{"id":2056,"date":"2016-03-27T01:55:14","date_gmt":"2016-03-27T01:55:14","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2056"},"modified":"2024-08-21T14:38:49","modified_gmt":"2024-08-21T14:38:49","slug":"dilatometria","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/fisica-termica\/dilatometria\/","title":{"rendered":"Dilatometria"},"content":{"rendered":"

Dilatometria <\/b><\/span><\/span><\/span><\/p>\n

Dilata\u00e7\u00e3o linear, superficial, volum\u00e9trica e dilata\u00e7\u00e3o dos l\u00edquidos<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\u00a0<\/span><\/p>\n

Dilatometria<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Efeitos da dilata\u00e7\u00e3o sobre corpos s\u00f3lidos<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Dilata\u00e7\u00e3o linear dos s\u00f3lidos<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Trata-se da <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o de uma das dimens\u00f5es de um corpo<\/b><\/span><\/span><\/span>, como por exemplo<\/b><\/span><\/span><\/span>, seu comprimento. <\/b><\/span><\/span><\/span>Considere uma <\/b><\/span><\/span><\/span>haste met\u00e1lica de comprimento L<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0e \u00e0 temperatura t<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

Quando aquecida ter\u00e1 comprimento L a uma temperatura t.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Caracter\u00edsticas da dilata\u00e7\u00e3o linear<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o linear \u0394L <\/b><\/span><\/span><\/span>\u00e9 <\/b><\/span><\/span><\/span>diretamente proporcional \u00e0 varia\u00e7\u00e3o de temperatura \u0394t.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o linear \u0394L \u00e9 diretamente proporcional ao comprimento inicial L<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o linear \u0394L depende do material de que \u00e9 constitu\u00eddo o corpo.<\/b><\/span><\/span><\/span><\/p>\n

Matematicamente:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Sendo:<\/b><\/span><\/span><\/span><\/p>\n

\u0394L<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o linear <\/b><\/span><\/span><\/span>(de quanto dilatou o comprimento ou uma dimens\u00e3o)<\/b><\/span><\/span><\/span><\/p>\n

\u03b1<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>coeficiente de dilata\u00e7\u00e3o linear m\u00e9dio<\/b><\/span><\/span><\/span>, caracter\u00edstica do material que constitui a barra.<\/b><\/span><\/span><\/span><\/p>\n

L<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>comprimento inicial<\/b><\/span><\/span><\/span><\/p>\n

L<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>comprimento final<\/b><\/span><\/span><\/span><\/p>\n

\u0394t<\/b><\/span><\/span><\/span>\u00a0 \"\" <\/b><\/span><\/span><\/span>intervalo de temperatura<\/b><\/span><\/span><\/span><\/p>\n

Unidades do coeficiente de dilata\u00e7\u00e3o linear \u03b1<\/b><\/span><\/span><\/span><\/p>\n

Isolando <\/b><\/span><\/span><\/span>\u03b1<\/b><\/span><\/span><\/span> na <\/b><\/span><\/span><\/span>equa\u00e7\u00e3o \u0394L = L<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.\u03b1.\u0394t\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>\u03b1<\/b><\/span><\/span><\/span> <\/b>= \"\"<\/b><\/span><\/span><\/span>\u00a0\"\"\u00a0 como <\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0e \u0394L devem ter a mesma unidade<\/b><\/span><\/span><\/span>, elas <\/b><\/span><\/span><\/span>se<\/b><\/span><\/span><\/span> <\/b>cancelam\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 ent\u00e3o a <\/b><\/span><\/span><\/span>unidade em que se exprime o coeficiente de dilata\u00e7\u00e3o linear \u00e9 o<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe que o <\/b><\/span><\/span><\/span>coeficiente de dilata\u00e7\u00e3o linear representa a dilata\u00e7\u00e3o de um corpo de comprimento unit\u00e1rio, quando sua temperatura varia de um grau.<\/b><\/span><\/span><\/span><\/p>\n

Gr\u00e1fico do comprimento L em fun\u00e7\u00e3o da temperatura \u03b8<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Aplica\u00e7\u00f5es pr\u00e1ticas de dilata\u00e7\u00e3o linear<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

L\u00e2minas bimet\u00e1licas<\/b><\/span><\/span><\/span><\/p>\n

Quando voc\u00ea <\/b><\/span><\/span><\/span>solda duas barras de materiais diferentes <\/b><\/span><\/span><\/span>voc\u00ea obt\u00e9m uma\u00a0<\/b><\/span><\/span><\/span>l\u00e2mina bimet\u00e1lica\u00a0<\/b><\/span><\/span><\/span>e, se voc\u00ea <\/b><\/span><\/span><\/span>as submeter \u00e0 mesma varia\u00e7\u00e3o de temperatura<\/b><\/span><\/span><\/span>, o sistema vai <\/b><\/span><\/span><\/span>curvar-se para o lado da barra de menor coeficiente de dilata\u00e7\u00e3o, quando aquecida e para o lado da barra de maior coeficiente de dilata\u00e7\u00e3o, quando resfriada.<\/b><\/span><\/span><\/span><\/p>\n

Observe nas <\/b><\/span><\/span><\/span>figuras abaixo uma l\u00e2mina bimet\u00e1lica constitu\u00edda de alum\u00ednio \u00a0(\u03b1<\/b><\/span><\/span><\/span>aluminio<\/b><\/span><\/span><\/sub><\/span>=22.10<\/b><\/span><\/span><\/span>-6 o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>) <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>invar (liga de ferro e n\u00edquel \u2013 \u03b1<\/b><\/span><\/span><\/span>invar<\/b><\/span><\/span><\/sub><\/span>=1,0 .10<\/b><\/span><\/span><\/span>-6<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>–<\/b><\/span><\/span><\/sup><\/span>1<\/b><\/span><\/span><\/sup><\/span>) e observe <\/b><\/span><\/span><\/span>como a l\u00e2mina se inclina quando a temperatura aumenta ou diminui.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

As <\/b><\/span><\/span><\/span>l\u00e2minas bimet\u00e1licas s\u00e3o muito utilizadas nos rel\u00e9s t\u00e9rmicos<\/b><\/span><\/span><\/span> (termostatos \u2013 dispositivos que <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

desligam automaticamente um circuito quando a temperatura atinge determinado valor) para <\/b><\/span><\/span><\/span>controlar a temperatura de um dado ambiente, <\/b><\/span><\/span><\/span>nas geladeiras, freezers, ferro el\u00e9trico autom\u00e1tico, aparelhos de ar condicionado, fornos de fog\u00f5es el\u00e9tricos, etc. <\/b><\/span><\/span><\/span><\/p>\n

Quando a <\/b><\/span><\/span><\/span>temperatura do ambiente superar certo limite<\/b><\/span><\/span><\/span>, o <\/b><\/span><\/span><\/span>termostato deve desligar o aquecedor fazendo sua l\u00e2mina bimet\u00e1lica\u00a0envergar, abrindo os contatos, e desligando o aparelho da rede el\u00e9trica.<\/b><\/span><\/span><\/span><\/p>\n

Quando a <\/b><\/span><\/span><\/span>temperatura cair abaixo de certo limite<\/b><\/span><\/span><\/span>, o <\/b><\/span><\/span><\/span>aquecedor deve ser novamente ligado com <\/b><\/span><\/span><\/span>a l\u00e2mpada curvando-se em sentido oposto e fecha os contatos.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Esse <\/b><\/span><\/span><\/span>mesmo processo \u00e9 utilizado na preven\u00e7\u00e3o de inc\u00eandio por motivo de sobrecarga el\u00e9trica, desligando o circuito quando a temperatura atingir certos limites.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Nos <\/b><\/span><\/span><\/span>ferros el\u00e9tricos autom\u00e1ticos,<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>temperatura de funcionamento<\/b><\/span><\/span><\/span>, que \u00e9 <\/b><\/span><\/span><\/span>previamente regulada <\/b><\/span><\/span><\/span>por um <\/b><\/span><\/span><\/span>parafuso<\/b><\/span><\/span><\/span>, \u00e9 controlada por um <\/b><\/span><\/span><\/span>termostato constitu\u00eddo de duas l\u00e2minas bimet\u00e1licas de igual composi\u00e7\u00e3o<\/b><\/span><\/span><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

Os <\/b><\/span><\/span><\/span>dois metais <\/b><\/span><\/span><\/span>que formam <\/b><\/span><\/span><\/span>cada uma das l\u00e2minas t\u00eam coeficientes de dilata\u00e7\u00e3o \u03b1<\/b><\/span><\/span><\/span>I<\/b><\/span><\/span><\/sub><\/span> (o mais interno) e <\/b><\/span><\/span><\/span>\u03b1<\/b><\/span><\/span><\/span>II<\/b><\/span><\/span><\/sub><\/span> o mais externo). <\/b><\/span><\/span><\/span>As <\/b><\/span><\/span><\/span>duas l\u00e2minas est\u00e3o encurvadas e dispostas em contato el\u00e9trico<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>uma no interior da outra, <\/b><\/span><\/span><\/span>como indicam as figuras.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>corrente, suposta cont\u00ednua, entra pelo ponto 1 e sai pelo ponto 2,<\/b><\/span><\/span><\/span> conforme a figura 1, <\/b><\/span><\/span><\/span>aquecendo a resist\u00eancia. <\/b><\/span><\/span><\/span>\"\"<\/p>\n

\u00c0 medida que a <\/b><\/span><\/span><\/span>temperatura aumenta<\/b><\/span><\/span><\/span>, as <\/b><\/span><\/span><\/span>l\u00e2minas v\u00e3o se encurvando, devido \u00e0 dilata\u00e7\u00e3o dos metais, sem interromper o contato. <\/b><\/span><\/span><\/span><\/p>\n

Quando a <\/b><\/span><\/span><\/span>temperatura desejada \u00e9 alcan\u00e7ada,<\/b><\/span><\/span><\/span> <\/b>uma das l\u00e2minas \u00e9 detida pelo parafuso<\/b><\/span><\/span><\/span>, enquanto a <\/b><\/span><\/span><\/span>outra continua encurvando-se, interrompendo o contato entre elas, conforme a figura 2.<\/b><\/span><\/span><\/span><\/p>\n

Observe que as <\/b><\/span><\/span><\/span>l\u00e2minas est\u00e3o se encurvando para dentro, ent\u00e3o \u03b1<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0> \u03b1<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e, quanto mais baixo estiver o contato (mais apertado o parafuso), menor ser\u00e1 a dilata\u00e7\u00e3o das l\u00e2minas e consequentemente menor ser\u00e1 a temperatura.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

L\u00e2mpada Pisca-pisca<\/b><\/span><\/span><\/span><\/p>\n

Quando voc\u00ea <\/b><\/span><\/span><\/span>liga a l\u00e2mpada, a corrente el\u00e9trica flui da l\u00e2mina bimet\u00e1lica para o filamento no qual<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

ela est\u00e1 em contato, que, por sua vez flui para todos os outros, tornando-os incandescentes <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>acendendo a l\u00e2mpada<\/b><\/span><\/span><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

Quando a <\/b><\/span><\/span><\/span>l\u00e2mina bimet\u00e1lica ficar suficientemente quente ela se encurvar\u00e1<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>interrompendo<\/b><\/span><\/span><\/span> a corrente el\u00e9trica e <\/b><\/span><\/span><\/span>apagando a l\u00e2mpada. <\/b><\/span><\/span><\/span><\/p>\n

Em seguida <\/b><\/span><\/span><\/span>ela se resfria e se curva, restabelecendo o contato e acendendo novamente a l\u00e2mpada.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

E <\/b><\/span><\/span><\/span>assim por diante.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\"\"<\/span><\/p>\n

Term\u00f4metro de l\u00e2mina bimet\u00e1lica<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Constitu\u00eddo por <\/b><\/span><\/span><\/span>duas l\u00e2minas bimet\u00e1licas com metais diferentes, e soldadas uma com a outra, conforme a figura.<\/b><\/span><\/span><\/span><\/p>\n

Sendo os <\/b><\/span><\/span><\/span>metais diferentes, quando aquecidos eles sofrem diferentes dilata\u00e7\u00f5es<\/b><\/span><\/span><\/span>, provocando um <\/b><\/span><\/span><\/span>encurvamento diferente da l\u00e2mina para cada varia\u00e7\u00e3o de temperatura. <\/b><\/span><\/span><\/span><\/p>\n

S\u00e3o muito usados no <\/b><\/span><\/span><\/span>controle de temperaturas de fornos, saunas, etc.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Dilata\u00e7\u00e3o superficial dos s\u00f3lidos<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Um <\/b><\/span><\/span><\/span>corpo s\u00f3lido<\/b><\/span><\/span><\/span> sofre <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o superficial <\/b><\/span><\/span><\/span>quando <\/b><\/span><\/span><\/span>sofre aumento em duas de suas dimens\u00f5es.<\/b><\/span><\/span><\/span><\/p>\n

Considere uma <\/b><\/span><\/span><\/span>placa met\u00e1lica de comprimento C<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>, largura L<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0e espessura desprez\u00edvel<\/b><\/span><\/span><\/span>, que se encontra a uma <\/b><\/span><\/span><\/span>temperatura t<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>\u00e1rea de sua superf\u00edcie antes do aquecimento ser\u00e1 S<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sub><\/span>= C<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.L<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>ap\u00f3s o aquecimento ser\u00e1 S = C.L.<\/b><\/span><\/span><\/span><\/p>\n

Todas as leis v\u00e1lidas para a dilata\u00e7\u00e3o linear s\u00e3o tamb\u00e9m v\u00e1lidas para a dilata\u00e7\u00e3o superficial<\/b><\/span><\/span><\/span>, ou seja:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Na <\/b><\/span><\/span><\/span>express\u00e3o acima, a letra grega \u03b2 (beta) \u00e9 uma grandeza constante<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>caracter\u00edstica do material,<\/b><\/span><\/span><\/span> <\/b>denominada <\/b><\/span><\/span><\/span>coeficiente de dilata\u00e7\u00e3o superficial m\u00e9dio.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Dilata\u00e7\u00e3o volum\u00e9trica ou c\u00fabica dos s\u00f3lidos<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

A <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o volum\u00e9trica ou c\u00fabica <\/b><\/span><\/span><\/span>ocorre quando, devido a uma <\/b><\/span><\/span><\/span>eleva\u00e7\u00e3o de temperatura, um corpo <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

sofre um aumento em suas tr\u00eas dimens\u00f5es (volume).<\/b><\/span><\/span><\/span><\/p>\n

Todas as leis v\u00e1lidas para as dilata\u00e7\u00f5es linear e superficial s\u00e3o tamb\u00e9m v\u00e1lidas para a dilata\u00e7\u00e3o volum\u00e9trica, <\/b><\/span><\/span><\/span>ou seja:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Rela\u00e7\u00e3o entre os coeficientes de dilata\u00e7\u00e3o linear, superficial e volum\u00e9trica.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Dilata\u00e7\u00e3o dos l\u00edquidos<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Os <\/b><\/span><\/span><\/span>l\u00edquidos s\u00e3o amorfos, <\/b><\/span><\/span><\/span>ou seja, <\/b><\/span><\/span><\/span>n\u00e3o possuem forma pr\u00f3pria, adquirindo o formato do recipiente <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

onde est\u00e3o\u00a0contidos. <\/b><\/span><\/span><\/span><\/p>\n

Por esse motivo sofrem apenas dilata\u00e7\u00e3o volum\u00e9trica<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Dilata\u00e7\u00e3o aparente dos l\u00edquidos<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Dilata\u00e7\u00e3o real ou absoluta<\/b><\/span><\/span><\/span><\/p>\n

Nela, <\/b><\/span><\/span><\/span>leva-se em conta apenas a\u00a0dilata\u00e7\u00e3o do l\u00edquido<\/b><\/span><\/span><\/span>, sem considerar a <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o do recipiente. <\/b><\/span><\/span><\/span><\/p>\n

Pode-se <\/b><\/span><\/span><\/span>verificar<\/b><\/span><\/span><\/span> que um <\/b><\/span><\/span><\/span>mesmo l\u00edquido<\/b><\/span><\/span><\/span>, em <\/b><\/span><\/span><\/span>diferentes frascos<\/b><\/span><\/span><\/span>, possui <\/b><\/span><\/span><\/span>um s\u00f3 coeficiente de dilata\u00e7\u00e3o absoluta ou real, caracter\u00edstico desse l\u00edquido. <\/b><\/span><\/span><\/span><\/p>\n

Por\u00e9m, <\/b><\/span><\/span><\/span>tem v\u00e1rios coeficientes de dilata\u00e7\u00e3o aparente, <\/b><\/span><\/span><\/span>dependendo da <\/b><\/span><\/span><\/span>natureza dos frascos que a encerram.<\/b><\/span><\/span><\/span><\/p>\n

Dilata\u00e7\u00e3o do frasco<\/b><\/span><\/span><\/span><\/p>\n

Lembre-se de que o <\/b><\/span><\/span><\/span>frasco se comporta como se fosse maci\u00e7o e constitu\u00eddo do mesmo material das paredes do recipiente.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Assim, o <\/b><\/span><\/span><\/span>coeficiente de dilata\u00e7\u00e3o que se deve usar \u00e9 o coeficiente de dila\u00e7\u00e3o do material de que \u00e9 feito o frasco.<\/b><\/span><\/span><\/span><\/p>\n

Equa\u00e7\u00f5es que envolvem a dilata\u00e7\u00e3o dos l\u00edquidos<\/b><\/span><\/span><\/span><\/p>\n

Observe <\/b><\/span><\/span><\/span>atentamente as explica\u00e7\u00f5es a seguir:<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>frasco da figura abaixo <\/b><\/span><\/span><\/span>cont\u00e9m um <\/b><\/span><\/span><\/span>\u201cladr\u00e3o\u201d com o l\u00edquido preenchendo o recipiente at\u00e9 seu n\u00edvel (figura I).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Ap\u00f3s o <\/b><\/span><\/span><\/span>conjunto ser aquecido de \u0394t, <\/b><\/span><\/span><\/span>como <\/b><\/span><\/span><\/span>normalmente os l\u00edquidos se dilatam mais que os s\u00f3lidos, parte do l\u00edquido extravasa pelo \u201cladr\u00e3o\u201d (figura II).<\/b><\/span><\/span><\/span><\/p>\n

Esse <\/b><\/span><\/span><\/span>volume de l\u00edquido extravasado corresponde \u00e0 dilata\u00e7\u00e3o aparente do l\u00edquido (\u0394V<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>, de <\/b><\/span><\/span><\/span>volume inicial V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0e coeficiente de dilata\u00e7\u00e3o volum\u00e9trica aparente (\u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>) <\/b><\/span><\/span><\/span>e n\u00e3o \u00e0 dilata\u00e7\u00e3o real do l\u00edquido, j\u00e1 que o frasco tamb\u00e9m se dilata.<\/b><\/span><\/span><\/span><\/p>\n

Se voc\u00ea conhecer a <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o do frasco (\u0394V<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span>) que corresponde \u00e0 quanto seu volume aumentou, poder\u00e1 determinar <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o real sofrida pelo l\u00edquido.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Exemplo num\u00e9rico:<\/b><\/span><\/span><\/span><\/p>\n

Se <\/b><\/span><\/span><\/span>o volume do frasco que cont\u00e9m o l\u00edquido (at\u00e9 o n\u00edvel do \u201cladr\u00e3o), aumentar, por exemplo, de 1 cm<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0(\u0394V<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span>) = 1 cm<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>e, se o <\/b><\/span><\/span><\/span>volume de l\u00edquido extravasado for de 3 cm<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0(\u0394V<\/b><\/span><\/span><\/span>ap <\/b><\/span><\/span><\/sub><\/span>= 3 cm<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>), <\/b><\/span><\/span><\/span>voc\u00ea pode obter a <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o real do l\u00edquido (\u0394V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>), pois, \u0394V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0= \u0394V<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>\u00a0+ \u0394V<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 \u0394V<\/b><\/span><\/span><\/span>R <\/b><\/span><\/span><\/sub><\/span>= 3 + 1 = 4 cm<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/sub><\/span><\/p>\n

Equa\u00e7\u00f5es:<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span>Dilata\u00e7\u00e3o real do l\u00edquido\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394V<\/b><\/span><\/span><\/span>R <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.\u03b3<\/b><\/span><\/span><\/span>l\u00edquido<\/b><\/span><\/span><\/sub><\/span>.\u0394t<\/b><\/span><\/span><\/span> \"\" (V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> \"\" volume inicial do l\u00edquido)<\/b><\/span><\/span><\/span><\/p>\n

\"\" Dilata\u00e7\u00e3o aparente (volume de l\u00edquido extravasado)\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394V<\/b><\/span><\/span><\/span>ap <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.\u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>.\u0394t<\/b><\/span><\/span><\/span>\u00a0 \"\" (V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> \"\" volume inicial do l\u00edquido)<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span>Dilata\u00e7\u00e3o do frasco (recipiente) \u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394V<\/b><\/span><\/span><\/span>f <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.\u03b3<\/b><\/span><\/span><\/span>frasco<\/b><\/span><\/span><\/sub><\/span>.\u0394t \"\"<\/b><\/span><\/span><\/span> (V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> \"\" volume inicial do l\u00edquido)<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0\u0394V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0= \u0394V<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>\u00a0+ \u0394V<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span> <\/b>(veja exemplo num\u00e9rico acima)<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span>\u03b3<\/b><\/span><\/span><\/span>R <\/b><\/span><\/span><\/sub><\/span>= \u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>\u00a0+ \u03b3<\/b><\/span><\/span><\/span>frasco<\/b><\/span><\/span><\/sub><\/span> ( <\/b><\/span><\/span><\/sub><\/span>\uf067<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span> \u00e9 o coeficiente de dilata\u00e7\u00e3o volum\u00e9trica real do l\u00edquido <\/b><\/span><\/span><\/span>\uf067<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span> \u00e9 o coeficiente de dilata\u00e7\u00e3o volum\u00e9trica aparente e <\/b><\/span><\/span><\/span>\uf067<\/b><\/span><\/span><\/span>frasco<\/b><\/span><\/span><\/sub><\/span> \u00e9 o coeficiente de dilata\u00e7\u00e3o volum\u00e9trica do frasco)<\/b><\/span><\/span><\/span>.<\/span><\/p>\n

Analise alguns exerc\u00edcios resolvidos sobre dilata\u00e7\u00e3o dos l\u00edquidos<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Um <\/b><\/span><\/span><\/span>frasco de capacidade para 10 litros <\/b><\/span><\/span><\/span>est\u00e1 <\/b><\/span><\/span><\/span>completamente cheio de glicerina <\/b><\/span><\/span><\/span>e encontra-se \u00e0 <\/b><\/span><\/span><\/span>temperatura\u00a0de 10\u00baC.<\/b><\/span><\/span><\/span><\/p>\n

Aquecendo-se o frasco com a glicerina at\u00e9 atingir 90\u00baC<\/b><\/span><\/span><\/span>, observa-se que <\/b><\/span><\/span><\/span>352 mL de glicerina transborda do frasco.\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

Sabendo-se que o <\/b><\/span><\/span><\/span>coeficiente de dilata\u00e7\u00e3o volum\u00e9trica da glicerina \u00e9 <\/b><\/span><\/span><\/span><\/p>\n

5,0.10<\/b><\/span><\/span><\/span>-4<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00baC<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>, calcule o coeficiente de dilata\u00e7\u00e3o linear do\u00a0frasco \u00e9 \u00baC<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

S\u00e3o dados: V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> = 10 L <\/b><\/span><\/span><\/span>(do frasco e da glicerina) \"\" <\/b><\/span><\/span><\/span>t<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> = 10 <\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C \"\"<\/b><\/span><\/span><\/span> <\/b>t = 90 <\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C \"\"<\/b><\/span><\/span><\/span> <\/b>\u0394V<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span> <\/b>= 352 mL = <\/b><\/span><\/span><\/span>352.<\/b><\/span><\/span><\/span><\/p>\n

10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span> L \"\" <\/b><\/span><\/span><\/span>\u03b3<\/b><\/span><\/span><\/span>glicerina <\/b><\/span><\/span><\/sub><\/span>= 5,0.10<\/b><\/span><\/span><\/span>-4<\/b><\/span><\/span><\/sup><\/span> <\/b>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>volume de glicerina que extravasou corresponde \u00e0 dilata\u00e7\u00e3o aparente\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>\u0394V<\/b><\/span><\/span><\/span>ap <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>. \u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>.\u0394t\u00a0 <\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span><\/p>\n

352.10<\/b><\/span><\/span><\/span>-3 <\/b><\/span><\/span><\/sup><\/span>= 10.\u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>.(90 \u2013 10)\u00a0 \"\"\u00a0 \u03b3<\/b><\/span><\/span><\/span>ap <\/b><\/span><\/span><\/sub><\/span>=\"\"\"\"\u00a0 <\/b><\/span><\/span><\/span>\u03b3<\/b><\/span><\/span><\/span>ap <\/b><\/span><\/span><\/sub><\/span>= 44.10<\/b><\/span><\/span><\/span>-5<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\u03b3<\/b><\/span><\/span><\/span>glicerina <\/b><\/span><\/span><\/sub><\/span>= \u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>+ \u03b3<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 5,0.10<\/b><\/span><\/span><\/span>-4 <\/b><\/span><\/span><\/sup><\/span>= 44.10<\/b><\/span><\/span><\/span>-5<\/b><\/span><\/span><\/sup><\/span>\u00a0+ \u03b3<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00a0\"\"\u00a0 \u03b3<\/b><\/span><\/span><\/span>f <\/b><\/span><\/span><\/sub><\/span>= 5,0.10<\/b><\/span><\/span><\/span>-4<\/b><\/span><\/span><\/sup><\/span>\u00a0\u2013 4,4.10<\/b><\/span><\/span><\/span>-4<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>\u03b3<\/b><\/span><\/span><\/span>f <\/b><\/span><\/span><\/sub><\/span>= 6,0.10<\/b><\/span><\/span><\/span>-5<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span> (coeficiente de dilata\u00e7\u00e3o volum\u00e9trica do frasco). <\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Acontece que o <\/b><\/span><\/span><\/span>exerc\u00edcio quer o coeficiente de dilata\u00e7\u00e3o linear do frasco \u03b1<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span> = \u03b3<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span>\/3 <\/b><\/span><\/span><\/span><\/p>\n

\u03b1<\/b><\/span><\/span><\/span>f <\/b><\/span><\/span><\/sub><\/span>= \"\" \u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>\u03b1<\/b><\/span><\/span><\/span>f <\/b><\/span><\/span><\/sub><\/span>= 2,0.10<\/b><\/span><\/span><\/span>-5<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>\u00a0.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o aparente corresponde <\/b><\/span><\/span><\/span>ao <\/b><\/span><\/span><\/span>aumento na indica\u00e7\u00e3o da escala \"\" \u0394V<\/b><\/span><\/span><\/span>ap <\/b><\/span><\/span><\/sub><\/span>=<\/b><\/span><\/span><\/span> <\/b>525 \u2013 500 <\/b><\/span><\/span><\/span>= 25 cm<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span> \"\"<\/b><\/span><\/span><\/span> <\/b>\u0394V<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span> <\/b>= V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.\u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>.\u0394t\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 25 = 500.\u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>.50\u00a0 \"\"\u00a0 \u03b3<\/b><\/span><\/span><\/span> p<\/b><\/span><\/span><\/sub><\/span>= \"\"\u00a0\"\"\u00a0 <\/b><\/span><\/span><\/span>\u03b3<\/b><\/span><\/span><\/span>ap <\/b><\/span><\/span><\/sub><\/span>= 10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/sub><\/span>\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

\u03b3<\/b><\/span><\/span><\/span>l\u00edq <\/b><\/span><\/span><\/sub><\/span>= \u03b3<\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/sub><\/span>\u00a0+ \u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 \u03b3<\/b><\/span><\/span><\/span>l\u00edq <\/b><\/span><\/span><\/sub><\/span>= 0,001 + 0,00001\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>\u03b3<\/b><\/span><\/span><\/span>l\u00edq <\/b><\/span><\/span><\/sub><\/span>= 0,00101\u00a0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Um <\/b><\/span><\/span><\/span>recipiente de vidro tem capacidade de 100cm<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0a 10<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span> e cont\u00e9m, a essa temperatura, <\/b><\/span><\/span><\/span>99cm<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0de um certo l\u00edquido de coeficiente de dilata\u00e7\u00e3o c\u00fabica \u03b3 = 2.10<\/b><\/span><\/span><\/span>-4<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>. A que temperatura o recipiente <\/b><\/span><\/span><\/span>estar\u00e1 <\/b><\/span><\/span><\/span>completamente cheio de l\u00edquido?<\/b><\/span><\/span><\/span>\"\"<\/p>\n

\u00a0<\/span>(Considere o coeficiente de dilata\u00e7\u00e3o c\u00fabica do vidro como sendo <\/b><\/span><\/span><\/span><\/p>\n

10<\/b><\/span><\/span><\/span>-5<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Quando o recipiente <\/b><\/span><\/span><\/span>estiver completamente cheio de l\u00edquido<\/b><\/span><\/span><\/span>, eles (recipiente e l\u00edquido) <\/b><\/span><\/span><\/span>dever\u00e3o ter o mesmo volume\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>\u0394V<\/b><\/span><\/span><\/span>vidro <\/b><\/span><\/span><\/sub><\/span>= \u0394V<\/b><\/span><\/span><\/span>l\u00edquido<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 100(1 + 10<\/b><\/span><\/span><\/span>-5<\/b><\/span><\/span><\/sup><\/span> (t \u2013 10) = 99.(1 + 2.10<\/b><\/span><\/span><\/span>-4<\/b><\/span><\/span><\/sup><\/span>).(t \u2013 10)\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

t = 19,6.10<\/b><\/span><\/span><\/span>-2<\/b><\/span><\/span><\/sup><\/span> \/18,6.10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00a0t \u2248 <\/b><\/span><\/span><\/span>10,5 <\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Um <\/b><\/span><\/span><\/span>recipiente de vidro <\/b><\/span><\/span><\/span>encontra-se <\/b><\/span><\/span><\/span>completamente cheio <\/b><\/span><\/span><\/span>de um <\/b><\/span><\/span><\/span>l\u00edquido a 0 \u00baC.<\/b><\/span><\/span><\/span> Quando o<\/b><\/span><\/span><\/span>\"\"<\/p>\n

conjunto \u00e9 aquecido at\u00e9 80 \u00baC, o volume do l\u00edquido que transborda corresponde a 4% do volume<\/b><\/span><\/span><\/span>
\n<\/b><\/span><\/span><\/span>que o l\u00edquido possu\u00eda a 0 \u00baC. <\/b><\/span><\/span><\/span>Sabendo que o <\/b><\/span><\/span><\/span>coeficiente de dilata\u00e7\u00e3o volum\u00e9trica do vidro<\/b><\/span><\/span><\/span> \u00e9 igual
\na <\/b><\/span><\/span><\/span>27.10<\/b><\/span><\/span><\/span>-6<\/b><\/span><\/span><\/sup><\/span> \u00baC<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>, determine o <\/b><\/span><\/span><\/span>coeficiente de dilata\u00e7\u00e3o real do l\u00edquido<\/b><\/span><\/span><\/span>.
\n<\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> = <\/b><\/span><\/span><\/span>volume inicial do recipiente <\/b><\/span><\/span><\/span>= volume inicial do l\u00edquido a 0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C.<\/b><\/span><\/span><\/span><\/p>\n

Dilata\u00e7\u00e3o do vidro com V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> = volume inicial do l\u00edquido \"\" <\/b><\/span><\/span><\/span>V = V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.(1+\u03b3.(t \u2013 t<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>) \"\" V = V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.(1+.27.10<\/b><\/span><\/span><\/span>-5<\/b><\/span><\/span><\/sup><\/span> .80) \"\" <\/b><\/span><\/span><\/span>V = 1,00216.V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> <\/b>(volume final do recipiente).<\/b><\/span><\/span><\/span>
\n<\/b><\/span><\/span><\/span>O l\u00edquido se dilatou V\u2019 que \u00e9 o volume do recipiente V + o volume de l\u00edquido derramado que \u00e9 de 4% de V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.
\nV\u2019 = V + 0,04V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> \"\"<\/b><\/span><\/span><\/span> <\/b>Dilata\u00e7\u00e3o do l\u00edquido<\/b><\/span><\/span><\/span> \"\" <\/b><\/span><\/span>V’ = V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.(1+\u03b3’.\u0394t) <\/b><\/span><\/span><\/span>onde <\/b><\/span><\/span><\/span>\u03b3’<\/b><\/span><\/span><\/span> \u00e9 o <\/b><\/span><\/span><\/span>coeficiente de dilata\u00e7\u00e3o aparente <\/b><\/span><\/span><\/span>do l\u00edquido.
\n<\/b><\/span><\/span><\/span>V’ = V + 0,04V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> \"\" <\/b><\/span><\/span><\/span>V’ = (1,00216V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>) + 0,04V<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sub><\/span> \"\"<\/b><\/span><\/span><\/span> V’ = 1,04216V<\/b><\/span><\/span><\/span>o
\n<\/b><\/span><\/span><\/sub><\/span>V’ = V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.(1+\u03b3’.\u0394t) \"\" 1,04216V<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>(1+\u03b3’.80) \"\" <\/b><\/span><\/span><\/span>1,04216 = 1 + 80\u03b3’ \"\" <\/b><\/span><\/span><\/span>
\n<\/b><\/span><\/span><\/span>80\u03b3’=0,04216 \"\"<\/b><\/span><\/span><\/span> <\/b>\u03b3\u2019 = 5,27.10<\/b><\/span><\/span><\/span>-4<\/b><\/span><\/span><\/sup><\/span> \u00baC<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

O que voc\u00ea deve saber, orienta\u00e7\u00f5es e dicas<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Sendo:<\/b><\/span><\/span><\/span><\/p>\n

\u0394L<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o linear <\/b><\/span><\/span><\/span>(de quanto dilatou o comprimento ou uma dimens\u00e3o)<\/b><\/span><\/span><\/span><\/p>\n

\u03b1<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>coeficiente de dilata\u00e7\u00e3o linear m\u00e9dio<\/b><\/span><\/span><\/span>, caracter\u00edstica do material que constitui a barra.<\/b><\/span><\/span><\/span><\/p>\n

L<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>comprimento inicial<\/b><\/span><\/span><\/span><\/p>\n

L<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>comprimento final<\/b><\/span><\/span><\/span><\/p>\n

\u0394t<\/b><\/span><\/span><\/span>\u00a0 \"\" <\/b><\/span><\/span><\/span>intervalo de temperatura<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"\u00a0<\/span><\/p>\n

Se as <\/b><\/span><\/span><\/span>arma\u00e7\u00f5es met\u00e1licas das figuras forem de mesmo material, homog\u00eaneas e de sec\u00e7\u00e3o transversal constante <\/b><\/span><\/span><\/span>e se <\/b><\/span><\/span><\/span>sofrerem<\/b><\/span><\/span><\/span>\"\"<\/p>\n

a <\/b><\/span><\/span><\/span>mesma varia\u00e7\u00e3o de temperatura <\/b><\/span><\/span><\/span>(por exemplo, sendo aquecidas), elas <\/b><\/span><\/span><\/span>n\u00e3o se deformar\u00e3o, os pontos de contato n\u00e3o trocar\u00e3o for\u00e7as entre si, elas manter\u00e3o o formato inicial<\/b><\/span><\/span><\/span>, mas com <\/b><\/span><\/span><\/span>dimens\u00f5es maiores e<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>todos<\/b><\/span><\/span><\/span> os <\/b><\/span><\/span><\/span>\u00e2ngulos internos permanecer\u00e3o os mesmos. <\/b><\/span><\/span><\/span><\/p>\n

Observe que seus <\/b><\/span><\/span><\/span>comprimentos n\u00e3o se dilatam por igual, a hipotenusa se dilata mais que os catetos.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

L\u00e2minas bimet\u00e1licas<\/b><\/span><\/span><\/span><\/p>\n

Quando voc\u00ea <\/b><\/span><\/span><\/span>solda duas barras de materiais diferentes <\/b><\/span><\/span><\/span>voc\u00ea obt\u00e9m uma\u00a0<\/b><\/span><\/span><\/span>l\u00e2mina bimet\u00e1lica\u00a0<\/b><\/span><\/span><\/span>e, se voc\u00ea as <\/b><\/span><\/span><\/span>submeter \u00e0 mesma varia\u00e7\u00e3o de temperatura, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>sistema vai curvar-se para o lado da barra de menor coeficiente de dilata\u00e7\u00e3o, quando aquecida <\/b><\/span><\/span><\/span>e para o lado da barra <\/b><\/span><\/span><\/span>de maior coeficiente de dilata\u00e7\u00e3o, quando resfriada.<\/b><\/span><\/span><\/span><\/p>\n

Observe nas figuras abaixo uma <\/b><\/span><\/span><\/span>l\u00e2mina bimet\u00e1lica constitu\u00edda de alum\u00ednio (\u03b1<\/b><\/span><\/span><\/span>aluminio <\/b><\/span><\/span><\/sub><\/span>= 22.10<\/b><\/span><\/span><\/span>-6 o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>) <\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

invar<\/b><\/span><\/span><\/span> (liga de ferro e n\u00edquel<\/b><\/span><\/span><\/span>, \u03b1<\/b><\/span><\/span><\/span>invar <\/b><\/span><\/span><\/sub><\/span>= 1,0 .10<\/b><\/span><\/span><\/span>-6<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>) e <\/b><\/span><\/span><\/span>observe<\/b><\/span><\/span><\/span> como a <\/b><\/span><\/span><\/span>l\u00e2mina se inclina quando a temperatura aumenta ou diminui.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\"\"<\/span><\/p>\n

Utilidades das l\u00e2minas bimet\u00e1licas<\/b><\/span><\/span><\/span><\/p>\n

As <\/b><\/span><\/span><\/span>l\u00e2minas bimet\u00e1licas <\/b><\/span><\/span><\/span>s\u00e3o muito utilizadas nos <\/b><\/span><\/span><\/span>rel\u00e9s t\u00e9rmicos <\/b><\/span><\/span><\/span>(<\/b><\/span><\/span><\/span>termostatos, <\/b><\/span><\/span><\/span>que s\u00e3o dispositivos que desligam automaticamente um circuito quando a temperatura atinge determinado valor) para <\/b><\/span><\/span><\/span>controlar a temperatura de um dado ambiente, <\/b><\/span><\/span><\/span>nas geladeiras, freezers, ferro el\u00e9trico autom\u00e1tico, aparelhos de ar condicionado, fornos de fog\u00f5es el\u00e9tricos, etc. <\/b><\/span><\/span><\/span><\/p>\n

Quando a <\/b><\/span><\/span><\/span>temperatura do ambiente superar certo limite, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>termostato deve desligar o aquecedor <\/b><\/span><\/span><\/span>fazendo sua <\/b><\/span><\/span><\/span>l\u00e2mina bimet\u00e1lica envergar<\/b><\/span><\/span><\/span> <\/b>abrindo os contatos<\/b><\/span><\/span><\/span>, e <\/b><\/span><\/span><\/span>desligando <\/b><\/span><\/span><\/span>o aparelho da rede el\u00e9trica.<\/b><\/span><\/span><\/span><\/p>\n

Quando a <\/b><\/span><\/span><\/span>temperatura cair abaixo de certo limite<\/b><\/span><\/span><\/span>, o <\/b><\/span><\/span><\/span>aquecedor deve ser novamente ligado <\/b><\/span><\/span><\/span>com a <\/b><\/span><\/span><\/span>l\u00e2mpada curvando-se em sentido oposto e fecha os contatos.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Esse <\/b><\/span><\/span><\/span>mesmo processo \u00e9 utilizado na preven\u00e7\u00e3o de inc\u00eandio <\/b><\/span><\/span><\/span>por motivo de <\/b><\/span><\/span><\/span>sobrecarga el\u00e9trica, desligando<\/b><\/span><\/span><\/span> o circuito quando a <\/b><\/span><\/span><\/span>temperatura atingir certos limites.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

P\u00eandulo simples<\/b><\/span><\/span><\/span><\/p>\n

Trata-se de <\/b><\/span><\/span><\/span>corpo de massa m suspenso por um fio inextens\u00edvel e de massa desprez\u00edvel. <\/b><\/span><\/span><\/span><\/p>\n

Quando <\/b><\/span><\/span><\/span>afastado de sua posi\u00e7\u00e3o de equil\u00edbrio e solto,<\/b><\/span><\/span><\/span> o p\u00eandulo <\/b><\/span><\/span><\/span>oscilar\u00e1 em um plano vertical <\/b><\/span><\/span><\/span>sob \u00e0 a\u00e7\u00e3o da <\/b><\/span><\/span><\/span>gravidade g;<\/b><\/span><\/span><\/span> o movimento \u00e9 <\/b><\/span><\/span><\/span>peri\u00f3dico e oscilat\u00f3rio e o seu per\u00edodo <\/b><\/span><\/span><\/span>(tempo que ele demora para efetuar um <\/b><\/span><\/span><\/span>\u201cvai e vem\u201d completo<\/b><\/span><\/span><\/span>) \u00e9 fornecido por <\/b><\/span><\/span><\/span>T=2\u03c0\"\"<\/b><\/span><\/span><\/span>\"\"<\/p>\n

O <\/b><\/span><\/span><\/span>P\u00eandulo Simples, <\/b><\/span><\/span><\/span>atrav\u00e9s da <\/b><\/span><\/span><\/span>equa\u00e7\u00e3o acima<\/b><\/span><\/span><\/span>, tamb\u00e9m fornece um <\/b><\/span><\/span><\/span>m\u00e9todo para medi\u00e7\u00f5es do valor <\/b><\/span><\/span><\/span>da <\/b><\/span><\/span><\/span>acelera\u00e7\u00e3o da gravidade g num dado local<\/b><\/span><\/span><\/span>, medindo-se o <\/b><\/span><\/span><\/span>comprimento do fio L <\/b><\/span><\/span><\/span>e o <\/b><\/span><\/span><\/span>per\u00edodo de oscila\u00e7\u00e3o T, substituindo esses dois dados na equa\u00e7\u00e3o acima voc\u00ea acha o valor da acelera\u00e7\u00e3o da gravidade g nesse local.<\/b><\/span><\/span><\/span><\/p>\n

Observe que o <\/b><\/span><\/span><\/span>per\u00edodo T, \u00e9 independente da massa m do corpo suspenso <\/b><\/span><\/span><\/span>(n\u00e3o aparece na f\u00f3rmula).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Veja a resolu\u00e7\u00e3o desse exerc\u00edcio:<\/b><\/span><\/span><\/span><\/p>\n

A figura <\/b><\/span><\/span><\/span>mostra uma ponte apoiada <\/b><\/span><\/span><\/span>sobre <\/b><\/span><\/span><\/span>dois pilares feitos de materiais diferentes.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Como se v\u00ea, o <\/b><\/span><\/span><\/span>pilar mais longo, de comprimento L<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0= 40 m, possui coeficiente de dilata\u00e7\u00e3o linear \u03b1 = 18. 10<\/b><\/span><\/span><\/span>-6 <\/b><\/span><\/span><\/sup><\/span>\u00b0C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>pilar mais curto tem comprimento L<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0= 30 m. <\/b><\/span><\/span><\/span>Para que a <\/b><\/span><\/span><\/span>ponte permane\u00e7a sempre na horizontal<\/b><\/span><\/span><\/span>, determine o <\/b><\/span><\/span><\/span>coeficiente linear do material do segundo pilar.<\/b><\/span><\/span><\/span><\/p>\n

Para que a <\/b><\/span><\/span><\/span>ponte permane\u00e7a sempre na horizontal<\/b><\/span><\/span><\/span>, os <\/b><\/span><\/span><\/span>dois pilares devem sofrer a mesma dilata\u00e7\u00e3o para a mesma varia\u00e7\u00e3o de temperatura\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>\u0394L<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>= \u0394L<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/span>01<\/b><\/span><\/span><\/sub><\/span>.\u03b1<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.\u0394t = L<\/b><\/span><\/span><\/span>02<\/b><\/span><\/span><\/sub><\/span>.\u03b1<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.\u0394t\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 40.18.10<\/b><\/span><\/span><\/span>-6 <\/b><\/span><\/span><\/sup><\/span>= 30.\u03b1<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>\u03b1<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= 24.10<\/b><\/span><\/span><\/span>-6<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Se uma <\/b><\/span><\/span><\/span>placa met\u00e1lica com orif\u00edcio for aquecida<\/b><\/span><\/span><\/span>, verifica-se que o <\/b><\/span><\/span><\/span>orif\u00edcio aumenta, <\/b><\/span><\/span><\/span>como se fosse <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

constitu\u00eddo pelo material da placa<\/b><\/span><\/span><\/span>, pois tudo se passa como se o <\/b><\/span><\/span><\/span>furo tivesse um coeficiente de dilata\u00e7\u00e3o superficial igual \u00e0quele da subst\u00e2ncia da placa.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Se voc\u00ea <\/b><\/span><\/span><\/span>despejar \u00e1gua fervente num copo de vidro<\/b><\/span><\/span><\/span>, ele pode se <\/b><\/span><\/span><\/span>quebrar<\/b><\/span><\/span><\/span>, pois a <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o n\u00e3o \u00e9 uniforme,<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>parte interna se dilata mais que a externa.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

O mesmo poderia ocorrer se voc\u00ea <\/b><\/span><\/span><\/span>despejasse \u00e1gua gelada num copo quente <\/b><\/span><\/span><\/span>e, nesse caso a parte <\/b><\/span><\/span><\/span>interna se contrai mais que a externa<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Se <\/b><\/span><\/span><\/span>voc\u00ea despejar \u00e1gua fervente num copo de vidro at\u00e9 a metade, <\/b><\/span><\/span><\/span>ele pode <\/b><\/span><\/span><\/span>quebrar mais facilmente <\/b><\/span><\/span><\/span>do que quando <\/b><\/span><\/span><\/span>cheio completamente, <\/b><\/span><\/span><\/span>porque a <\/b><\/span><\/span><\/span>temperatura dele muda uniformemente<\/b><\/span><\/span><\/span>, o que <\/b><\/span><\/span><\/span>causa a quebra do copo \u00e9 o fato de que a parte de baixo fique mais quente e se dilate mais do que a de cima, podendo provocar a ruptura.
\n<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe tamb\u00e9m que <\/b><\/span><\/span><\/span>se voc\u00ea tiver dois copos de diferentes coeficientes de dilata\u00e7\u00e3o<\/b><\/span><\/span><\/span>, o de <\/b><\/span><\/span><\/span>menor coeficiente apresenta maior<\/b><\/span><\/span><\/span>\"\"<\/p>\n

dificuldade de se quebrar quando aquecido, pois se dilata menos.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Se as <\/b><\/span><\/span><\/span>duas esferas da figura abaixo forem id\u00eanticas<\/b><\/span><\/span><\/span> (mesmas dimens\u00f5es e mesmo material) e sofrerem <\/b><\/span><\/span><\/span>a mesma varia\u00e7\u00e3o de temperatura,<\/b><\/span><\/span><\/span> elas sofrem a <\/b><\/span><\/span><\/span>mesma dilata\u00e7\u00e3o volum\u00e9trica.<\/b><\/span><\/span><\/span> <\/b>\"\"<\/p>\n

Corpos ocos se dilatam como se fossem maci\u00e7os <\/b><\/span><\/span><\/span>e sua <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o \u00e9 calculada utilizando o coeficiente de dilata\u00e7\u00e3o volum\u00e9trica do material que constitui sua superf\u00edcie.<\/b><\/span><\/span><\/span><\/p>\n

<\/a><\/a> O mesmo acontece se ele <\/b><\/span><\/span><\/span>tiver um furo, <\/b><\/span><\/span><\/span>e se a esfera com o furo for <\/b><\/span><\/span><\/span>aquecida, <\/b><\/span><\/span><\/span>verifica-se que o <\/b><\/span><\/span><\/span>furo aumenta,<\/b><\/span><\/span><\/span> como se fosse como se fosse constitu\u00eddo pelo material da esfera.<\/b><\/span><\/span><\/span><\/p>\n

Assim, o furo se comporta <\/b><\/span><\/span><\/span>como tivesse o mesmo coeficiente de dilata\u00e7\u00e3o volum\u00e9trica que o da subst\u00e2ncia que constitui a esfera. \u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Equa\u00e7\u00f5es utilizadas na dilata\u00e7\u00e3o de l\u00edquidos<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span>Dilata\u00e7\u00e3o real do l\u00edquido\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394V<\/b><\/span><\/span><\/span>R <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.\u03b3<\/b><\/span><\/span><\/span>l\u00edquido<\/b><\/span><\/span><\/sub><\/span>.\u0394t<\/b><\/span><\/span><\/span> \"\" (V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> \"\" volume inicial do l\u00edquido)<\/b><\/span><\/span><\/span><\/p>\n

\"\" Dilata\u00e7\u00e3o aparente (volume de l\u00edquido extravasado)\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394V<\/b><\/span><\/span><\/span>ap <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.\u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>.\u0394t<\/b><\/span><\/span><\/span>\u00a0 \"\" (V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> \"\" volume inicial do l\u00edquido)<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span>Dilata\u00e7\u00e3o do frasco (recipiente) \u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394V<\/b><\/span><\/span><\/span>f <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.\u03b3<\/b><\/span><\/span><\/span>frasco<\/b><\/span><\/span><\/sub><\/span>.\u0394t \"\"<\/b><\/span><\/span><\/span> (V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> \"\" volume inicial do l\u00edquido)<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0\u0394V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0= \u0394V<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>\u00a0+ \u0394V<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span> <\/b>(veja exemplo num\u00e9rico acima)<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span>\u03b3<\/b><\/span><\/span><\/span>R <\/b><\/span><\/span><\/sub><\/span>= \u03b3<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span>\u00a0+ \u03b3<\/b><\/span><\/span><\/span>frasco<\/b><\/span><\/span><\/sub><\/span> ( <\/b><\/span><\/span><\/sub><\/span>\uf067<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span> \u00e9 o coeficiente de dilata\u00e7\u00e3o volum\u00e9trica real do l\u00edquido <\/b><\/span><\/span><\/span>\uf067<\/b><\/span><\/span><\/span>ap<\/b><\/span><\/span><\/sub><\/span> \u00e9 o coeficiente de dilata\u00e7\u00e3o volum\u00e9trica aparente e <\/b><\/span><\/span><\/span>\uf067<\/b><\/span><\/span><\/span>frasco<\/b><\/span><\/span><\/sub><\/span> \u00e9 o coeficiente de dilata\u00e7\u00e3o volum\u00e9trica do frasco)<\/b><\/span><\/span><\/span>.<\/span><\/p>\n

\"\"<\/p>\n

O <\/b><\/span><\/span><\/span>coeficiente de dilata\u00e7\u00e3o aparente <\/b><\/span><\/span><\/span>depende da <\/b><\/span><\/span><\/span>natureza do l\u00edquido e do material que constitui o recipiente que o cont\u00e9m.<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

Confira os exerc\u00edcios com resolu\u00e7\u00e3o comentada<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Dilatometria Dilata\u00e7\u00e3o linear, superficial, volum\u00e9trica e dilata\u00e7\u00e3o dos l\u00edquidos \u00a0\u00a0 Dilatometria Efeitos da dilata\u00e7\u00e3o sobre corpos s\u00f3lidos Dilata\u00e7\u00e3o linear dos s\u00f3lidos \u00a0 Trata-se da dilata\u00e7\u00e3o de uma das dimens\u00f5es de um corpo, como por exemplo, seu comprimento. Considere uma haste met\u00e1lica de comprimento Lo\u00a0e \u00e0 temperatura to. Quando aquecida ter\u00e1 comprimento L a uma temperatura t. Caracter\u00edsticas da dilata\u00e7\u00e3o linear<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":122,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-2056","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2056","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=2056"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2056\/revisions"}],"predecessor-version":[{"id":2062,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2056\/revisions\/2062"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/122"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=2056"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}