal | author = Mendeleef D. | authorlink = Dmitri Mendeleev | year = 1877 | title = Researches on Mariotte's Law | journal = [[Nature (journal)|Nature]] | volume = 15 (388) | pages = 498–500 }}  doi: 10.1038/015498a0.</ref>

== Vienādojums ==
Ierastais matemātiskais ideālās gāzes likuma pieraksts ir šāds:

:<math>pV=nRT\,</math>

kur:
* ''p'' — gāzes [[spiediens]] ([[Paskāls|Pa]])
* ''V'' — gāzes [[tilpums]] ([[kubikmetrs|m<sup>3</sup>]])
* ''n'' — [[vielas daudzums]] ([[mols|mol]])
* ''R'' — universālā [[gāzu konstante]]
* ''T'' — gāzes absolūtā [[temperatūra]] ([[Kelvins|K]])

=== Molārā forma ===
Aizvietojot ''n'' ar ''m / M'', iegūst šādu vienādojumu, kā arī ieviešot [[blīvums|blīvumu]] ''ρ'' = ''m''/''V'':

: <math>\ pV = \frac{m}{M}RT </math>
: <math>\ p = \rho \frac{R}{M}T </math>

kur:
* ''m'' — gāzes [[masa]] ([[grams|g]]) 
* ''M'' — gāzes [[molmasa]] ([[grams|g]]/[[mols|mol]])
* ''ρ'' — gāzes [[blīvums]] ([[kilograms|kg]]/[[kvadrātmetrs|m<sup>3</sup>]])

=== Statistiskā mehānika ===
Statistiskajā mehānikā ideālās gāzes likumu pieraksta šādi:

: <math>\ pV = NkT</math>

* ''N'' — koncentrācija
* ''k'' — [[Bolcmaņa konstante]]

== Termodinamiskie procesi ==
{| class="wikitable"
|-
! Process
! Konstantais<br/>lielums
! Zināmā<br/>attiecība
! P<sub>2</sub>
! V<sub>2</sub>
! T<sub>2</sub>
|-
|rowspan="2"|[[Izobārisks process]]
|rowspan="2"| <center>Spiediens</center>
| <center>V<sub>2</sub>/V<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>
| V<sub>2</sub> = V<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)
| T<sub>2</sub> = T<sub>1</sub>(V<sub>2</sub>/V<sub>1</sub>)
|-
| <center>T<sub>2</sub>/T<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>
| V<sub>2</sub> = V<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)
| T<sub>2</sub> = T<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)
|-
|rowspan="2"| [[Izohorisks process]]
|rowspan="2"| <center>Tilpums</center>
| <center>P<sub>2</sub>/P<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>(P<sub>2</sub>/P<sub>1</sub>)
| V<sub>2</sub> = V<sub>1</sub>
| T<sub>2</sub> = T<sub>1</sub>(P<sub>2</sub>/P<sub>1</sub>)
|-
| <center>T<sub>2</sub>/T<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)
| V<sub>2</sub> = V<sub>1</sub>
| T<sub>2</sub> = T<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)
|-
|rowspan="2"| [[Izotermisks process]]
|rowspan="2"| <center>&nbsp;Temperatūra&nbsp;</center>
| <center>P<sub>2</sub>/P<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>(P<sub>2</sub>/P<sub>1</sub>)
| V<sub>2</sub> = V<sub>1</sub>/(P<sub>2</sub>/P<sub>1</sub>)
| T<sub>2</sub> = T<sub>1</sub>
|-
| <center>V<sub>2</sub>/V<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>/(V<sub>2</sub>/V<sub>1</sub>)
| V<sub>2</sub> = V<sub>1</sub>(V<sub>2</sub>/V<sub>1</sub>)
| T<sub>2</sub> = T<sub>1</sub>
|-
|rowspan="3"| [[Izentropisks process]]<br>(atgriezenisks [[adiabātisks process]])
|rowspan="3"| <center>[[Entropija]]</center>
| <center>P<sub>2</sub>/P<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>(P<sub>2</sub>/P<sub>1</sub>)
| V<sub>2</sub> = V<sub>1</sub>(P<sub>2</sub>/P<sub>1</sub>)<sup>(−1/γ)</sup>
| T<sub>2</sub> = T<sub>1</sub>(P<sub>2</sub>/P<sub>1</sub>)<sup>(1 − 1/γ)</sup>
|-
| <center>V<sub>2</sub>/V<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>(V<sub>2</sub>/V<sub>1</sub>)<sup>−γ</sup>
| V<sub>2</sub> = V<sub>1</sub>(V<sub>2</sub>/V<sub>1</sub>)
| T<sub>2</sub> = T<sub>1</sub>(V<sub>2</sub>/V<sub>1</sub>)<sup>(1 − γ)</sup>
|-
| <center>T<sub>2</sub>/T<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)<sup>γ/(γ − 1)</sup>
| V<sub>2</sub> = V<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)<sup>1/(1 − γ) </sup>
| T<sub>2</sub> = T<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)
|-
|rowspan="3"| [[Politropisks process]]<br>
|rowspan="3"| <center>P V<sup>n</sup></center>
| <center>P<sub>2</sub>/P<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>(P<sub>2</sub>/P<sub>1</sub>)
| V<sub>2</sub> = V<sub>1</sub>(P<sub>2</sub>/P<sub>1</sub>)<sup>(-1/n)</sup>
| T<sub>2</sub> = T<sub>1</sub>(P<sub>2</sub>/P<sub>1</sub>)<sup>(1 - 1/n)</sup>
|-
| <center>V<sub>2</sub>/V<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>(V<sub>2</sub>/V<sub>1</sub>)<sup>−n</sup>
| V<sub>2</sub> = V<sub>1</sub>(V<sub>2</sub>/V<sub>1</sub>)
| T<sub>2</sub> = T<sub>1</sub>(V<sub>2</sub>/V<sub>1</sub>)<sup>(1−n)</sup>
|-
| <center>T<sub>2</sub>/T<sub>1</sub></center>
| P<sub>2</sub> = P<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)<sup>n/(n − 1)</sup>
| V<sub>2</sub> = V<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)<sup>1/(1 − n) </sup>
| T<sub>2</sub> = T<sub>1</sub>(T<sub>2</sub>/T<sub>1</sub>)
|}

== Atsauces ==
{{Atsauces}}

== Ārējās saites ==
* [http://www.webqc.org/ideal_gas_law.html Ideālas gāzes stāvokļa vienādojuma kalkulators]


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[[Kategorija:Gāzu likumi]]