115年 - 115 中央警察大學_碩士班入學考試試題_消防科學研究所：火災科學#139854

科目：研究所、轉學考(插大)◆火災科學 | 年份：115年 | 選擇題數：0 | 申論題數：6

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所屬科目：研究所、轉學考(插大)◆火災科學

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申論題 (6)

一、求解下列問題：
(a)A tank contains 1000 liters of water in which initially 100 kilograms
of salt is dissolved. Brine runs in a rate of 10 liters per minute, and
each liter contains 5 kilograms of dissolved salt. The mixture in the
tank is kept uniform by stirring. Brine runs out at 10 liters per minute.
Find the amount of salt in the tank at any time t. (15 分)

(b)Find the general solution of this equation.
y'=Ay−B?2(10 分)

二、 (a)Find the eigenvalues and eigenfunctions of the problems.
?′′ + λ? = 0; ?(0) = 0, ?′(?) = 0(13 分)
(b)Find the power series solution of Legendre’s equation. λ is a
constant.(1 − ?2)?
′′ − 2??′ + λ? = 0(12 分)

三、自然發火原因有關氧化熱蓄積而發火之機制為何？並請舉例說明。

四、請說明熱量傳遞方式有哪些？其在火災的各階段扮演何種燃燒機
制？

(b)Find the power series solution of Legendre’s equation. λ is a constant.(1 − ?2)? ′′ − 2??′ + λ? = 0(12 分)