# 330 uma derivac ao mais formal usa a definic ao de

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330
Como o volume espec´ ıfico V ´ e dado por: V 1 ρ -→ dV = - 1 ρ 2 -→ - PdV = + P ρ 2 dρ, d dt 3 2 k m T = + P ρ 2 dt + ε - 1 4 πr 2 ρ dL r dr . Usando a equa¸c˜ ao de estado de um g´as ideal (23.101), podemos escrever: P = k m ρT -→ k m T = P ρ , d dt 3 2 P ρ - P ρ 2 dt = ε - 1 4 πr 2 ρ dL r dr . Como 3 2 ρ 2 3 d dt ˆ P ρ 5 3 ! = 3 2 ρ 2 3 " 1 ρ 2 3 d dt P ρ + P ρ d dt ˆ 1 ρ 2 3 !# = 3 2 d dt P ρ + 3 2 ρ - 1 3 P - 2 3 1 ρ 5 3 dt = 3 2 d dt P ρ - P ρ 2 dt . ´ e igual ao termo da esquerda, podemos escrever: 3 2 ρ 2 3 d dt ˆ P ρ 5 3 ! = ε - 1 4 πr 2 ρ dL r dr , ou dL r dr = 4 πr 2 ρ " ε - 3 2 ρ 2 3 d dt ˆ P ρ 5 3 !# (23.143) Essa equa¸c˜ ao deve ser usada em lugar da equa¸c˜ ao (23.142) durante as fases em que as mudan¸ cas evolucion´ arias s˜ao r´apidas. Ela ´ e idˆ entica `a (23.142) nas fases normais, em que as mudan¸cas s˜ao t˜ao lentas que o termo com a derivada temporal na equa¸c˜ ao (23.143) pode ser ignorado. At´ e agora, somente consideramos a condi¸c˜ ao que o fluxo de energia deve obedecer para balan¸car a produ¸c˜ ao de energia. Fisicamente, entretanto, o fluxo ´ e determinando pelos mecanismos de transporte de energia, que po- dem ser condu¸c˜ ao (transporte de energia atrav´ es dos corpos), convec¸c˜ ao 332

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