Eficiência termodinâmica

Na termodinâmica, a eficiência, simbolizada por ( $\eta$ ), é uma medida do desempenho de uma máquina térmica. Maior eficiência significa transformar a maior parte possível da energia disponível em trabalho, que é o interesse de qualquer máquina térmica. Simboliza a fração do calor fornecido ao sistema que é convertido em trabalho líquido e, é definida matematicamente por:

$\eta \equiv {\frac {W}{Q_{Q}}}$

onde

$Q_{Q}$ é a quantidade de calor fornecido ao ciclo pelo reservatório de alta temperatura e $W$ é o valor absoluto do trabalho mecânico realizado por um ciclo termodinâmico, definido pela diferença entre o calor que entra na máquina e o que é liberado para a fonte fria ( $Q_{F}$ ), assim:

$W=Q_{Q}-Q_{F}$

Substituindo na fórmula da eficiência, podemos reescrevê-la da seguinte forma:

$\eta ={\frac {Q_{Q}-Q_{F}}{Q_{Q}}}\Rightarrow \eta =1-{\frac {Q_{F}}{Q_{Q}}}$

História

Em 1824, o físico francês Sadi Carnot derivou a eficiência térmica para uma máquina térmica ideal como sendo uma função da temperatura de seus reservatórios frios e quentes:

$\eta \equiv {\frac {T_{Q}-T_{F}}{T_{Q}}}$

onde

$T_{Q}$ é a temperatura do reservatório quente;

$T_{F}$ é a temperatura do reservatório frio.

Ambas as temperaturas são absolutas, logo, em Kelvin.

A equação demonstra que maiores níveis de eficiência são obtidos com um maior gradiente de temperatura entre os fluidos quentes e frios. Na prática, quanto mais quente o fluido, maior será a eficiência do motor.

Máximo rendimento

O calor que sai da máquina, nunca é zerado, logo, a eficiência da máquina nunca será 100%, já que $Q_{Q}$ e $Q_{F}$ são grandezas positivas. Para provar que o rendimento nunca será máximo, podemos mostrar que o rendimento de Carnot nunca é 100% e, depois, que nenhuma máquina pode ultrapassar o rendimento desta.

Pela equação $\eta =1-{\frac {T_{F}}{T_{Q}}}$ vemos que só seria possível uma eficiência igual a 1 (100%), se a temperatura da fonte fria fosse 0 ou a da fonte quente infinita, duas situações impossíveis, já que as temperaturas são em Kelvin.

Nenhuma máquina térmica pode ter eficiência maior que a máquina de Carnot, se isso fosse possível, ela violaria a Segunda lei da termodinâmica, o que pode ser provado da seguinte forma:

Supomos $e_{c}$ a eficiência de Carnot e $e_{x}$ a eficiência de uma máquina maior que $e_{c}$ . Acoplamos essa máquina com $e_{x}$ a um refrigerador de Carnot, onde $Q_{C}^{X}$ seria o calor que sai da máquina x e é utilizado pelo refrigerador. Se $e_{x}>e_{c}$ , então: ${\frac {W}{Q_{Q}^{X}}}>{\frac {W}{Q_{Q}^{C}}}$ , onde $Q_{Q}^{C}$ é o calor desperdiçado pelo refrigerador de Carnot e utilizado pela máquina. Desta forma, $Q_{Q}^{C}>Q_{Q}^{X}$ , o que é impossível, pois a máquina deveria receber mais calor do que o que o refrigerador é capaz de liberar. Assim, a maior eficiência possível de uma máquina térmica é a de Carnot, que, como provado anteriormente, é sempre menor que a unidade, logo, não existe máquina térmica perfeita com eficiência de 100%.^[1]^[2]

Ver também

Eficiência

Referências

↑ A. Çengel, Yunos; A. Boles, Michael (2013). Termodinâmica 7ª ed. [S.l.]: AMGH
↑ Walker, Jearl. Halliday e Resnick: Fundamentos de Física. [S.l.: s.n.] ISBN 9788521619048

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