Miscela gassosa - Wikipedia

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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">nascondi</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inizio</div> </a> </li> <li id="toc-Miscele_reali_e_miscele_ideali" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Miscele_reali_e_miscele_ideali"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Miscele reali e miscele ideali</span> </div> </a> <ul id="toc-Miscele_reali_e_miscele_ideali-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Comportamento_pVT_delle_miscele_gassose_reali" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Comportamento_pVT_delle_miscele_gassose_reali"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Comportamento pVT delle miscele gassose reali</span> </div> </a> <button aria-controls="toc-Comportamento_pVT_delle_miscele_gassose_reali-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Attiva/disattiva la sottosezione Comportamento pVT delle miscele gassose reali</span> </button> <ul id="toc-Comportamento_pVT_delle_miscele_gassose_reali-sublist" class="vector-toc-list"> <li id="toc-Approssimazione_di_Dalton" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Approssimazione_di_Dalton"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Approssimazione di Dalton</span> </div> </a> <ul id="toc-Approssimazione_di_Dalton-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Approssimazione_di_Amagat" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Approssimazione_di_Amagat"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Approssimazione di Amagat</span> </div> </a> <ul id="toc-Approssimazione_di_Amagat-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Regole_di_miscela" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Regole_di_miscela"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Regole di miscela</span> </div> </a> <ul id="toc-Regole_di_miscela-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Metodo_delle_costanti_pseudocritiche" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Metodo_delle_costanti_pseudocritiche"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Metodo delle costanti pseudocritiche</span> </div> </a> <ul id="toc-Metodo_delle_costanti_pseudocritiche-sublist" class="vector-toc-list"> <li id="toc-Regola_di_Kay" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Regola_di_Kay"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4.1</span> <span>Regola di Kay</span> </div> </a> <ul id="toc-Regola_di_Kay-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Regola_di_Lorentz_&_Berthelot" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Regola_di_Lorentz_&_Berthelot"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4.2</span> <span>Regola di Lorentz & Berthelot</span> </div> </a> <ul id="toc-Regola_di_Lorentz_&_Berthelot-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voci_correlate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voci_correlate"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Voci correlate</span> </div> </a> <ul id="toc-Voci_correlate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Collegamenti_esterni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Collegamenti_esterni"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Collegamenti esterni</span> </div> </a> <ul id="toc-Collegamenti_esterni-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Indice" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Mostra/Nascondi l'indice" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Mostra/Nascondi l'indice</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Miscela gassosa</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Questa voce esiste solo in questa lingua. 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class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Miscela_gassosa&veaction=edit" title="Modifica questa pagina [v]" accesskey="v"><span>Modifica</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Miscela_gassosa&action=edit" title="Modifica il wikitesto di questa pagina [e]" accesskey="e"><span>Modifica wikitesto</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Miscela_gassosa&action=history" title="Versioni precedenti di questa pagina [h]" accesskey="h"><span>Cronologia</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Strumenti pagine"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Strumenti" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Strumenti</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Strumenti</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">nascondi</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Altre opzioni" > <div class="vector-menu-heading"> Azioni </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Miscela_gassosa"><span>Leggi</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Miscela_gassosa&veaction=edit" title="Modifica questa pagina [v]" accesskey="v"><span>Modifica</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Miscela_gassosa&action=edit" title="Modifica il wikitesto di questa pagina [e]" accesskey="e"><span>Modifica wikitesto</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Miscela_gassosa&action=history"><span>Cronologia</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generale </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciale:PuntanoQui/Miscela_gassosa" title="Elenco di tutte le pagine che sono collegate a questa [j]" accesskey="j"><span>Puntano qui</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciale:ModificheCorrelate/Miscela_gassosa" rel="nofollow" title="Elenco delle ultime modifiche alle pagine collegate a questa [k]" accesskey="k"><span>Modifiche correlate</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speciale:PagineSpeciali" title="Elenco di tutte le pagine speciali [q]" accesskey="q"><span>Pagine speciali</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Miscela_gassosa&oldid=117423759" title="Collegamento permanente a questa versione di questa pagina"><span>Link permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Miscela_gassosa&action=info" title="Ulteriori informazioni su questa pagina"><span>Informazioni pagina</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speciale:Cita&page=Miscela_gassosa&id=117423759&wpFormIdentifier=titleform" title="Informazioni su come citare questa pagina"><span>Cita questa voce</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speciale:UrlShortener&url=https%3A%2F%2Fit.wikipedia.org%2Fwiki%2FMiscela_gassosa"><span>Ottieni URL breve</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speciale:QrCode&url=https%3A%2F%2Fit.wikipedia.org%2Fwiki%2FMiscela_gassosa"><span>Scarica codice QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Stampa/esporta </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speciale:Libro&bookcmd=book_creator&referer=Miscela+gassosa"><span>Crea un libro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciale:DownloadAsPdf&page=Miscela_gassosa&action=show-download-screen"><span>Scarica come PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Miscela_gassosa&printable=yes" title="Versione stampabile di questa pagina [p]" accesskey="p"><span>Versione stampabile</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In altri progetti </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q3858977" title="Collegamento all'elemento connesso dell'archivio dati [g]" accesskey="g"><span>Elemento Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Strumenti pagine"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspetto"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspetto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">nascondi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Da Wikipedia, l'enciclopedia libera.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="it" dir="ltr"><p>Una <b>miscela gassosa</b> è una <a href="/wiki/Miscela_(chimica)" class="mw-redirect" title="Miscela (chimica)">miscela</a> di due o più <a href="/wiki/Gas" title="Gas">gas</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Miscele_reali_e_miscele_ideali">Miscele reali e miscele ideali</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=1" title="Modifica la sezione Miscele reali e miscele ideali" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=1" title="Edit section's source code: Miscele reali e miscele ideali"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Una miscela gassosa è detta <b>reale</b> quando gli effetti di miscelamento sono non nulli, ovvero quando il volume della miscela gassosa è diverso dalla somma dei volumi che avrebbero i singoli gas se non fossero miscelati, considerati alla <a href="/wiki/Pressione" title="Pressione">pressione</a> pari alla loro <a href="/wiki/Pressione_parziale" class="mw-redirect" title="Pressione parziale">pressione parziale</a> nella miscela. Nel caso contrario la miscela è detta <b>ideale</b> (secondo Lewis e Randall).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Comportamento_pVT_delle_miscele_gassose_reali">Comportamento pVT delle miscele gassose reali</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=2" title="Modifica la sezione Comportamento pVT delle miscele gassose reali" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=2" title="Edit section's source code: Comportamento pVT delle miscele gassose reali"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nella letteratura scientifica non si trovano molti dati riguardo al <a href="/wiki/Stato_termodinamico" title="Stato termodinamico">comportamento pVT</a> delle miscele gassose, essendo possibile incontrare un'infinità di miscele gassose per dati componenti. Sono presenti in letteratura solo alcuni casi particolari in cui le concentrazioni dei componenti in miscela sono fissate, ad esempio l'<a href="/wiki/Aria" title="Aria">aria</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Si ricorre quindi ai seguenti metodi per studiare il comportamento pVT di una miscela gassosa reale: </p> <ul><li>approssimazione di Dalton</li> <li>approssimazione di Amagat</li> <li>regole di miscela</li> <li>metodo delle costanti pseudocritiche.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Approssimazione_di_Dalton">Approssimazione di Dalton</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=3" title="Modifica la sezione Approssimazione di Dalton" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=3" title="Edit section's source code: Approssimazione di Dalton"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nell'approssimazione di Dalton, basata sulla <a href="/wiki/Legge_delle_pressioni_parziali" title="Legge delle pressioni parziali">legge delle pressioni parziali</a>, il <a href="/wiki/Fattore_di_comprimibilit%C3%A0" title="Fattore di comprimibilità">fattore di comprimibilità</a> <i>Z</i> viene ricavato dall'espressione seguente: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z=\sum _{i=1}^{n}y_{i}Z_{i}|_{T,v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>v</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z=\sum _{i=1}^{n}y_{i}Z_{i}|_{T,v}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bef437e2a20a9a110212f674334fdf31f4c838c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:16.138ex; height:6.843ex;" alt="{\displaystyle Z=\sum _{i=1}^{n}y_{i}Z_{i}|_{T,v}}"></span></dd></dl> <p>in cui si assume che il componente i-esimo occupa l'intero volume della miscela a temperatura <i>T</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Approssimazione_di_Amagat">Approssimazione di Amagat</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=4" title="Modifica la sezione Approssimazione di Amagat" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=4" title="Edit section's source code: Approssimazione di Amagat"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nell'approssimazione di Amagat, basata sulla <a href="/wiki/Legge_di_Amagat" title="Legge di Amagat">legge di Amagat</a>, il fattore di comprimibilità <i>Z</i> viene ricavato dall'espressione seguente: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z=\sum _{i=1}^{n}y_{i}Z_{i}|_{p,T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z=\sum _{i=1}^{n}y_{i}Z_{i}|_{p,T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34779750ab1b453ac0f24eecd6f9b30f99ad4ada" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:16.167ex; height:6.843ex;" alt="{\displaystyle Z=\sum _{i=1}^{n}y_{i}Z_{i}|_{p,T}}"></span></dd></dl> <p>in cui si assume che il componente i-esimo esiste alla pressione <i>p</i> e temperatura <i>T</i> della miscela. </p> <div class="mw-heading mw-heading3"><h3 id="Regole_di_miscela">Regole di miscela</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=5" title="Modifica la sezione Regole di miscela" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=5" title="Edit section's source code: Regole di miscela"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nel caso di miscele binarie<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>, le regole di miscela (in inglese "mixing rules" o "combination rules") stabiliscono un legame tra i coefficienti <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="{\displaystyle a_{i}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40a8c2db2990a53c683e75961826167c5adac7c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.797ex; height:2.509ex;" alt="{\displaystyle b_{i}}"></span> utilizzati nelle equazioni di stato cubiche, relativi al componente i-esimo e i cosiddetti "cross-coefficients" <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebea6cd2813c330c798921a2894b358f7b643917" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.707ex; height:2.343ex;" alt="{\displaystyle a_{ij}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b_{ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/843634a5063d0ce92ab37442cd5d0f845ef8317a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.475ex; height:2.843ex;" alt="{\displaystyle b_{ij}}"></span>, relativi alla miscela binaria dei due componenti <i>i</i> e <i>j</i>. </p><p>Il coefficiente <i>a</i> è correlato alla <a href="/wiki/Pressione_di_coesione" class="mw-redirect" title="Pressione di coesione">pressione di coesione</a>, mentre il coefficiente <i>b</i> è il <a href="/wiki/Covolume" class="mw-redirect" title="Covolume">covolume</a>. Questi coefficienti descrivono lo scostamento della miscela dalle condizioni di idealità. </p><p>Il coefficiente <i>b</i> può essere determinato come: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=\sum _{i=1}^{n}y_{i}b_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=\sum _{i=1}^{n}y_{i}b_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42259c11d59e55d147c81968135f63999f552db1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:11.574ex; height:6.843ex;" alt="{\displaystyle b=\sum _{i=1}^{n}y_{i}b_{i}}"></span></dd></dl> <p>in cui <i>n</i> è il numero di componenti della miscela gassosa e <i>y<sub>i</sub></i> è la <a href="/wiki/Frazione_molare" title="Frazione molare">frazione molare</a> del componente i-esimo. </p><p>Il coefficiente <i>a</i> può essere ricavato in vari modi. Uno di questi e la cosiddetta "correzione di Zudkevich e Joffe": </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=\sum \sum y_{i}y_{j}a_{ij}=\sum \sum y_{i}y_{j}(a_{i}a_{j})^{0,5}(1-k_{ij})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mo>∑</mo> <mo>∑</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mo>∑</mo> <mo>∑</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mo>,</mo> <mn>5</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=\sum \sum y_{i}y_{j}a_{ij}=\sum \sum y_{i}y_{j}(a_{i}a_{j})^{0,5}(1-k_{ij})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3d5c0f4f84c374a5e8c960ed25fb500874fd6d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:49.89ex; height:3.843ex;" alt="{\displaystyle a=\sum \sum y_{i}y_{j}a_{ij}=\sum \sum y_{i}y_{j}(a_{i}a_{j})^{0,5}(1-k_{ij})}"></span></dd></dl> <p>in cui la costante <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9db60ff245b7d793444196f9f8f1c3f990180c7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.688ex; height:2.843ex;" alt="{\displaystyle k_{ij}}"></span> è tabellata, ed è nulla per miscele ideali o se uno dei componenti è l'<a href="/wiki/Idrogeno" title="Idrogeno">idrogeno</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Metodo_delle_costanti_pseudocritiche">Metodo delle costanti pseudocritiche</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=6" title="Modifica la sezione Metodo delle costanti pseudocritiche" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=6" title="Edit section's source code: Metodo delle costanti pseudocritiche"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Il metodo delle costanti pseudocritiche consiste nel descrivere il comportamento pVT di una miscela come se questa fosse un gas con costanti critiche <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/836639c3805ca867b1ff24dc6db7a6b24fc69158" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.203ex; height:2.009ex;" alt="{\displaystyle p_{c}}"></span> (<a href="/wiki/Pressione_critica" title="Pressione critica">pressione critica</a>) e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66261e3cbed8035b2bf7a9ccb878c786cf7556c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.302ex; height:2.509ex;" alt="{\displaystyle T_{c}}"></span> (<a href="/wiki/Temperatura_critica" title="Temperatura critica">temperatura critica</a>), correlate alle costanti critiche dei singoli componenti. Nel caso delle miscele si parla di "costanti pseudocritiche", in quanto corrispondono ad un gas fittizio. </p><p>Esistono vari modi (o "regole") per determinare le costanti pseudocritiche, ad esempio la "regola di Kay", la "regola di Prausnitz & Gunn" e la "regola di Lorentz & Berthelot". </p> <div class="mw-heading mw-heading4"><h4 id="Regola_di_Kay">Regola di Kay</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=7" title="Modifica la sezione Regola di Kay" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=7" title="Edit section's source code: Regola di Kay"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Diagramma_generalizzato_fattore_di_compressibilit%C3%A0.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Diagramma_generalizzato_fattore_di_compressibilit%C3%A0.jpg/400px-Diagramma_generalizzato_fattore_di_compressibilit%C3%A0.jpg" decoding="async" width="400" height="290" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Diagramma_generalizzato_fattore_di_compressibilit%C3%A0.jpg/600px-Diagramma_generalizzato_fattore_di_compressibilit%C3%A0.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Diagramma_generalizzato_fattore_di_compressibilit%C3%A0.jpg/800px-Diagramma_generalizzato_fattore_di_compressibilit%C3%A0.jpg 2x" data-file-width="950" data-file-height="689" /></a><figcaption>Diagramma generalizzato fattore di compressibilità.</figcaption></figure> <p>La "regola di Kay" afferma che: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{c}=\sum _{i=1}^{n}y_{i}T_{c,i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{c}=\sum _{i=1}^{n}y_{i}T_{c,i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da728706c9fb2b0e47d298e4051efdc2af3d4b01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:14.408ex; height:6.843ex;" alt="{\displaystyle T_{c}=\sum _{i=1}^{n}y_{i}T_{c,i}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{c}=\sum _{i=1}^{n}y_{i}p_{c,i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{c}=\sum _{i=1}^{n}y_{i}p_{c,i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f47be6b6a44ea8b4d3e6a6f25c46fad412712bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-left: -0.089ex; width:14.121ex; height:6.843ex;" alt="{\displaystyle p_{c}=\sum _{i=1}^{n}y_{i}p_{c,i}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{mix}=\sum y_{i}\omega _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mo>∑</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{mix}=\sum y_{i}\omega _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/746550b436d5ea43bb878b3863b1916c50e60a9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:15.653ex; height:3.843ex;" alt="{\displaystyle \omega _{mix}=\sum y_{i}\omega _{i}}"></span></dd></dl> <p>in cui <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e174c191a5ba3889c66597461ef260811cce0481" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.245ex; height:2.009ex;" alt="{\displaystyle \omega _{i}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{mix}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{mix}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/935538ca653c9cd724b5c1ac294c6ba440bc7a1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.628ex; height:2.009ex;" alt="{\displaystyle \omega _{mix}}"></span> rappresentano il <a href="/wiki/Fattore_acentrico" title="Fattore acentrico">fattore acentrico</a> del componente i-esimo e della miscela gassosa. </p><p>A partire dalle costanti pseudocritiche così ricavate si possono quindi determinare i coefficienti <i>a</i> e <i>b</i> (da sostituire nelle equazioni cubiche) oppure il "fattore di comprimibilità della miscela", definito come: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{mix}=Z^{0}+\omega Z^{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mo>+</mo> <mi>ω</mi> <msup> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{mix}=Z^{0}+\omega Z^{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a02d914adc911080a5c1c38f44ebf23ce1e6a42c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.68ex; height:3.009ex;" alt="{\displaystyle Z_{mix}=Z^{0}+\omega Z^{1}}"></span></dd></dl> <p>in cui <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z^{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z^{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55d38fc33d7f7d43b807ba8e0f54ba56741be5cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.763ex; height:2.676ex;" alt="{\displaystyle Z^{0}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z^{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z^{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/deb81b3c11c0b31215bd220c5b6767bdbfbd8eb1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.763ex; height:2.676ex;" alt="{\displaystyle Z^{1}}"></span> sono dei parametri che vengono determinati dal "diagramma generalizzato di Nelson-Obert" (o "diagramma generalizzato del fattore di compressibilità").<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Quest'ultima espressione è chiamata <i>correlazione di Lee-Kesler</i>, ed è una conseguenza del <a href="/wiki/Teorema_degli_stati_corrispondenti" title="Teorema degli stati corrispondenti">teorema degli stati corrispondenti</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Regola_di_Lorentz_&_Berthelot"><span id="Regola_di_Lorentz_.26_Berthelot"></span>Regola di Lorentz & Berthelot</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=8" title="Modifica la sezione Regola di Lorentz & Berthelot" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=8" title="Edit section's source code: Regola di Lorentz & Berthelot"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Secondo la "regola di Lorentz & Berthelot", le costanti pseudocritiche sono calcolate come: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{c,ij}=(T_{c,i}\cdot T_{c,j})^{0.5}(1-k_{ij})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>⋅</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0.5</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{c,ij}=(T_{c,i}\cdot T_{c,j})^{0.5}(1-k_{ij})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20dbec44428ab37eea0edcdc5a4c7484b9f616fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:28.188ex; height:3.343ex;" alt="{\displaystyle T_{c,ij}=(T_{c,i}\cdot T_{c,j})^{0.5}(1-k_{ij})}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{c,ij}={\frac {RT_{c,ij}Z_{c,ij}}{V_{c,ij}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{c,ij}={\frac {RT_{c,ij}Z_{c,ij}}{V_{c,ij}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b81883b7f564995a18a9474c16501e387de6f54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.075ex; height:6.176ex;" alt="{\displaystyle P_{c,ij}={\frac {RT_{c,ij}Z_{c,ij}}{V_{c,ij}}}}"></span></dd></dl> <p>in cui <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{c,ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{c,ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc19d79f94f6e5a51843a0d694a7a6958ab9541c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.858ex; height:2.843ex;" alt="{\displaystyle k_{c,ij}}"></span> è un parametro di interazione binaria tabellato, mentre il fattore di compressibilità critico di miscela <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{c,ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{c,ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2bd157a0a557a958a45ba7541fb7df59693fec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.234ex; height:2.843ex;" alt="{\displaystyle Z_{c,ij}}"></span> è calcolato come: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{c,ij}={\frac {Z_{c,i}+Z_{c,j}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{c,ij}={\frac {Z_{c,i}+Z_{c,j}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f83229e6d43549adb8b2e12b840e71aa90a08d49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.232ex; height:5.509ex;" alt="{\displaystyle Z_{c,ij}={\frac {Z_{c,i}+Z_{c,j}}{2}}}"></span></dd></dl> <p>mentre il volume critico della miscela è pari a: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{c,ij}=\left({\frac {V_{c,i}^{1/3}+V_{c,j}^{1/3}}{2}}\right)^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msubsup> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{c,ij}=\left({\frac {V_{c,i}^{1/3}+V_{c,j}^{1/3}}{2}}\right)^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/beec3e971db8bdfd28dce353956db19573e56fdc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:25.128ex; height:9.176ex;" alt="{\displaystyle V_{c,ij}=\left({\frac {V_{c,i}^{1/3}+V_{c,j}^{1/3}}{2}}\right)^{3}}"></span></dd></dl> <p>Una volta determinati <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{c,ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{c,ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2bd157a0a557a958a45ba7541fb7df59693fec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.234ex; height:2.843ex;" alt="{\displaystyle Z_{c,ij}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{c,ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{c,ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48b0e8ae83083ec56fbe5a8284345e754eaa3de6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.002ex; height:2.843ex;" alt="{\displaystyle V_{c,ij}}"></span>, si calcolano i valori delle costanti pseudocritiche, e quindi le costanti <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ij}^{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ij}^{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7758fdfdf2113473055c27c4cda3c96c6958cf2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:3.241ex; height:3.509ex;" alt="{\displaystyle B_{ij}^{0}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ij}^{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ij}^{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4dd357c9ebad1774216b0b76217c653e7feed1d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:3.241ex; height:3.509ex;" alt="{\displaystyle B_{ij}^{1}}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b176035c8c1d870be65f2d28da0483651ca9db4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.923ex; height:2.343ex;" alt="{\displaystyle \omega _{ij}}"></span> utilizzando le seguenti correlazioni analitiche: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ij}^{0}=0,083-{\frac {0,422}{T_{r,ij}^{1,6}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>083</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0</mn> <mo>,</mo> <mn>422</mn> </mrow> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>,</mo> <mn>6</mn> </mrow> </msubsup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ij}^{0}=0,083-{\frac {0,422}{T_{r,ij}^{1,6}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2cb8a52a5cb82befbe813ea84ae0b64fd65382b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:21.384ex; height:7.009ex;" alt="{\displaystyle B_{ij}^{0}=0,083-{\frac {0,422}{T_{r,ij}^{1,6}}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ij}^{1}=0,139-{\frac {0,172}{T_{r,ij}^{4,2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>139</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0</mn> <mo>,</mo> <mn>172</mn> </mrow> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> <mo>,</mo> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ij}^{1}=0,139-{\frac {0,172}{T_{r,ij}^{4,2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6858740de128a40f511bba3bd2e789de27a46b93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:21.384ex; height:7.009ex;" alt="{\displaystyle B_{ij}^{1}=0,139-{\frac {0,172}{T_{r,ij}^{4,2}}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{ij}={\frac {\omega _{i}+\omega _{j}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{ij}={\frac {\omega _{i}+\omega _{j}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67442470e604383908b7508e08789c01c4a0ea6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.299ex; height:5.343ex;" alt="{\displaystyle \omega _{ij}={\frac {\omega _{i}+\omega _{j}}{2}}}"></span></dd></dl> <p>e quindi: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ii}\left({\frac {P_{c,i}}{RT_{c,i}}}\right)=B_{i}^{0}+\omega _{i}B_{i}^{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mrow> <mi>R</mi> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ii}\left({\frac {P_{c,i}}{RT_{c,i}}}\right)=B_{i}^{0}+\omega _{i}B_{i}^{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/393d326a59031d760d508074fb35edfb9c910653" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:26.687ex; height:6.176ex;" alt="{\displaystyle B_{ii}\left({\frac {P_{c,i}}{RT_{c,i}}}\right)=B_{i}^{0}+\omega _{i}B_{i}^{1}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ij}\left({\frac {P_{c,ij}}{RT_{c,ij}}}\right)=B_{i}j^{0}+\omega _{i}jB_{i}j^{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mi>R</mi> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>,</mo> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>j</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ij}\left({\frac {P_{c,ij}}{RT_{c,ij}}}\right)=B_{i}j^{0}+\omega _{i}jB_{i}j^{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c95be66e96a1a8da05da045a33de5a3d2f238f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.948ex; height:6.176ex;" alt="{\displaystyle B_{ij}\left({\frac {P_{c,ij}}{RT_{c,ij}}}\right)=B_{i}j^{0}+\omega _{i}jB_{i}j^{1}}"></span></dd></dl> <p>si ricava quindi il coefficiente viriale <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B=\sum \sum y_{i}y_{j}B_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mo>∑</mo> <mo>∑</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B=\sum \sum y_{i}y_{j}B_{ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b23f20a6fa2b52e0ce8e502e50e4016951931562" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:19.576ex; height:3.843ex;" alt="{\displaystyle B=\sum \sum y_{i}y_{j}B_{ij}}"></span></dd></dl> <p>e si applica l'<a href="/w/index.php?title=Equazione_viriale&action=edit&redlink=1" class="new" title="Equazione viriale (la pagina non esiste)">equazione viriale</a> troncata (o "prima correlazione di Pitzer"): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z=1+{\frac {BP}{RT}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>B</mi> <mi>P</mi> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z=1+{\frac {BP}{RT}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/042b25a0b6413212d317847d26ecfc45d751a1b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.127ex; height:5.343ex;" alt="{\displaystyle Z=1+{\frac {BP}{RT}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=9" title="Modifica la sezione Note" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=9" title="Edit section's source code: Note"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1"><b>^</b></a> <span class="reference-text">Il concetto di "miscela reale" non va confuso con il concetto di miscela di <a href="/wiki/Gas_reale" title="Gas reale">gas reali</a>.</span> </li> <li id="cite_note-2"><a href="#cite_ref-2"><b>^</b></a> <span class="reference-text">Infatti l'aria è una miscela gassosa ben determinata, per cui si ha un "rapporto molare omogeneo", ovvero le concentrazioni dei vari componenti (<a href="/wiki/Azoto" title="Azoto">azoto</a> e <a href="/wiki/Ossigeno" title="Ossigeno">ossigeno</a> principalmente) sono fissate.</span> </li> <li id="cite_note-3"><a href="#cite_ref-3"><b>^</b></a> <span class="reference-text">ovvero a due componenti.</span> </li> <li id="cite_note-4"><a href="#cite_ref-4"><b>^</b></a> <span class="reference-text">Si parla in questo caso di "correlazione grafica".</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=10" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=10" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation libro" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) J. M. Smith, H.C.Van Ness; M. M. Abbot, <span style="font-style:italic;">Introduction to Chemical Engineering Thermodynamics</span>, 6ª ed., McGraw-Hill, 2000, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/0-07-240296-2" title="Speciale:RicercaISBN/0-07-240296-2">0-07-240296-2</a>.</cite></li> <li><cite class="citation libro" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a href="/wiki/Robert_H._Perry" title="Robert H. Perry">Robert Perry</a>, Don W. Green, <span style="font-style:italic;"><a href="/wiki/Perry%27s_Chemical_Engineers%27_Handbook" title="Perry's Chemical Engineers' Handbook">Perry's Chemical Engineers' Handbook</a></span>, 8ª ed., McGraw-Hill, 2007, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/0-07-142294-3" title="Speciale:RicercaISBN/0-07-142294-3">0-07-142294-3</a>.</cite></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=11" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=11" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Equazione_di_stato" title="Equazione di stato">Equazione di stato</a></li> <li><a href="/wiki/Fattore_di_comprimibilit%C3%A0" title="Fattore di comprimibilità">Fattore di comprimibilità</a></li> <li><a href="/wiki/Gas" title="Gas">Gas</a></li> <li><a href="/wiki/Gas_reale" title="Gas reale">Gas reale</a></li> <li><a href="/wiki/Miscela_(chimica)" class="mw-redirect" title="Miscela (chimica)">Miscela (chimica)</a></li> <li><a href="/wiki/Temperatura_critica" title="Temperatura critica">Temperatura critica</a></li> <li><a href="/wiki/Pressione_critica" title="Pressione critica">Pressione critica</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Miscela_gassosa&veaction=edit&section=12" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Miscela_gassosa&action=edit&section=12" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r140554517">.mw-parser-output .chiarimento{background:#ffeaea;color:#444444}.mw-parser-output .chiarimento-apice{color:#EE0700}@media screen{html.skin-theme-clientpref-night .mw-parser-output .chiarimento{background:rgba(179,36,36,0.21);color:inherit}html.skin-theme-clientpref-night .mw-parser-output .chiarimento-apice{color:#b32424}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .chiarimento{background:rgba(179,36,36,0.21);color:inherit}html.skin-theme-clientpref-os .mw-parser-output .chiarimento-apice{color:#b32424}}</style><span class="chiarimento" title="A volte può capitare che un link presente su Wikipedia non sia più raggiungibile. 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