{"id":155,"date":"2019-11-26T10:07:27","date_gmt":"2019-11-26T13:07:27","guid":{"rendered":"http:\/\/fiziko.net\/?page_id=155"},"modified":"2019-11-26T10:08:20","modified_gmt":"2019-11-26T13:08:20","slug":"ciclo-de-carnot","status":"publish","type":"page","link":"https:\/\/fiziko.net\/?page_id=155","title":{"rendered":"Ciclo de Carnot"},"content":{"rendered":"\t\t
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O Ciclo de Carnot<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Suponha que 0,2 mols de um g\u00e1s ideal diat\u00f4mico passe por um ciclo de Carnot com temperaturas de 227\u00b0C e 27\u00b0C. A press\u00e3o inicial \u00e9 Pa<\/sub> = 10×105<\/sup> Pa e, durante a expans\u00e3o isot\u00e9rmica, na temperatura mais elevada o volume dobra.<\/span><\/h3>

a) Ache a press\u00e3o e o volume em cada um dos pontos a, b, c <\/i> e d<\/i> do ciclo de Carnot.<\/span><\/h3>

b) Calcule o calor Q, o trabalho W e a \u0394<\/span>U<\/span> varia\u00e7\u00e3o de energia interna para cada processo do ciclo.<\/span><\/h3>

c) Calcule o calor Qciclo<\/sub>, o trabalho Wciclo<\/sub> e a \u0394<\/span>U<\/span>ciclo<\/span><\/sub> varia\u00e7\u00e3o de energia interna para o ciclo.<\/span><\/h3>

d) Determine a efici\u00eancia da m\u00e1quina de Carnot.<\/span><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Figura 1: Ciclo de Carnot para um g\u00e1s ideal, com seus respectivos processos termodin\u00e2micos.<\/i><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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No Geogebra<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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1 \u2013 Em primeiro lugar, analise as unidades de cada grandeza f\u00edsica;<\/span><\/h3>

2 \u2013 O estudante dever\u00e1 construir o diagrama (P vs V) para o ciclo de Carnot, dessa forma, utilize as escalas como P(105 <\/sup>Pa) e V(10-4<\/sup> m3<\/sup>).<\/span><\/h3>

3 \u2013 Com os dados calculados, encontre as fun\u00e7\u00f5es P(V) para os processos de expans\u00e3o, ab <\/i>(Expans\u00e3o Isot\u00e9rmica) e bc<\/i> (Expans\u00e3o Adiab\u00e1tica). Os intervalos devem ser V<\/span>a<\/span><\/sub> \u2264<\/span> V <\/span>\u2264<\/span> V<\/span>b<\/span><\/sub> e P<\/span>a<\/span><\/sub> \u2264<\/span> P <\/span>\u2264<\/span> P<\/span>b<\/span><\/sub> para o processo <\/span>ab<\/i><\/span> e, V<\/span>b<\/span><\/sub> \u2264<\/span> V <\/span>\u2264<\/span> V<\/span>c<\/span><\/sub> e P<\/span>b<\/span><\/sub> \u2264<\/span> P <\/span>\u2264<\/span> P<\/span>c<\/span><\/sub> para o processo <\/span>bc<\/i><\/span>.<\/span><\/span><\/h3>

4 \u2013 Encontre as fun\u00e7\u00f5es P(V) para <\/span>os processos de <\/span>compres<\/span>s\u00e3o, <\/span>cd<\/span> <\/i>(<\/span>Compress\u00e3o<\/span> Isot\u00e9rmica) e <\/span>da<\/i><\/span> (<\/span>Compres<\/span>s\u00e3o Adiab\u00e1tica). Os intervalos devem ser V<\/span>c<\/span><\/sub> \u2264<\/span> V <\/span>\u2264<\/span> V<\/span>d<\/span><\/sub> e P<\/span>c<\/span><\/sub> \u2264<\/span> P <\/span>\u2264<\/span> P<\/span>d<\/span><\/sub> para o processo <\/span>cd<\/i><\/span> e, V<\/span>d<\/span><\/sub> \u2264<\/span> V <\/span>\u2264<\/span> V<\/span>a<\/span><\/sub> e P<\/span>d<\/span><\/sub> \u2264<\/span> P <\/span>\u2264<\/span> P<\/span>a<\/span><\/sub> para o processo <\/span>da<\/i><\/span>. <\/span><\/span><\/h3>

Obs: O estudante deve ter aten\u00e7\u00e3o <\/span>a<\/span>s unidades f\u00edsicas.<\/span><\/span><\/h3>

5 \u2013 Desenhe o ciclo de Carnot escrevendo as fun\u00e7\u00f5es abaixo:<\/span><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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6 \u2013 <\/span>Crie dois controles deslizantes: V<\/span>a<\/span><\/sub> \u2264<\/span> h <\/span>\u2264<\/span> V<\/span>c<\/span><\/sub> e V<\/span>a<\/span><\/sub> \u2264<\/span> r <\/span>\u2264<\/span> V<\/span>c<\/span><\/sub>.<\/span><\/span><\/h3>

7 \u2013 <\/span>Encontre os valores num\u00e9ricos das fun\u00e7\u00f5es f(x) e g(x), como segue:<\/span><\/span><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Obs.: f1 e g1 ser\u00e3o n\u00fameros, correspondendo a press\u00e3o em cada intervalo de volume, controlados pelos controles deslizantes.<\/span><\/h3>

8 \u2013 Crie dois pontos A(h,f1) e B(r,g1). Fa\u00e7a o teste variando h e r. O estudante dever\u00e1 perceber que os pontos acompanham as curvas de expans\u00e3o e compress\u00e3o.<\/span><\/h3>

9 \u2013 Escreva as equa\u00e7\u00f5es dos trabalhos de cada processo em fun\u00e7\u00e3o do volume. Note que para a expans\u00e3o W<\/span>ab<\/span><\/sub>(h) e W<\/span>bc<\/span><\/sub>(h), para a compress\u00e3o W<\/span>cd<\/span><\/sub>(r) e W<\/span>da<\/span><\/sub>(r). Lembre-se que os valores dos trabalhos devem obedecer os intervalos de cada processo. Os trabalhos s\u00e3o valores num\u00e9rico.<\/span><\/span><\/h3>

10 \u2013 Monte uma tabela apresentando os valores do Calor Q, do trabalho W e da varia\u00e7\u00e3o de energia interna \u0394U para cada processo, veja a figura 2.<\/span><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Figura 2: Diagrama (P vs V) do Ciclo de Carnot simulando as energias de cada processo e a efici\u00eancia da m\u00e1quina.<\/i><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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