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Disponibile in 25 lingue" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-25" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">25 lingue</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AE%D8%A7%D8%B5%D9%8A%D8%A9_%D9%85%D9%83%D8%AB%D9%81%D8%A9_%D9%88%D8%AE%D8%A7%D8%B5%D9%8A%D8%A9_%D8%B4%D9%85%D9%88%D9%84%D9%8A%D8%A9" title="خاصية مكثفة وخاصية شمولية - arabo" lang="ar" hreflang="ar" data-title="خاصية مكثفة وخاصية شمولية" data-language-autonym="العربية" data-language-local-name="arabo" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Propiedaes_intensives_y_estensives" title="Propiedaes intensives y estensives - asturiano" lang="ast" hreflang="ast" data-title="Propiedaes intensives y estensives" data-language-autonym="Asturianu" data-language-local-name="asturiano" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%82%E0%A6%95%E0%A7%80%E0%A6%B0%E0%A7%8D%E0%A6%A3_%E0%A6%93_%E0%A6%AC%E0%A6%BF%E0%A6%95%E0%A7%80%E0%A6%B0%E0%A7%8D%E0%A6%A3_%E0%A6%A7%E0%A6%B0%E0%A7%8D%E0%A6%AE%E0%A6%B8%E0%A6%AE%E0%A7%82%E0%A6%B9" title="সংকীর্ণ ও বিকীর্ণ ধর্মসমূহ - bengalese" lang="bn" hreflang="bn" data-title="সংকীর্ণ ও বিকীর্ণ ধর্মসমূহ" data-language-autonym="বাংলা" data-language-local-name="bengalese" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Propietats_intensives_i_extensives" title="Propietats intensives i extensives - catalano" lang="ca" hreflang="ca" data-title="Propietats intensives i extensives" data-language-autonym="Català" data-language-local-name="catalano" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Intensive_og_ekstensive_egenskaber" title="Intensive og ekstensive egenskaber - danese" lang="da" hreflang="da" data-title="Intensive og ekstensive egenskaber" data-language-autonym="Dansk" data-language-local-name="danese" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Intensive_und_extensive_Gr%C3%B6%C3%9Fen" title="Intensive und extensive Größen - tedesco" lang="de" hreflang="de" data-title="Intensive und extensive Größen" data-language-autonym="Deutsch" data-language-local-name="tedesco" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Intensive_and_extensive_properties" title="Intensive and extensive properties - inglese" lang="en" hreflang="en" data-title="Intensive and extensive properties" data-language-autonym="English" data-language-local-name="inglese" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Propiedades_intensivas_y_extensivas" title="Propiedades intensivas y extensivas - spagnolo" lang="es" hreflang="es" data-title="Propiedades intensivas y extensivas" data-language-autonym="Español" data-language-local-name="spagnolo" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AE%D9%88%D8%A7%D8%B5_%D8%B4%D8%AF%D8%AA%DB%8C_%D9%88_%D9%85%D9%82%D8%AF%D8%A7%D8%B1%DB%8C" title="خواص شدتی و مقداری - persiano" lang="fa" hreflang="fa" data-title="خواص شدتی و مقداری" data-language-autonym="فارسی" data-language-local-name="persiano" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Intensiivi-_ja_ekstensiivisuureet" title="Intensiivi- ja ekstensiivisuureet - finlandese" lang="fi" hreflang="fi" data-title="Intensiivi- ja ekstensiivisuureet" data-language-autonym="Suomi" data-language-local-name="finlandese" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Extensivit%C3%A9_et_intensivit%C3%A9_(physique)" title="Extensivité et intensivité (physique) - francese" lang="fr" hreflang="fr" data-title="Extensivité et intensivité (physique)" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%93%D7%9C%D7%99%D7%9D_%D7%90%D7%A7%D7%A1%D7%98%D7%A0%D7%A1%D7%99%D7%91%D7%99%D7%99%D7%9D_%D7%95%D7%90%D7%99%D7%A0%D7%98%D7%A0%D7%A1%D7%99%D7%91%D7%99%D7%99%D7%9D" title="גדלים אקסטנסיביים ואינטנסיביים - ebraico" lang="he" hreflang="he" data-title="גדלים אקסטנסיביים ואינטנסיביים" data-language-autonym="עברית" data-language-local-name="ebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A4%BE%E0%A4%B0%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%AE%E0%A4%95_%E0%A4%A4%E0%A4%A5%E0%A4%BE_%E0%A4%85%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A4%BE%E0%A4%B0%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%AE%E0%A4%95_%E0%A4%97%E0%A5%81%E0%A4%A3%E0%A4%A7%E0%A4%B0%E0%A5%8D%E0%A4%AE" title="विस्तारात्मक तथा अविस्तारात्मक गुणधर्म - hindi" lang="hi" hreflang="hi" data-title="विस्तारात्मक तथा अविस्तारात्मक गुणधर्म" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sifat_ekstensif_dan_intensif" title="Sifat ekstensif dan intensif - indonesiano" lang="id" hreflang="id" data-title="Sifat ekstensif dan intensif" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%A4%BA%E9%87%8F%E6%80%A7%E3%81%A8%E7%A4%BA%E5%BC%B7%E6%80%A7" title="示量性と示強性 - giapponese" lang="ja" hreflang="ja" data-title="示量性と示強性" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%84%B8%EA%B8%B0_%EC%84%B1%EC%A7%88%EA%B3%BC_%ED%81%AC%EA%B8%B0_%EC%84%B1%EC%A7%88" title="세기 성질과 크기 성질 - coreano" lang="ko" hreflang="ko" data-title="세기 성질과 크기 성질" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Intensive_og_ekstensive_egenskaper" title="Intensive og ekstensive egenskaper - norvegese bokmål" lang="nb" hreflang="nb" data-title="Intensive og ekstensive egenskaper" data-language-autonym="Norsk bokmål" data-language-local-name="norvegese bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Propriedades_extensivas_e_intensivas" title="Propriedades extensivas e intensivas - portoghese" lang="pt" hreflang="pt" data-title="Propriedades extensivas e intensivas" data-language-autonym="Português" data-language-local-name="portoghese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Propriet%C4%83%C8%9Bi_intensive_%C8%99i_extensive" title="Proprietăți intensive și extensive - rumeno" lang="ro" hreflang="ro" data-title="Proprietăți intensive și extensive" data-language-autonym="Română" data-language-local-name="rumeno" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%BD%D1%81%D0%B8%D0%B2%D0%BD%D1%8B%D0%B5_%D0%B8_%D1%8D%D0%BA%D1%81%D1%82%D0%B5%D0%BD%D1%81%D0%B8%D0%B2%D0%BD%D1%8B%D0%B5_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD%D1%8B" title="Интенсивные и экстенсивные величины - russo" lang="ru" hreflang="ru" data-title="Интенсивные и экстенсивные величины" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Intensiv_och_extensiv_storhet" title="Intensiv och extensiv storhet - svedese" lang="sv" hreflang="sv" data-title="Intensiv och extensiv storhet" data-language-autonym="Svenska" data-language-local-name="svedese" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D0%BD%D1%82%D0%B5%D0%BD%D1%81%D0%B8%D0%B2%D0%BD%D1%96_%D1%82%D0%B0_%D0%B5%D0%BA%D1%81%D1%82%D0%B5%D0%BD%D1%81%D0%B8%D0%B2%D0%BD%D1%96_%D0%B2%D0%BB%D0%B0%D1%81%D1%82%D0%B8%D0%B2%D0%BE%D1%81%D1%82%D1%96" title="Інтенсивні та екстенсивні властивості - ucraino" lang="uk" hreflang="uk" data-title="Інтенсивні та екстенсивні властивості" data-language-autonym="Українська" data-language-local-name="ucraino" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BA%A1i_l%C6%B0%E1%BB%A3ng_m%E1%BB%9F_r%E1%BB%99ng_v%C3%A0_%C4%91%E1%BA%A1i_l%C6%B0%E1%BB%A3ng_b%E1%BB%95_sung" title="Đại lượng mở rộng và đại lượng bổ sung - vietnamita" lang="vi" hreflang="vi" data-title="Đại lượng mở rộng và đại lượng bổ sung" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%85%A7%E5%90%AB%E5%8F%8A%E5%A4%96%E5%BB%B6%E6%80%A7%E8%B3%AA" title="內含及外延性質 - cinese" lang="zh" hreflang="zh" data-title="內含及外延性質" data-language-autonym="中文" data-language-local-name="cinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%85%A7%E5%90%AB%E5%90%8C%E5%A4%96%E5%BB%B6%E6%80%A7%E8%B3%AA" title="內含同外延性質 - cantonese" lang="yue" hreflang="yue" data-title="內含同外延性質" data-language-autonym="粵語" data-language-local-name="cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q911916#sitelinks-wikipedia" title="Modifica collegamenti 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class="mbox-text-div"><b>Questa voce o sezione  sull'argomento termodinamica <a href="/wiki/Wikipedia:Uso_delle_fonti" title="Wikipedia:Uso delle fonti">non cita le fonti necessarie</a> o quelle presenti sono insufficienti</b>. <div class="hide-when-compact"> <div class="noprint"><hr />Puoi <a class="external text" href="https://it.wikipedia.org/w/index.php?title=Propriet%C3%A0_intensive_ed_estensive&action=edit">migliorare questa voce</a> aggiungendo citazioni da <a href="/wiki/Wikipedia:Fonti_attendibili" title="Wikipedia:Fonti attendibili">fonti attendibili</a> secondo le <a href="/wiki/Wikipedia:Uso_delle_fonti" title="Wikipedia:Uso delle fonti">linee guida sull'uso delle fonti</a>. </div> </div> </div> </div> </div> <p>In <a href="/wiki/Termodinamica" title="Termodinamica">termodinamica</a> le <b>proprietà intensive</b> sono quelle <a href="/wiki/Propriet%C3%A0_fisica" title="Proprietà fisica">proprietà</a> il cui valore non dipende dalla quantità di <a href="/wiki/Materia_(fisica)" title="Materia (fisica)">materia</a> o dalle dimensioni del <a href="/wiki/Campione_(scienze)" class="mw-redirect" title="Campione (scienze)">campione</a>,<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> ma soltanto dalla sua natura e dalle <a href="/wiki/Stato_termodinamico" title="Stato termodinamico">condizioni</a> nelle quali si trova. Al contrario, una <b>proprietà</b> si dice <b>estensiva</b> se il suo valore dipende dalle dimensioni del <a href="/wiki/Corpo_(fisica)" title="Corpo (fisica)">corpo</a> a cui ci si riferisce. La <a href="/wiki/Temperatura" title="Temperatura">temperatura</a>, la <a href="/wiki/Pressione" title="Pressione">pressione</a>, il <a href="/wiki/Volume_specifico" class="mw-redirect" title="Volume specifico">volume specifico</a>, il <a href="/wiki/Punto_di_fusione" title="Punto di fusione">punto di fusione</a>, il <a href="/wiki/Punto_di_ebollizione" title="Punto di ebollizione">punto di ebollizione</a> e la <a href="/wiki/Densit%C3%A0" title="Densità">densità</a> sono esempi di grandezze intensive;<sup id="cite_ref-DOE_2-0" class="reference"><a href="#cite_note-DOE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> viceversa la <a href="/wiki/Massa_(fisica)" title="Massa (fisica)">massa</a>, il volume, la lunghezza sono grandezze estensive.<sup id="cite_ref-DOE_2-1" class="reference"><a href="#cite_note-DOE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Infatti se, ad esempio, il sistema in esame è costituito dall'acqua in un contenitore tutta alla stessa temperatura, rimuovere acqua varia il volume (estensivo) ma non la temperatura (intensiva). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Descrizione">Descrizione</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Propriet%C3%A0_intensive_ed_estensive&veaction=edit&section=1" title="Modifica la sezione Descrizione" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Propriet%C3%A0_intensive_ed_estensive&action=edit&section=1" title="Edit section's source code: Descrizione"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Qui con <i>dimensioni</i> del sistema si fa riferimento alla sua eventuale <i>composizione</i> in termini di sottosistemi. Più formalmente, si consideri il sistema costituito dall'unione di due sottosistemi identici: le <a href="/wiki/Propriet%C3%A0_fisica" title="Proprietà fisica">proprietà</a> <i>estensive</i> (come la <a href="/wiki/Massa_(fisica)" title="Massa (fisica)">massa</a>, il <a href="/wiki/Volume" title="Volume">volume</a>) saranno diverse da quelle dei singoli sottosistemi, mentre le proprietà <i>intensive</i> (come la <a href="/wiki/Temperatura" title="Temperatura">temperatura</a> o la <a href="/wiki/Densit%C3%A0" title="Densità">densità</a>, o la <a href="/wiki/Pressione" title="Pressione">pressione</a>) saranno le stesse. In particolare il valore di <a href="/wiki/Grandezza_fisica" title="Grandezza fisica">grandezze</a> estensive di sistemi composti sarà semplicemente <i>la somma</i> dei valori di ciascun sottosistema. </p><p>In particolare se il sistema <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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> è composto da <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> sotto-sistemi si ha 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 E(S)=\sum _{k=1}^{n}E(S_{k})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(S)=\sum _{k=1}^{n}E(S_{k})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/356d8e3122f35427534749ae10028c3d55430d3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:18.023ex; height:6.843ex;" alt="{\displaystyle E(S)=\sum _{k=1}^{n}E(S_{k})}"></span></dd></dl> <p>dove <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 E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> è la proprietà estensiva in esame, ed <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 S_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd1325d812cf88e5341ac097d8bda175723da887" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.514ex; height:2.509ex;" alt="{\displaystyle S_{k}}"></span> e' il valore che assume la proprietà estensiva in ciascun sotto-sistema. </p> <div class="mw-heading mw-heading2"><h2 id="Composizione_di_proprietà_intensive_ed_estensive"><span id="Composizione_di_propriet.C3.A0_intensive_ed_estensive"></span>Composizione di proprietà intensive ed estensive</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Propriet%C3%A0_intensive_ed_estensive&veaction=edit&section=2" title="Modifica la sezione Composizione di proprietà intensive ed estensive" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Propriet%C3%A0_intensive_ed_estensive&action=edit&section=2" title="Edit section's source code: Composizione di proprietà intensive ed estensive"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dato un insieme <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"> <mo fence="false" stretchy="false">{</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </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/434434a3a4c297856e0eff9f57d2d25053f830b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.354ex; height:2.843ex;" alt="{\displaystyle \{a_{i}\}}"></span> di proprietà intensive e un insieme <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_{j}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{A_{j}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4ece00859f4f7d4450a7d80c5f627d50b5c43ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.978ex; height:3.009ex;" alt="{\displaystyle \{A_{j}\}}"></span> di proprietà estensive, una generica funzione <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 I(\{a_{i}\},\{A_{j}\})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo stretchy="false">(</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I(\{a_{i}\},\{A_{j}\})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/720936f1394bf9f24cf494df375f0ebb94bd95ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.347ex; height:3.009ex;" alt="{\displaystyle I(\{a_{i}\},\{A_{j}\})}"></span> sarà una proprietà intensiva se per ogni <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> vale </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 I(\{a_{i}\},\{\alpha A_{j}\})=I(\{a_{i}\},\{A_{j}\}).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo stretchy="false">(</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <mi>α</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mi>I</mi> <mo stretchy="false">(</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I(\{a_{i}\},\{\alpha A_{j}\})=I(\{a_{i}\},\{A_{j}\}).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30bfb81f3ca0c5c7e4f64680431a5abebac5497f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:31.927ex; height:3.009ex;" alt="{\displaystyle I(\{a_{i}\},\{\alpha A_{j}\})=I(\{a_{i}\},\{A_{j}\}).}"></span></dd></dl> <p>Come caso particolare, il rapporto di due <a href="/wiki/Grandezza_fisica" title="Grandezza fisica">grandezze</a> estensive costituisce una grandezza intensiva. Tale situazione viene usata molto frequentemente per creare grandezze solitamente chiamate <i>densità-di</i> e costituite dal rapporto fra una grandezza estensiva e il volume (ad esempio la densità di energia di un campo elettromagnetico). La densità (<i>tout-court</i>), ad esempio, è proprio il rapporto fra massa e volume. </p><p>Ci sono proprietà, invece, che sono intrinsecamente <i>intensive</i>, ovvero non sono il rapporto col volume di nessuna grandezza estensiva. Il caso più notevole è quello della <a href="/wiki/Temperatura" title="Temperatura">temperatura</a> che, tra l'altro, non costituisce nemmeno una vera e propria grandezza fisica. </p><p>Analogamente, una funzione <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 E(\{a_{i}\},\{A_{j}\})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(\{a_{i}\},\{A_{j}\})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d89ed16d3c670dd98c642f30ea456038220a5f2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.951ex; height:3.009ex;" alt="{\displaystyle E(\{a_{i}\},\{A_{j}\})}"></span> sarà estensiva se vale </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 E(\{a_{i}\},\{\alpha A_{j}\})=\alpha E(\{a_{i}\},\{A_{j}\}).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <mi>α</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mi>α</mi> <mi>E</mi> <mo stretchy="false">(</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(\{a_{i}\},\{\alpha A_{j}\})=\alpha E(\{a_{i}\},\{A_{j}\}).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f83e23668204fe2c3ea2df59898b40e1fc5d63c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:34.623ex; height:3.009ex;" alt="{\displaystyle E(\{a_{i}\},\{\alpha A_{j}\})=\alpha E(\{a_{i}\},\{A_{j}\}).}"></span></dd></dl> <p>Dunque le proprietà estensive saranno <a href="/wiki/Funzione_omogenea" title="Funzione omogenea">funzioni omogenee</a> (di grado 1) rispetto ad <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_{j}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{A_{j}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4ece00859f4f7d4450a7d80c5f627d50b5c43ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.978ex; height:3.009ex;" alt="{\displaystyle \{A_{j}\}}"></span>. E quindi, per il <a href="/wiki/Funzione_omogenea#Teorema_di_Eulero_sulle_funzioni_omogenee" title="Funzione omogenea">Teorema di Eulero sulle funzioni omogenee</a>, si ha che E deve essere della forma: </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 E(\{a_{i}\},\{A_{i}\})=\sum _{j}A_{j}\left({\frac {\partial E}{\partial A_{j}}}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>E</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(\{a_{i}\},\{A_{i}\})=\sum _{j}A_{j}\left({\frac {\partial E}{\partial A_{j}}}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bfec0428368b03b564edfe77396dcbd4c1d7894" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:32.984ex; height:7.009ex;" alt="{\displaystyle E(\{a_{i}\},\{A_{i}\})=\sum _{j}A_{j}\left({\frac {\partial E}{\partial A_{j}}}\right),}"></span></dd></dl> <p>in cui la <a href="/wiki/Derivata_parziale" title="Derivata parziale">derivata parziale</a> va considerata rispetto a tutti i parametri tenuti costanti ad eccezione di <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_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6019bb70c912e59e9d5f442e9217517743ed4831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.653ex; height:2.843ex;" alt="{\displaystyle A_{j}}"></span>. Anche l'inverso è vero: ogni funzione che soddisfa la precedente relazione sarà una proprietà estensiva. </p><p><br /> </p> <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=Propriet%C3%A0_intensive_ed_estensive&veaction=edit&section=3" 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=Propriet%C3%A0_intensive_ed_estensive&action=edit&section=3" 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">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="http://goldbook.iupac.org/I03074.html">IUPAC Gold Book, "intensive quantity"</a></span> </li> <li id="cite_note-DOE-2"><span class="mw-cite-backlink"><b>^</b> <sup><i><a href="#cite_ref-DOE_2-0">a</a></i></sup> <sup><i><a href="#cite_ref-DOE_2-1">b</a></i></sup></span> <span class="reference-text">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="http://energy.gov/sites/prod/files/2013/06/f2/h1012v1.pdf">DOE Fundamentals Handbook - "Thermodynamics, Heat transfer, and fluid flow", p. 4.</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161220052153/https://energy.gov/sites/prod/files/2013/06/f2/h1012v1.pdf">Archiviato</a> il 20 dicembre 2016 in <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a>.</span> </li> </ol></div> <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=Propriet%C3%A0_intensive_ed_estensive&veaction=edit&section=4" 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=Propriet%C3%A0_intensive_ed_estensive&action=edit&section=4" 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/Grandezza_fisica" title="Grandezza fisica">Grandezza fisica</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=Propriet%C3%A0_intensive_ed_estensive&veaction=edit&section=5" 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=Propriet%C3%A0_intensive_ed_estensive&action=edit&section=5" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="http://goldbook.iupac.org/E02281.html"><span style="font-style:italic;">IUPAC Gold Book, "extensive quantity"</span></a>, su <span style="font-style:italic;">goldbook.iupac.org</span>.</cite></li></ul> <div class="noprint" style="width:100%; padding: 3px 0; display: flex; flex-wrap: wrap; row-gap: 4px; column-gap: 8px; box-sizing: border-box;"><div style="flex-grow: 1"><style data-mw-deduplicate="TemplateStyles:r140555418">.mw-parser-output .itwiki-template-occhiello{width:100%;line-height:25px;border:1px solid #CCF;background-color:#F0EEFF;box-sizing:border-box}.mw-parser-output .itwiki-template-occhiello-progetto{background-color:#FAFAFA}@media screen{html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}</style><div class="itwiki-template-occhiello"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Thermodynamics_icon.svg" class="mw-file-description" title="Termodinamica"><img alt=" " src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Thermodynamics_icon.svg/25px-Thermodynamics_icon.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Thermodynamics_icon.svg/38px-Thermodynamics_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Thermodynamics_icon.svg/50px-Thermodynamics_icon.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <b><a href="/wiki/Portale:Termodinamica" title="Portale:Termodinamica">Portale Termodinamica</a></b>: accedi alle voci di Wikipedia che trattano di termodinamica</div></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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