{"id":47983,"date":"2019-11-07T14:55:37","date_gmt":"2019-11-07T13:55:37","guid":{"rendered":"https:\/\/www.thermal-engineering.org\/o-que-e-a-teoria-do-ciclo-de-rankine-equacoes-e-calculo-definicao\/"},"modified":"2020-01-26T13:42:33","modified_gmt":"2020-01-26T12:42:33","slug":"o-que-e-a-teoria-do-ciclo-de-rankine-equacoes-e-calculo-definicao","status":"publish","type":"post","link":"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-a-teoria-do-ciclo-de-rankine-equacoes-e-calculo-definicao\/","title":{"rendered":"O que \u00e9 a teoria do ciclo de Rankine &#8211; Equa\u00e7\u00f5es e c\u00e1lculo &#8211; Defini\u00e7\u00e3o"},"content":{"rendered":"<div class=\"su-quote su-quote-style-default\">\n<div class=\"su-quote-inner su-clearfix\">Teoria do Ciclo de Rankine &#8211; Equa\u00e7\u00f5es e C\u00e1lculo.\u00a0O c\u00e1lculo do ciclo Rankine \u00e9 simples com tabelas a vapor.\u00a0Engenheiros usam entalpias espec\u00edficas em todas as equa\u00e7\u00f5es.\u00a0Engenharia T\u00e9rmica<\/div>\n<\/div>\n<div class=\"su-divider su-divider-style-dotted\"><\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2>Teoria do Ciclo de Rankine<\/h2>\n<p>O\u00a0<strong>ciclo Rankine<\/strong>\u00a0recebeu seu nome e descreve o desempenho de\u00a0<strong>sistemas de turbinas a vapor<\/strong>\u00a0, embora o princ\u00edpio te\u00f3rico tamb\u00e9m se aplique a motores alternativos, como locomotivas a vapor.\u00a0Em geral, o\u00a0<strong>ciclo Rankine<\/strong>\u00a0\u00e9 um ciclo termodin\u00e2mico idealizado de um motor t\u00e9rmico de press\u00e3o constante que converte parte do calor em trabalho mec\u00e2nico.\u00a0Nesse ciclo, o calor \u00e9 fornecido externamente a um circuito fechado, que geralmente usa \u00e1gua (na fase l\u00edquida e de vapor) como fluido de trabalho.\u00a0Em contraste com o\u00a0<a title=\"Ciclo de Brayton - Motor de turbina a g\u00e1s\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-o-ciclo-de-brayton-motor-de-turbina-a-gas-definicao\/\">ciclo de Brayton<\/a>\u00a0, o fluido de trabalho no\u00a0<strong>ciclo Rankine<\/strong>\u00a0\u00a0passa pela\u00a0<strong>mudan\u00e7a de fase<\/strong>\u00a0\u00a0de uma fase l\u00edquida para vapor e vice-versa.<\/p>\n<p>Embora muitas subst\u00e2ncias possam ser usadas como fluido de trabalho no ciclo Rankine (inorg\u00e2nico ou mesmo org\u00e2nico), a\u00a0<a title=\"Propriedades da \u00c1gua\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/\"><strong>\u00e1gua<\/strong><\/a>\u00a0\u00e9 geralmente o fluido de escolha devido \u00e0s suas propriedades favor\u00e1veis, como qu\u00edmica n\u00e3o t\u00f3xica e n\u00e3o reativa, abund\u00e2ncia e baixo custo, bem como suas propriedades termodin\u00e2micas.\u00a0Por exemplo, a\u00a0<strong>\u00e1gua<\/strong>\u00a0possui o\u00a0<strong>calor espec\u00edfico mais alto<\/strong>\u00a0de qualquer subst\u00e2ncia comum &#8211; 4,19 kJ \/ kg K. Al\u00e9m disso, possui um\u00a0<a title=\"Calor latente de vaporiza\u00e7\u00e3o\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/latent-heat-of-vaporization\/\"><strong>calor de vaporiza\u00e7\u00e3o<\/strong><\/a>\u00a0muito alto\u00a0, o que a torna um\u00a0<strong>fluido de arrefecimento eficaz<\/strong>\u00a0e\u00a0<strong>m\u00e9dio<\/strong>\u00a0em usinas termel\u00e9tricas e outras ind\u00fastrias de energia.\u00a0No caso do ciclo Rankine, a\u00a0<a title=\"Lei do g\u00e1s ideal\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/ideal-gas-law\/\">Lei do G\u00e1s Ideal<\/a>quase n\u00e3o pode ser usado (o vapor n\u00e3o segue pV = nRT), portanto, todos os par\u00e2metros importantes de \u00e1gua e vapor s\u00e3o tabulados nas chamadas &#8221;\u00a0<strong><a title=\"Tabelas de Vapor - Propriedades Espec\u00edficas da \u00c1gua e Vapor\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/steam-tables\/\">Tabelas de Vapor<\/a><\/strong>\u00a0&#8220;.<\/p>\n<p>Uma das principais\u00a0<strong>vantagens<\/strong>\u00a0do\u00a0<strong>ciclo Rankine<\/strong>\u00a0\u00e9 que o\u00a0processo de\u00a0<strong>compress\u00e3o<\/strong>\u00a0na bomba ocorre\u00a0<strong>em um l\u00edquido<\/strong>\u00a0.\u00a0Ao condensar o vapor de trabalho em um l\u00edquido (dentro de um condensador), a press\u00e3o na sa\u00edda da turbina \u00e9 reduzida e a energia requerida pela bomba de alimenta\u00e7\u00e3o consome apenas 1% a 3% da pot\u00eancia de sa\u00edda da turbina e esses fatores contribuem para uma maior efici\u00eancia para o ciclo.<\/p>\n<p>Em um ciclo Rankine ideal, o sistema que executa o ciclo passa por uma s\u00e9rie de quatro processos: dois processos isentr\u00f3picos (adiab\u00e1ticos revers\u00edveis) alternados com dois processos isob\u00e1ricos:<\/p>\n<ul>\n<li>\n<figure id=\"attachment_17766\" class=\"wp-caption alignright\" aria-describedby=\"caption-attachment-17766\"><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-Cycle-Ts-Diagram-min.png\"><img loading=\"lazy\" class=\"size-medium wp-image-17766 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-Cycle-Ts-Diagram-min-300x300.png\" alt=\"Ciclo de Rankine - Diagrama Ts\" width=\"300\" height=\"300\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-Cycle-Ts-Diagram-min-300x300.png\" \/><\/a><figcaption id=\"caption-attachment-17766\" class=\"wp-caption-text\">Ciclo de Rankine &#8211; Diagrama Ts<\/figcaption><\/figure>\n<p><strong>Compress\u00e3o isentr\u00f3pica<\/strong>\u00a0(compress\u00e3o em bombas centr\u00edfugas) &#8211; O condensado l\u00edquido \u00e9 comprimido adiabaticamente do estado 1 ao estado 2 por bombas centr\u00edfugas (geralmente por bombas de condensa\u00e7\u00e3o e depois por bombas de \u00e1gua de alimenta\u00e7\u00e3o).\u00a0Os condensados \u200b\u200bl\u00edquidos s\u00e3o bombeados do condensador para a caldeira de alta press\u00e3o.\u00a0Nesse processo, o ambiente trabalha com o fluido, aumentando sua entalpia (h = u + pv) e comprimindo-o (aumentando sua press\u00e3o).\u00a0Por outro lado, a entropia permanece inalterada.\u00a0O trabalho necess\u00e1rio para o compressor \u00e9 dado por\u00a0<strong>W\u00a0<\/strong><strong><sub>Pumps<\/sub><\/strong><strong>\u00a0= H\u00a0<\/strong><strong><sub>2<\/sub><\/strong><strong>\u00a0&#8211; H\u00a0<\/strong><strong><sub>1<\/sub><\/strong><strong>\u00a0.<\/strong><\/li>\n<li><strong>Adi\u00e7\u00e3o de calor isob\u00e1rico<\/strong>\u00a0(em um trocador de calor &#8211; caldeira) &#8211; Nesta fase (entre o estado 2 e o estado 3), h\u00e1 uma transfer\u00eancia de calor de press\u00e3o constante para o condensado l\u00edquido de uma fonte externa, uma vez que a c\u00e2mara est\u00e1 aberta para entrar e sair .\u00a0A \u00e1gua de alimenta\u00e7\u00e3o (circuito secund\u00e1rio) \u00e9 aquecida at\u00e9 o ponto de ebuli\u00e7\u00e3o (2 \u2192 3a) desse fluido e depois evaporada na caldeira (3a \u2192 3).\u00a0O calor l\u00edquido adicionado \u00e9 dado por\u00a0<strong>Q\u00a0<\/strong><strong><sub>add<\/sub><\/strong><strong>\u00a0= H\u00a0<\/strong><strong><sub>3<\/sub><\/strong><strong>\u00a0&#8211; H\u00a0<\/strong><strong><sub>2<\/sub><\/strong><\/li>\n<li><strong>Expans\u00e3o isentr\u00f3pica<\/strong>\u00a0(expans\u00e3o em uma turbina a vapor) &#8211; O vapor da caldeira se expande adiabaticamente do estado 3 para o estado 4 em uma turbina a vapor para produzir trabalho e depois \u00e9 descarregado no condensador (parcialmente condensado).\u00a0O vapor trabalha nos arredores (p\u00e1s da turbina) e perde uma quantidade de entalpia igual ao trabalho que sai do sistema.\u00a0O trabalho realizado pela turbina \u00e9 dado por\u00a0<strong>W\u00a0<\/strong><strong><sub>T<\/sub><\/strong><strong>\u00a0= H\u00a0<\/strong><strong><sub>4<\/sub><\/strong><strong>\u00a0&#8211; H\u00a0<\/strong><strong><sub>3<\/sub><\/strong><strong>\u00a0.\u00a0<\/strong>Novamente a entropia permanece inalterada.<\/li>\n<li><strong>Rejei\u00e7\u00e3o de calor isob\u00e1rica (em um trocador de calor)<\/strong>\u00a0&#8211; Nesta fase, o ciclo \u00e9 conclu\u00eddo por um processo de press\u00e3o constante no qual o calor \u00e9 rejeitado pelo vapor parcialmente condensado.\u00a0H\u00e1 transfer\u00eancia de calor do vapor para a \u00e1gua de resfriamento que flui em um circuito de resfriamento.\u00a0O vapor condensa e a temperatura da \u00e1gua de resfriamento aumenta.\u00a0O calor l\u00edquido rejeitado \u00e9 dado por\u00a0<strong>Q\u00a0<\/strong><strong><sub>re<\/sub><\/strong><strong>\u00a0= H\u00a0<\/strong><strong><sub>4<\/sub><\/strong><strong>\u00a0&#8211; H\u00a0<\/strong><strong><sub>1<\/sub><\/strong><\/li>\n<\/ul>\n<p>Durante um ciclo de Rankine, o trabalho \u00e9 realizado no fluido pelas bombas entre os estados 1 e 2 (\u00a0<strong>i\u00a0<\/strong><strong>compress\u00e3o sentropic<\/strong>\u00a0).\u00a0O trabalho \u00e9 feito pelo fluido na turbina entre as fases 3 e 4 (\u00a0<strong>i\u00a0<\/strong><strong>expans\u00e3o sentropic<\/strong>\u00a0).\u00a0A diferen\u00e7a entre o trabalho realizado pelo fluido e o trabalho realizado no fluido \u00e9 o trabalho l\u00edquido produzido pelo ciclo e corresponde \u00e0 \u00e1rea delimitada pela curva do ciclo (no diagrama pV).\u00a0O fluido de trabalho em um ciclo Rankine segue um circuito fechado e \u00e9 reutilizado constantemente.<\/p>\n<p>Como pode ser visto, \u00e9 conveniente usar a entalpia e a primeira lei em termos de entalpia na an\u00e1lise desse ciclo termodin\u00e2mico.\u00a0Esta forma da lei\u00a0<strong>simplifica a descri\u00e7\u00e3o da transfer\u00eancia de energia<\/strong>\u00a0.\u00a0<strong>A press\u00e3o constante<\/strong>\u00a0, a\u00a0<strong>mudan\u00e7a de entalpia<\/strong>\u00a0\u00e9 igual \u00e0\u00a0<strong>energia<\/strong>\u00a0transferida do ambiente atrav\u00e9s do aquecimento:<\/p>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights  lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<p><strong><span>Processo isob\u00e1rico (Vdp = 0):<\/span><\/strong><\/p>\n<p><strong><span>dH = dQ \u2192 Q = H\u00a0<\/span><\/strong><strong><sub><span>2<\/span><\/sub><\/strong><strong><span>\u00a0&#8211; H\u00a0<\/span><\/strong><strong><sub><span>1<\/span><\/sub><\/strong><\/p>\n<p><strong><span>Na entropia constante<\/span><\/strong><span>\u00a0, ou seja, no processo isentr\u00f3pico, a\u00a0<\/span><strong><span>mudan\u00e7a de entalpia<\/span><\/strong><span>\u00a0\u00e9 igual ao\u00a0<\/span><strong><span>trabalho do processo de fluxo<\/span><\/strong><span>\u00a0realizado no ou pelo sistema:<\/span><\/p>\n<p><strong><span>Processo isentr\u00f3pico (dQ = 0):<\/span><\/strong><\/p>\n<p><strong><span>dH = Vdp \u2192 W = H\u00a0<\/span><\/strong><strong><sub><span>2<\/span><\/sub><\/strong><strong><span>\u00a0&#8211; H\u00a0<\/span><\/strong><strong><sub><span>1<\/span><\/sub><\/strong><\/p>\n<p><span>Veja tamb\u00e9m:\u00a0<\/span><a title=\"Primeira lei em termos de entalpia dH = dQ + Vdp\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/first-law-in-terms-of-enthalpy-dh-dq-vdp\/\"><span>Por que os engenheiros de energia usam entalpia?\u00a0Resposta: dH = dQ + Vdp<\/span><\/a><\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights  lgc-first lgc-last\">\n<div class=\"inside-grid-column\"><\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-50 lgc-tablet-grid-50 lgc-mobile-grid-100 lgc-equal-heights  lgc-first\">\n<div class=\"inside-grid-column\">\n<h2><span>Processo isentr\u00f3pico<\/span><\/h2>\n<p><span>Um\u00a0<\/span><a title=\"Processo isentr\u00f3pico\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-processo-isentropico-definicao\/\"><strong><span>processo isentr\u00f3pico<\/span><\/strong><\/a><span>\u00a0\u00e9 um\u00a0<\/span><a title=\"Processos termodin\u00e2micos\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-processo-termodinamico-definicao\/\"><strong><span>processo termodin\u00e2mico<\/span><\/strong><\/a><span>\u00a0, no qual a\u00a0<\/span><a title=\"O que \u00e9 entropia\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-entropy\/\"><strong><span>entropia<\/span><\/strong>\u00a0<\/a><span>do fluido ou g\u00e1s permanece constante.\u00a0Isso significa que o\u00a0<\/span><strong><span>processo isentr\u00f3pico<\/span><\/strong><span>\u00a0\u00e9 um caso especial de um\u00a0<\/span><strong><span>processo adiab\u00e1tico<\/span><\/strong><span>\u00a0no qual n\u00e3o h\u00e1 transfer\u00eancia de calor ou mat\u00e9ria.\u00a0\u00c9 um\u00a0<\/span><strong><span>processo adiab\u00e1tico revers\u00edvel<\/span><\/strong><span>\u00a0.\u00a0A suposi\u00e7\u00e3o de que n\u00e3o h\u00e1 transfer\u00eancia de calor \u00e9 muito importante, pois podemos usar a aproxima\u00e7\u00e3o adiab\u00e1tica apenas em\u00a0<\/span><strong><span>processos muito r\u00e1pidos<\/span><\/strong><span>\u00a0.<\/span><\/p>\n<p><strong><span>Processo isentr\u00f3pico e a primeira lei<\/span><\/strong><\/p>\n<p><span>Para um sistema fechado, podemos escrever a\u00a0<\/span><strong><a title=\"Primeira lei em termos de entalpia dH = dQ + Vdp\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/first-law-in-terms-of-enthalpy-dh-dq-vdp\/\"><span>primeira lei da termodin\u00e2mica em termos de entalpia<\/span><\/a><\/strong><span>\u00a0:<\/span><\/p>\n<p><strong><span>dH = dQ + Vdp<\/span><\/strong><\/p>\n<p><strong><span>ou<\/span><\/strong><\/p>\n<p><strong><span>dH = TdS + Vdp<\/span><\/strong><\/p>\n<p><strong><span>Processo isentr\u00f3pico (dQ = 0):<\/span><\/strong><\/p>\n<p><strong><span>dH = Vdp \u2192 W = H\u00a0<\/span><\/strong><strong><sub><span>2<\/span><\/sub><\/strong><strong><span>\u00a0&#8211; H\u00a0<\/span><\/strong><strong><sub><span>1<\/span><\/sub><\/strong><strong>\u00a0 \u00a0\u00a0<\/strong><\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-50 lgc-tablet-grid-50 lgc-mobile-grid-100 lgc-equal-heights  lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2><span>Processo isob\u00e1rico<\/span><\/h2>\n<p><span>Um\u00a0<\/span><a title=\"Processo isob\u00e1rico\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-o-processo-isobarico-definicao\/\"><strong><span>processo isob\u00e1rico<\/span><\/strong><\/a><span>\u00a0\u00e9 um\u00a0<\/span><a title=\"Processos termodin\u00e2micos\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-processo-termodinamico-definicao\/\"><span>processo termodin\u00e2mico<\/span><\/a><span>\u00a0, no qual a\u00a0<\/span><a title=\"O que \u00e9 press\u00e3o - F\u00edsica\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/\"><strong><span>press\u00e3o<\/span><\/strong><\/a><span>\u00a0do sistema\u00a0<\/span><strong><span>permanece constante<\/span><\/strong><span>\u00a0(p = const).\u00a0A transfer\u00eancia de calor para dentro ou para fora do sistema funciona, mas tamb\u00e9m altera a energia interna do sistema.<\/span><\/p>\n<p><span>Como existem mudan\u00e7as na\u00a0<\/span><a href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-energia-interna-energia-termica-definicao\/\"><span>energia interna<\/span><\/a><span>\u00a0(dU) e no volume do sistema (\u2206V), os engenheiros costumam usar a\u00a0<\/span><a title=\"O que \u00e9 entalpia\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-enthalpy\/\"><strong><span>entalpia<\/span><\/strong><\/a><span>\u00a0do sistema, que \u00e9 definida como:<\/span><\/p>\n<p><em><strong><span>H = U + pV<\/span><\/strong><\/em><\/p>\n<p><strong><span>Processo isob\u00e1rico e a primeira lei<\/span><\/strong><\/p>\n<p><span>A forma cl\u00e1ssica da\u00a0<\/span><a title=\"Primeira Lei da Termodin\u00e2mica\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-a-primeira-lei-da-termodinamica-definicao\/\"><span>primeira lei da termodin\u00e2mica<\/span><\/a><span>\u00a0\u00e9 a seguinte equa\u00e7\u00e3o:<\/span><\/p>\n<p><strong><span>dU = dQ &#8211; dW<\/span><\/strong><\/p>\n<p><span>Nesta equa\u00e7\u00e3o, dW \u00e9 igual a\u00a0<\/span><strong><span>dW = pdV<\/span><\/strong><span>\u00a0e \u00e9 conhecido como\u00a0<\/span><a title=\"Trabalho p\u0394V - Trabalho de Fronteira e Trabalho V\u0394p\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/p%ce%b4v-work-boundary-work-and-v%ce%b4p-work\/\"><span>trabalho de fronteira<\/span><\/a><span>\u00a0.\u00a0Em um processo isob\u00e1rico e no g\u00e1s ideal,\u00a0<\/span><strong><span>parte do calor adicionado<\/span><\/strong><span>\u00a0ao sistema ser\u00e1 usada para\u00a0<\/span><strong><span>realizar o trabalho<\/span><\/strong><span>\u00a0e\u00a0<\/span><strong><span>parte do calor<\/span><\/strong><span>\u00a0adicionado aumentar\u00e1 a\u00a0<\/span><a href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-energia-interna-energia-termica-definicao\/\"><strong><span>energia interna<\/span><\/strong><\/a><span>\u00a0(aumentar\u00e1 a temperatura).\u00a0Portanto, \u00e9 conveniente usar a\u00a0<\/span><strong><span>entalpia em<\/span><\/strong><span>\u00a0vez da energia interna.<\/span><\/p>\n<p><strong><span>Processo isob\u00e1rico (Vdp = 0):<\/span><\/strong><\/p>\n<p><strong><span>dH = dQ \u2192 Q = H\u00a0<\/span><\/strong><strong><sub><span>2<\/span><\/sub><\/strong><strong><span>\u00a0&#8211; H\u00a0<\/span><\/strong><strong><sub><span>1<\/span><\/sub><\/strong><\/p>\n<p><strong><span>Na entropia constante<\/span><\/strong><span>\u00a0, ou seja, no processo isentr\u00f3pico, a\u00a0<\/span><strong><span>mudan\u00e7a de entalpia<\/span><\/strong><span>\u00a0\u00e9 igual ao\u00a0<\/span><strong><span>trabalho do processo de fluxo<\/span><\/strong><span>\u00a0realizado no sistema ou pelo mesmo.<\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights  lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2><span>Efici\u00eancia t\u00e9rmica do ciclo Rankine<\/span><\/h2>\n<p><span>Em geral, a\u00a0<a title=\"Efici\u00eancia t\u00e9rmica\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-eficiencia-termica-definicao\/\"><strong>efici\u00eancia t\u00e9rmica<\/strong><\/a><a title=\"Efici\u00eancia t\u00e9rmica\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-eficiencia-termica-definicao\/\">\u00a0,\u00a0<\/a><a title=\"Efici\u00eancia t\u00e9rmica\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-eficiencia-termica-definicao\/\"><strong><em>\u03b7\u00a0<\/em><\/strong><\/a><a title=\"Efici\u00eancia t\u00e9rmica\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-eficiencia-termica-definicao\/\"><strong><em><sub>th<\/sub><\/em><\/strong><\/a>\u00a0, de qualquer motor de calor \u00e9 definida como a raz\u00e3o entre o\u00a0<a href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-trabalho-em-termodinamica-definicao\/\">trabalho<\/a>\u00a0que faz,\u00a0<strong>W<\/strong>\u00a0, para o\u00a0<a href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-calor-na-fisica-calor-definicao\/\">calor<\/a>\u00a0de entrada a uma temperatura elevada, Q\u00a0<sub>H<\/sub>\u00a0.<\/span><\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-formula-1.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-16945 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-formula-1.png\" alt=\"f\u00f3rmula de efici\u00eancia t\u00e9rmica - 1\" width=\"125\" height=\"82\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-formula-1.png\" \/><\/a><\/p>\n<p><span>A\u00a0<\/span><strong><span>efici\u00eancia t\u00e9rmica<\/span><\/strong><span>\u00a0,\u00a0<\/span><strong><em><span>\u03b7\u00a0<\/span><\/em><\/strong><strong><em><sub><span>th<\/span><\/sub><\/em><\/strong><span>\u00a0, representa a fra\u00e7\u00e3o de\u00a0<\/span><strong><span>calor<\/span><\/strong><span>\u00a0,\u00a0<\/span><strong><span>Q\u00a0<\/span><\/strong><strong><sub><span>H<\/span><\/sub><\/strong><span>\u00a0, que \u00e9 convertida\u00a0<\/span><strong><span>em trabalho<\/span><\/strong><span>\u00a0.\u00a0Como a energia \u00e9 conservada de acordo com a\u00a0<\/span><a href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-a-primeira-lei-da-termodinamica-definicao\/\"><strong><span>primeira lei da termodin\u00e2mica<\/span><\/strong><\/a><span>\u00a0e a energia n\u00e3o pode ser convertida para funcionar completamente, a entrada de calor, Q\u00a0<\/span><sub><span>H<\/span><\/sub><span>\u00a0, deve ser igual ao trabalho realizado, W, mais o calor que deve ser dissipado como\u00a0<\/span><strong><span>calor residual Q\u00a0<\/span><\/strong><strong><sub><span>C<\/span><\/sub><\/strong><span>\u00a0no meio Ambiente.\u00a0Portanto, podemos reescrever a f\u00f3rmula da efici\u00eancia t\u00e9rmica como:<\/span><\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-formula-2.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-16944 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-formula-2.png\" alt=\"f\u00f3rmula de efici\u00eancia t\u00e9rmica - 2\" width=\"352\" height=\"83\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-formula-2.png\" \/><\/a><\/p>\n<p><span>Essa \u00e9 uma f\u00f3rmula muito \u00fatil, mas aqui expressamos a efici\u00eancia t\u00e9rmica usando a primeira lei em termos de\u00a0<\/span><a title=\"O que \u00e9 entalpia\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-enthalpy\/\"><span>entalpia<\/span><\/a><span>\u00a0.<\/span><\/p>\n<figure id=\"attachment_17781\" class=\"wp-caption alignright\" aria-describedby=\"caption-attachment-17781\"><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-Cycle-Ts-diagram.png\"><img loading=\"lazy\" class=\"size-medium wp-image-17781 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-Cycle-Ts-diagram-300x276.png\" alt=\"Ciclo de Rankine - diagrama de Ts\" width=\"300\" height=\"276\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-Cycle-Ts-diagram-300x276.png\" \/><\/a><figcaption id=\"caption-attachment-17781\" class=\"wp-caption-text\"><span>Ciclo de Rankine &#8211; diagrama de Ts<\/span><\/figcaption><\/figure>\n<p><span>Normalmente, a maioria das\u00a0<\/span><strong><span>usinas nucleares<\/span><\/strong><span>\u00a0opera\u00a0<\/span><strong><span>turbinas a vapor de condensa\u00e7\u00e3o de v\u00e1rios est\u00e1gios<\/span><\/strong><span>\u00a0.\u00a0Nessas turbinas, o est\u00e1gio de alta press\u00e3o recebe\u00a0<\/span><a href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-o-steam-propriedades-do-steam-definicao\/\"><span>vapor<\/span><\/a><span>\u00a0(esse vapor \u00e9 quase o vapor saturado &#8211; x = 0,995 &#8211; ponto C na figura;\u00a0<\/span><strong><span>6 MPa<\/span><\/strong><span>\u00a0; 275,6 \u00b0 C) de um gerador de vapor e o esgota no separador-reaquecedor de umidade (ponto D )\u00a0O vapor deve ser reaquecido para evitar danos que possam ser causados \u200b\u200b\u00e0s p\u00e1s da turbina a vapor por vapor de\u00a0<\/span><a title=\"Qualidade de Vapor - Fra\u00e7\u00e3o de Secura\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/vapor-quality-dryness-fraction\/\"><span>baixa qualidade<\/span><\/a><span>\u00a0.\u00a0O reaquecedor aquece o vapor (ponto D) e, em seguida, o vapor \u00e9 direcionado para o est\u00e1gio de baixa press\u00e3o da turbina a vapor, onde se expande (pontos E a F).\u00a0O vapor exaurido condensa no condensador e est\u00e1 a uma press\u00e3o bem abaixo da atmosf\u00e9rica (press\u00e3o absoluta de<\/span><strong><span>0,008 MPa<\/span><\/strong><span>\u00a0) e est\u00e1 em um estado parcialmente condensado (ponto F), tipicamente com uma qualidade pr\u00f3xima a 90%.<\/span><\/p>\n<p><span>Nesse caso, geradores de vapor, turbinas a vapor, condensadores e bombas de \u00e1gua de alimenta\u00e7\u00e3o constituem um motor t\u00e9rmico, sujeito \u00e0s limita\u00e7\u00f5es de efici\u00eancia impostas pela\u00a0<a title=\"Segunda Lei da Termodin\u00e2mica\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-a-segunda-lei-da-termodinamica-definicao\/\"><strong>segunda lei da termodin\u00e2mica<\/strong><\/a>\u00a0.\u00a0No caso ideal (sem atrito, processos revers\u00edveis, design perfeito), este motor t\u00e9rmico teria uma\u00a0<a title=\"Efici\u00eancia de Carnot - Efici\u00eancia do mecanismo de calor de Carnot\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/carnot-efficiency-efficiency-of-carnot-heat-engine\/\">efici\u00eancia<\/a>\u00a0de\u00a0<a title=\"Efici\u00eancia de Carnot - Efici\u00eancia do mecanismo de calor de Carnot\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/carnot-efficiency-efficiency-of-carnot-heat-engine\/\">Carnot<\/a>\u00a0de<\/span><\/p>\n<p><span>= 1 &#8211; T\u00a0<\/span><sub><span>frio<\/span><\/sub><span>\u00a0\/ T\u00a0<\/span><sub><span>quente<\/span><\/sub><span>\u00a0= 1 &#8211; 315\/549 = 42,6%<\/span><\/p>\n<p><span>onde a temperatura do reservat\u00f3rio quente \u00e9 de 275,6 \u00b0 C (548,7 K), a temperatura do reservat\u00f3rio frio \u00e9 de 41,5 \u00b0 C (314,7 K).\u00a0Mas a usina nuclear \u00e9 o\u00a0<\/span><strong><span>verdadeiro motor t\u00e9rmico<\/span><\/strong><span>\u00a0, no qual os processos termodin\u00e2micos s\u00e3o de alguma forma irrevers\u00edveis.\u00a0Eles n\u00e3o s\u00e3o feitos infinitamente devagar.\u00a0Em dispositivos reais (como turbinas, bombas e compressores), um atrito mec\u00e2nico e perdas de calor causam mais perdas de efici\u00eancia.<\/span><\/p>\n<p><span>Para calcular a\u00a0<\/span><strong><span>efici\u00eancia t\u00e9rmica<\/span><\/strong><span>\u00a0do\u00a0<\/span><strong><span>ciclo Rankine<\/span><\/strong><span>\u00a0mais simples\u00a0(sem reaquecer), os engenheiros usam a\u00a0<\/span><a title=\"Primeira lei em termos de entalpia dH = dQ + Vdp\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/first-law-in-terms-of-enthalpy-dh-dq-vdp\/\"><strong><span>primeira lei da termodin\u00e2mica em termos de entalpia<\/span><\/strong><\/a><span>\u00a0e n\u00e3o em energia interna.<\/span><\/p>\n<p><span>A primeira lei em termos de entalpia \u00e9:<\/span><\/p>\n<p><em><strong><span>dH = dQ + Vdp<\/span><\/strong><\/em><\/p>\n<p><span>Nesta equa\u00e7\u00e3o, o termo\u00a0<\/span><strong><em><span>Vdp<\/span><\/em><\/strong><span>\u00a0\u00e9 um\u00a0<\/span><strong><span>trabalho de processo de fluxo.\u00a0<\/span><\/strong><span>Este trabalho, \u00a0\u00a0<\/span><strong><em><span>Vdp<\/span><\/em><\/strong><span>\u00a0, \u00e9 usado para\u00a0<\/span><strong><span>sistemas de fluxo aberto<\/span><\/strong><span>\u00a0como uma\u00a0<\/span><strong><span>turbina<\/span><\/strong><span>\u00a0ou uma\u00a0<\/span><strong><span>bomba<\/span><\/strong><span>\u00a0na qual existe um\u00a0<\/span><strong><span>&#8220;dp&#8221;<\/span><\/strong><span>\u00a0, ou seja, mudan\u00e7a de press\u00e3o.\u00a0N\u00e3o h\u00e1 altera\u00e7\u00f5es no\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/fluid-dynamics\/control-volume-control-volume-analysis\/\"><span>volume de controle<\/span><\/a><span>\u00a0.\u00a0Como pode ser visto, essa forma de lei\u00a0<\/span><strong><span>simplifica a descri\u00e7\u00e3o da transfer\u00eancia de energia<\/span><\/strong><span>\u00a0.\u00a0<\/span><strong><span>A press\u00e3o constante<\/span><\/strong><span>\u00a0, a\u00a0<\/span><strong><span>mudan\u00e7a de entalpia<\/span><\/strong><span>\u00a0\u00e9 igual \u00e0\u00a0<\/span><strong><span>energia<\/span><\/strong><span>\u00a0transferida do ambiente atrav\u00e9s do aquecimento:<\/span><\/p>\n<p><strong><span>Processo isob\u00e1rico (Vdp = 0):<\/span><\/strong><\/p>\n<p><strong><span>dH = dQ \u2192 Q = H\u00a0<\/span><\/strong><strong><sub><span>2<\/span><\/sub><\/strong><strong><span>\u00a0&#8211; H\u00a0<\/span><\/strong><strong><sub><span>1<\/span><\/sub><\/strong><\/p>\n<p><strong><span>Na entropia constante<\/span><\/strong><span>\u00a0, ou seja, no processo isentr\u00f3pico, a\u00a0<\/span><strong><span>mudan\u00e7a de entalpia<\/span><\/strong><span>\u00a0\u00e9 igual ao\u00a0<\/span><strong><span>trabalho do processo de fluxo<\/span><\/strong><span>\u00a0realizado no ou pelo sistema:<\/span><\/p>\n<p><strong><span>Processo isentr\u00f3pico (dQ = 0):<\/span><\/strong><\/p>\n<p><strong><span>dH = Vdp \u2192 W = H\u00a0<\/span><\/strong><strong><sub><span>2<\/span><\/sub><\/strong><strong><span>\u00a0&#8211; H\u00a0<\/span><\/strong><strong><sub><span>1<\/span><\/sub><\/strong><\/p>\n<p><span>\u00c9 \u00f3bvio que ser\u00e1 muito \u00fatil na an\u00e1lise de ambos os ciclos termodin\u00e2micos usados \u200b\u200bna engenharia de energia, ou seja, no ciclo de Brayton e no ciclo de Rankine.<\/span><\/p>\n<p><span>A\u00a0<\/span><strong><span>entalpia<\/span><\/strong><span>\u00a0pode ser transformada em uma\u00a0vari\u00e1vel\u00a0<\/span><strong><span>intensiva<\/span><\/strong><span>\u00a0ou\u00a0<\/span><strong><span>espec\u00edfica<\/span><\/strong><span>\u00a0dividindo-se pela\u00a0<\/span><a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-mass-and-weight\/what-is-mass\/\"><span>massa<\/span><\/a><span>\u00a0.\u00a0<\/span><strong><span>Os engenheiros usam mais a\u00a0<\/span><\/strong><strong><span>entalpia espec\u00edfica<\/span><\/strong><span>\u00a0na an\u00e1lise termodin\u00e2mica do que a pr\u00f3pria entalpia.\u00a0Ele \u00e9 tabulado nas\u00a0<\/span><a title=\"Tabelas de Vapor - Propriedades Espec\u00edficas da \u00c1gua e Vapor\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/steam-tables\/\"><strong><span>tabelas de vapor,<\/span><\/strong><\/a><span>\u00a0juntamente com o\u00a0<\/span><a title=\"O que \u00e9 volume espec\u00edfico\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-specific-volume\/\"><span>volume\u00a0<\/span><\/a><a title=\"Energia interna espec\u00edfica\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/specific-internal-energy\/\"><span>espec\u00edfico<\/span><\/a><span>\u00a0e\u00a0<a title=\"Energia interna espec\u00edfica\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/specific-internal-energy\/\">a energia interna espec\u00edfica<\/a>\u00a0.\u00a0A efici\u00eancia t\u00e9rmica desse ciclo simples de Rankine e em termos de entalpias espec\u00edficas seria:<\/span><\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-rankine-cycle-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-16962 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-rankine-cycle-equation.png\" alt=\"efici\u00eancia t\u00e9rmica do ciclo Rankine\" width=\"535\" height=\"68\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-rankine-cycle-equation.png\" \/><\/a><\/p>\n<p><span>\u00c9 uma equa\u00e7\u00e3o muito simples e, para determinar a efici\u00eancia t\u00e9rmica, voc\u00ea pode usar os dados das\u00a0<\/span><strong><span>tabelas de vapor<\/span><\/strong><span>\u00a0.<\/span><\/p>\n<figure id=\"attachment_16961\" class=\"wp-caption alignright\" aria-describedby=\"caption-attachment-16961\"><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-engines-turbines-min.png\"><img loading=\"lazy\" class=\"wp-image-16961 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-engines-turbines-min.png\" alt=\"Takaishi, Tatsuo;  Numata, Akira;  Nakano, Ryouji;  Sakaguchi, Katsuhiko (mar\u00e7o de 2008).\" width=\"452\" height=\"334\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/thermal-efficiency-engines-turbines-min.png\" \/><\/a><figcaption id=\"caption-attachment-16961\" class=\"wp-caption-text\"><span>Takaishi, Tatsuo;\u00a0Numata, Akira;\u00a0Nakano, Ryouji;\u00a0Sakaguchi, Katsuhiko (mar\u00e7o de 2008).\u00a0\u201cAbordagem para motores a diesel e g\u00e1s de alta efici\u00eancia\u201d (PDF).\u00a0Revis\u00e3o t\u00e9cnica Mitsubishi Heavy Industries.\u00a045 (1).\u00a0P\u00e1gina visitada em 2011-02-04.<\/span><\/figcaption><\/figure>\n<p><span>Nas modernas usinas nucleares, a efici\u00eancia t\u00e9rmica geral \u00e9 de cerca de\u00a0<\/span><strong><span>um ter\u00e7o<\/span><\/strong><span>\u00a0(33%); portanto, s\u00e3o necess\u00e1rios\u00a0<\/span><strong><span>3000 MWth<\/span><\/strong><span>\u00a0de energia t\u00e9rmica da rea\u00e7\u00e3o de fiss\u00e3o para gerar\u00a0<\/span><strong><span>1000 MWe<\/span><\/strong><span>\u00a0de energia el\u00e9trica.\u00a0O motivo est\u00e1 na temperatura do vapor relativamente baixa (\u00a0<\/span><strong><span>6 MPa<\/span><\/strong><span>\u00a0; 275,6 \u00b0 C).\u00a0Efici\u00eancias mais altas podem ser alcan\u00e7adas aumentando a\u00a0<\/span><strong><span>temperatura<\/span><\/strong><span>do vapor.\u00a0Mas isso requer um aumento nas press\u00f5es dentro de caldeiras ou geradores de vapor.\u00a0No entanto, considera\u00e7\u00f5es metal\u00fargicas imp\u00f5em limites superiores a essas press\u00f5es.\u00a0Em compara\u00e7\u00e3o com outras fontes de energia, a efici\u00eancia t\u00e9rmica de 33% n\u00e3o \u00e9 grande.\u00a0Mas deve-se notar que as usinas nucleares s\u00e3o muito mais complexas que as usinas de combust\u00edveis f\u00f3sseis e \u00e9 muito mais f\u00e1cil queimar combust\u00edveis f\u00f3sseis do que gerar energia a partir de combust\u00edveis nucleares.\u00a0As usinas subcr\u00edticas de combust\u00edveis f\u00f3sseis, que s\u00e3o operadas sob\u00a0<\/span><a title=\"Press\u00e3o cr\u00edtica da \u00e1gua\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/critical-pressure-of-water\/\"><strong><span>press\u00e3o cr\u00edtica<\/span><\/strong>\u00a0<\/a><span>(ou seja, inferiores a 22,1 MPa), podem atingir uma efici\u00eancia de 36 a 40%.<\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights  lgc-first lgc-last\">\n<div class=\"inside-grid-column\">\n<div class=\"su-spacer\"><\/div>\n<h2><span>Ciclo de Rankine &#8211; Equa\u00e7\u00f5es e C\u00e1lculo<\/span><\/h2>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-Cycle-scheme.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-17771 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-Cycle-scheme.png\" alt=\"Ciclo Rankine\" width=\"300\" height=\"450\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-Cycle-scheme.png\" \/><\/a><span>Vamos assumir o\u00a0<\/span><strong><span>ciclo Rankine<\/span><\/strong><span>\u00a0, que \u00e9 um dos\u00a0<\/span><strong><span>ciclos termodin\u00e2micos<\/span><\/strong><span>\u00a0mais comuns\u00a0em usinas termel\u00e9tricas.\u00a0Nesse caso, assuma um ciclo simples, sem reaquecimento e sem a turbina a vapor de condensa\u00e7\u00e3o funcionando com\u00a0<\/span><a title=\"Vapor seco\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/dry-steam\/\"><span>vapor saturado<\/span><\/a><span>\u00a0\u00a0(vapor seco).\u00a0Nesse caso, a turbina opera em estado estacion\u00e1rio com condi\u00e7\u00f5es de entrada de 6 MPa, t = 275,6 \u00b0 C, x = 1 (ponto 3).\u00a0O vapor sai deste est\u00e1gio da turbina a uma press\u00e3o de 0,008 MPa, 41,5 \u00b0 C e x = ???\u00a0(ponto 4)<\/span><\/p>\n<p><span>Calcular:<\/span><\/p>\n<ol>\n<li><span>a qualidade do vapor do vapor de sa\u00edda<\/span><\/li>\n<li><span>a diferen\u00e7a de entalpia entre estes dois estados (3 \u2192 4), a qual corresponde ao trabalho realizado pelo vapor, W\u00a0<\/span><sub><span>t<\/span><\/sub><span>\u00a0.<\/span><\/li>\n<li><span>a diferen\u00e7a de entalpia entre estes dois estados (1 \u2192 2), que corresponde ao trabalho feito por bombas, W\u00a0<\/span><sub><span>P<\/span><\/sub><span>\u00a0.<\/span><\/li>\n<li><span>a diferen\u00e7a de entalpia entre esses dois estados (2 \u2192 3), que corresponde ao calor l\u00edquido adicionado no gerador de vapor<\/span><\/li>\n<li><span>a efici\u00eancia termodin\u00e2mica deste ciclo e compare esse valor com a efici\u00eancia de Carnot<\/span><\/li>\n<\/ol>\n<p><span>1)<\/span><\/p>\n<p><span>Como n\u00e3o sabemos a qualidade exata do vapor de sa\u00edda, precisamos determinar esse par\u00e2metro.\u00a0O estado 4 \u00e9 fixado pela press\u00e3o\u00a0<\/span><strong><span>p\u00a0<\/span><sub><span>4<\/span><\/sub><span>\u00a0= 0,008 MPa<\/span><\/strong><span>\u00a0e o fato de que a\u00a0<\/span><a title=\"Entropia espec\u00edfica\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-entropy\/specific-entropy\/\"><span>entropia espec\u00edfica<\/span><\/a><span>\u00a0\u00e9 constante para a expans\u00e3o isentr\u00f3pica (s\u00a0<\/span><sub><span>3<\/span><\/sub><span>\u00a0= s\u00a0<\/span><sub><span>4<\/span><\/sub><span>\u00a0= 5,89\u00a0<\/span><em><span>kJ \/ kgK para 6 MPa<\/span><\/em><span>\u00a0).\u00a0A entropia espec\u00edfica da \u00e1gua l\u00edquida saturada (x = 0) e do vapor seco (x = 1) pode ser selecionada nas\u00a0<\/span><a title=\"Tabelas de Vapor - Propriedades Espec\u00edficas da \u00c1gua e Vapor\" href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/steam-tables\/\"><span>tabelas de vapor<\/span><\/a><span>\u00a0.\u00a0No caso de vapor \u00famido, a entropia real pode ser calculada com a qualidade do vapor,\u00a0<\/span><em><span>x,<\/span><\/em><span>\u00a0e as entropias espec\u00edficas de \u00e1gua l\u00edquida saturada e vapor seco:<\/span><\/p>\n<p><em><span>s\u00a0<\/span><\/em><em><sub><span>4<\/span><\/sub><\/em><em><span>\u00a0= s\u00a0<\/span><\/em><em><sub><span>v<\/span><\/sub><\/em><em><span>\u00a0x + (1 &#8211; x) s\u00a0<\/span><\/em><em><sub><span>l<\/span><\/sub><\/em><em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/em><\/p>\n<p><em><span>Onde<\/span><\/em><\/p>\n<p><em><span>s\u00a0<\/span><\/em><em><sub><span>4<\/span><\/sub><\/em><em><span>\u00a0= entropia de vapor \u00famido (J \/ kg K) =<\/span><\/em><span>\u00a05,89\u00a0<\/span><em><span>kJ \/ kgK<\/span><\/em><\/p>\n<p><em><span>s\u00a0<\/span><\/em><em><sub><span>v<\/span><\/sub><\/em><em><span>\u00a0= entropia do vapor &#8220;seco&#8221; (J \/ kg K) = 8,227 kJ \/ kgK (para 0,008 MPa)<\/span><\/em><\/p>\n<p><em><span>s\u00a0<\/span><\/em><em><sub><span>l<\/span><\/sub><\/em><em><span>\u00a0= entropia de \u00e1gua l\u00edquida saturada (J \/ kg K) = 0,592 kJ \/ kgK (para 0,008 MPa)<\/span><\/em><\/p>\n<p><span>A partir desta equa\u00e7\u00e3o, a qualidade do vapor \u00e9:<\/span><\/p>\n<p><span>x\u00a0<\/span><sub><span>4<\/span><\/sub><span>\u00a0= (\u00a0<\/span><em><span>s\u00a0<\/span><\/em><em><sub><span>4<\/span><\/sub><\/em><em><span>\u00a0&#8211; s\u00a0<\/span><\/em><em><sub><span>l<\/span><\/sub><\/em><span>\u00a0) \/ (\u00a0<\/span><em><span>s\u00a0<\/span><\/em><em><sub><span>v<\/span><\/sub><\/em><em><span>\u00a0&#8211; s\u00a0<\/span><\/em><em><sub><span>l<\/span><\/sub><\/em><span>\u00a0) = (5,89 &#8211; 0,592) \/ (8,227 &#8211; 0,592) = 0,694 = 69,4%<\/span><\/p>\n<p><span>2)<\/span><\/p>\n<p><span>A entalpia para o estado 3 pode ser coletada diretamente das tabelas de vapor, enquanto a entalpia para o estado 4 deve ser calculada usando a qualidade do vapor:<\/span><\/p>\n<p><em><span>h\u00a0<\/span><\/em><em><sub><span>3, v<\/span><\/sub><\/em><em><span>\u00a0=<\/span><\/em><span>\u00a02785 kJ \/ kg<\/span><\/p>\n<p><em><span>h\u00a0<\/span><\/em><em><sub><span>4, molhado<\/span><\/sub><\/em><em><span>\u00a0= h\u00a0<\/span><\/em><em><sub><span>4, v<\/span><\/sub><\/em><em><span>\u00a0x + (1 &#8211; x) h\u00a0<\/span><\/em><em><sub><span>4, l<\/span><\/sub><\/em><span>\u00a0\u00a0= 2576.\u00a00,694 + (1 &#8211; 0,694).\u00a0174 = 1787 + 53,2 = 1840 kJ \/ kg<\/span><\/p>\n<p><span>Ent\u00e3o o trabalho realizado pelo vapor, W\u00a0<\/span><sub><span>T,<\/span><\/sub><span>\u00a0\u00e9<\/span><\/p>\n<p><strong><span>W\u00a0<\/span><\/strong><strong><sub><span>T<\/span><\/sub><\/strong><span>\u00a0= \u0394h =\u00a0<\/span><strong><span>945 kJ \/ kg<\/span><\/strong><\/p>\n<p><strong><span>3)<\/span><\/strong><\/p>\n<p><span>A entalpia para o estado 1 pode ser obtida diretamente das tabelas de vapor:<\/span><\/p>\n<p><em><span>h\u00a0<\/span><\/em><em><sub><span>1, l<\/span><\/sub><\/em><em><span>\u00a0=<\/span><\/em><span>\u00a0174 kJ \/ kg<\/span><\/p>\n<p><span>O estado 2 \u00e9 fixado pela press\u00e3o p\u00a0<\/span><sub><span>2<\/span><\/sub><span>\u00a0= 6,0 MPa e pelo fato de a entropia espec\u00edfica ser constante para a compress\u00e3o isentr\u00f3pica (s\u00a0<\/span><sub><span>1<\/span><\/sub><span>\u00a0= s\u00a0<\/span><sub><span>2<\/span><\/sub><span>\u00a0= 0,592\u00a0<\/span><em><span>kJ \/ kgK para 0,008 MPa<\/span><\/em><span>\u00a0).\u00a0Para esta entropia s\u00a0<\/span><sub><span>2<\/span><\/sub><span>\u00a0=\u00a0<\/span><strong><span>0,592\u00a0<\/span><em><span>kJ \/ kgK<\/span><\/em><\/strong><span>\u00a0ep\u00a0<\/span><sub><span>2<\/span><\/sub><span>\u00a0= 6,0 MPa, encontramos\u00a0<\/span><strong><em><span>h\u00a0<\/span><\/em><\/strong><strong><em><sub><span>2, sub-resfriado<\/span><\/sub><\/em><\/strong><span>\u00a0em tabelas de vapor para \u00e1gua comprimida (usando interpola\u00e7\u00e3o entre dois estados).<\/span><\/p>\n<p><strong><em><span>h\u00a0<\/span><\/em><\/strong><strong><em><sub><span>2, sub-resfriado<\/span><\/sub><\/em><\/strong><strong><em><span>\u00a0=<\/span><\/em><\/strong><strong><span>\u00a0179,7 kJ \/ kg<\/span><\/strong><\/p>\n<p><span>Ent\u00e3o, o trabalho realizado pelas bombas, W\u00a0<\/span><sub><span>P,<\/span><\/sub><span>\u00a0\u00e9<\/span><\/p>\n<p><strong><span>W\u00a0<\/span><\/strong><strong><sub><span>P<\/span><\/sub><\/strong><span>\u00a0= \u0394h =\u00a0<\/span><strong><span>5,7 kJ \/ kg<\/span><\/strong><\/p>\n<p><span>4)<\/span><\/p>\n<p><span>A diferen\u00e7a de entalpia entre (2 \u2192 3), que corresponde ao calor l\u00edquido adicionado no gerador de vapor, \u00e9 simplesmente:<\/span><\/p>\n<p><strong><em><span>Q\u00a0<\/span><\/em><\/strong><strong><em><sub><span>add<\/span><\/sub><\/em><\/strong><em><span>\u00a0= h\u00a0<\/span><\/em><em><sub><span>3, v<\/span><\/sub><\/em><em><span>\u00a0\u00a0&#8211; h\u00a0<\/span><\/em><em><sub><span>2, sub-resfriado<\/span><\/sub><\/em><em><span>\u00a0= 2785 &#8211; 179,7 = \u00a0\u00a0<\/span><strong><span>2605,3 kJ \/ kg<\/span><\/strong><\/em><\/p>\n<p><span>Observe que, n\u00e3o h\u00e1 regenera\u00e7\u00e3o de calor neste ciclo.\u00a0Por outro lado, a maior parte do calor adicionado \u00e9 para a entalpia da vaporiza\u00e7\u00e3o (isto \u00e9, para a mudan\u00e7a de fase).<\/span><\/p>\n<p><span>5)<\/span><\/p>\n<p><span>Nesse caso, geradores de vapor, turbinas a vapor, condensadores e bombas de \u00e1gua de alimenta\u00e7\u00e3o constituem um motor t\u00e9rmico, sujeito \u00e0s limita\u00e7\u00f5es de efici\u00eancia impostas pela\u00a0<a href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-a-segunda-lei-da-termodinamica-definicao\/\"><strong>segunda lei da termodin\u00e2mica<\/strong><\/a>\u00a0.\u00a0No caso ideal (sem atrito, processos revers\u00edveis, design perfeito), esse motor t\u00e9rmico teria uma\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/carnot-efficiency-efficiency-of-carnot-heat-engine\/\">efici\u00eancia<\/a>\u00a0de\u00a0<a href=\"https:\/\/www.nuclear-power.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/carnot-efficiency-efficiency-of-carnot-heat-engine\/\">Carnot<\/a>\u00a0de<\/span><\/p>\n<p><strong><em><span>\u03b7\u00a0<\/span><\/em><\/strong><strong><em><sub><span>Carnot<\/span><\/sub><\/em><\/strong><span>\u00a0= 1 &#8211; T<\/span><sub><span>\u00a0frio<\/span><\/sub><span>\u00a0\/ T<\/span><sub><span>\u00a0quente<\/span><\/sub><span>\u00a0= 1 &#8211; 315\/549 =<\/span><strong><span>\u00a042,6%<\/span><\/strong><\/p>\n<p><span>onde a temperatura do reservat\u00f3rio quente \u00e9 de 275,6 \u00b0 C (548,7 K), a temperatura do reservat\u00f3rio frio \u00e9 de 41,5 \u00b0 C (314,7 K).<\/span><\/p>\n<p><span>A efici\u00eancia termodin\u00e2mica deste ciclo pode ser calculada pela seguinte f\u00f3rmula:<\/span><\/p>\n<p><a href=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-cycle-example-thermal-efficiency.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-17792 lazy-loaded\" src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-cycle-example-thermal-efficiency.png\" alt=\"Ciclo de Rankine - exemplo - efici\u00eancia t\u00e9rmica\" width=\"159\" height=\"76\" data-lazy-type=\"image\" data-src=\"https:\/\/thermal-engineering.org\/wp-content\/uploads\/2019\/05\/Rankine-cycle-example-thermal-efficiency.png\" \/><\/a><\/p>\n<p><span>assim<\/span><br \/>\n<strong><em><span>\u03b7\u00a0<\/span><\/em><\/strong><strong><em><sub><span>th<\/span><\/sub><\/em><\/strong><span>\u00a0= (945 &#8211; 5,7) \/ 2605,3 = 0,361 =\u00a0<\/span><strong><span>36,1%<\/span><\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;.<\/p>\n<p>Este artigo \u00e9 baseado na tradu\u00e7\u00e3o autom\u00e1tica do artigo original em ingl\u00eas. Para mais informa\u00e7\u00f5es, consulte o artigo em ingl\u00eas. Voc\u00ea pode nos ajudar. Se voc\u00ea deseja corrigir a tradu\u00e7\u00e3o, envie-a para: translations@nuclear-power.com ou preencha o formul\u00e1rio de tradu\u00e7\u00e3o on-line. Agradecemos sua ajuda, atualizaremos a tradu\u00e7\u00e3o o mais r\u00e1pido poss\u00edvel. Obrigado.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Teoria do Ciclo de Rankine &#8211; Equa\u00e7\u00f5es e C\u00e1lculo.\u00a0O c\u00e1lculo do ciclo Rankine \u00e9 simples com tabelas a vapor.\u00a0Engenheiros usam entalpias espec\u00edficas em todas as equa\u00e7\u00f5es.\u00a0Engenharia T\u00e9rmica Teoria do Ciclo de Rankine O\u00a0ciclo Rankine\u00a0recebeu seu nome e descreve o desempenho de\u00a0sistemas de turbinas a vapor\u00a0, embora o princ\u00edpio te\u00f3rico tamb\u00e9m se aplique a motores alternativos, &#8230; <a title=\"O que \u00e9 a teoria do ciclo de Rankine &#8211; Equa\u00e7\u00f5es e c\u00e1lculo &#8211; Defini\u00e7\u00e3o\" class=\"read-more\" href=\"https:\/\/www.thermal-engineering.org\/pt-br\/o-que-e-a-teoria-do-ciclo-de-rankine-equacoes-e-calculo-definicao\/\" aria-label=\"More on O que \u00e9 a teoria do ciclo de Rankine &#8211; Equa\u00e7\u00f5es e c\u00e1lculo &#8211; Defini\u00e7\u00e3o\">Ler mais<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[14],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v15.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>O que \u00e9 a teoria do ciclo de Rankine - Equa\u00e7\u00f5es e c\u00e1lculo - Defini\u00e7\u00e3o<\/title>\n<meta name=\"description\" content=\"Teoria do Ciclo de Rankine - Equa\u00e7\u00f5es e C\u00e1lculo. 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