[{"data":1,"prerenderedAt":73},["ShallowReactive",2],{"q-fire-109-1-fire-science-032":3},{"subject":4,"subjectSlug":5,"subjectKicker":6,"subjectShort":7,"question":8,"related":27,"sameNumber":52,"hasEssay":26},"火災學概要","fire-science","火災學 · Fire Science","火災學",{"id":9,"webId":10,"year":11,"session":12,"subject":4,"number":13,"stem":14,"options":15,"answer":20,"answerNote":21,"images":22,"imagesPending":23,"lawTimestamp":11,"explanation":24,"explanationDeep":25,"freq":12,"indexable":26},"fire-109-1-火災學概要-032","fire-109-1-fire-science-032",109,1,32,"已知天花板噴流溫度攝氏 135℃，天花板噴流速度 1.8 m\u002Fs，環境初始溫度 20℃，感知撒水頭作動溫度攝氏 72℃，反應時間指數 67(m1\u002F2s1\u002F2)，感知撒水頭作動時間為下列何者？（提示： ln115=4.74, ln63=4.14）",{"A":16,"B":17,"C":18,"D":19},"30 秒","35 秒","40 秒","45 秒","A",null,[],false,"本題考點：以反應時間指數(RTI)推算感知型撒水頭在天花板噴流中的作動時間。\n【正解理由】感熱元件升溫屬集總熱容模型，時間常數 τ＝RTI\u002F√u，作動時間 t＝τ·ln[(T_g−T_a)\u002F(T_g−T_act)]，T_g 為噴流溫度、T_a 為環境初始溫度、T_act 為標示溫度。代入 135℃、20℃、72℃、1.8 m\u002Fs 與 RTI 67，得約 29.9 秒，最接近 30 秒，故選 A。\n【逐項排除】\n(A) 正確。與公式計算結果 29.9 秒相符，四捨五入即 30 秒。\n(B) 錯誤。35 秒對應對數值約 0.70，與題目提示的 0.60 不符。\n(C) 錯誤。40 秒相當於把 RTI 67 直接當成時間常數再乘 0.60，漏掉除以噴流速度平方根。\n(D) 錯誤。45 秒對應對數值約 0.90(溫差比約 2.5)，本題溫差比為 115\u002F63≈1.83，得不出此值。\n【演算步驟】\n① τ＝RTI\u002F√u＝67 m^½s^½ ÷ √(1.8 m\u002Fs)＝67÷1.342＝49.9 s。\n② 溫差比＝(135−20)℃ ÷ (135−72)℃＝115\u002F63。\n③ ln(115\u002F63)＝4.74−4.14＝0.60。\n④ t＝49.9 s×0.60≈29.9 s，即約 30 秒。\n【記憶點】RTI 除以根號風速得時間常數，再乘溫差比的自然對數即作動時間。","反應時間指數 RTI 的推導出自集總熱容(lumped capacitance)假設：感熱元件體積小、內部溫度均勻，其升溫速率正比於元件與周遭熱氣的溫差、反比於元件的熱容量。把對流熱傳係數對流速的依存性(h∝√u)代入，整理後可得 RTI＝mc\u002F(hA)·√u，量綱為 m^(1\u002F2)s^(1\u002F2)，這正是題目給定單位的由來。RTI 本身是元件的固有性質，與現場風速無關；現場的實際時間常數 τ＝RTI\u002F√u 才會隨天花板噴流速度改變——噴流愈快，對流熱傳愈強，元件升溫愈快、作動愈早。\n\n數值感要建立起來：標準反應型元件的 RTI 大致落在 80 至 350 之間，快速反應型則在 50 以下，兩者在同一火場中的作動時間可以差上數倍，這也是快速反應型被用於需要提早抑制火勢場合的原因。本題給 67，屬於偏快速的一端，因此在 135℃ 的噴流中僅約半分鐘即作動。另一個常被忽略的參數是傳導係數 C，用來修正元件經由支撐管件散失的熱量，精算式為 t 的積分形式；考題通常忽略 C 而採本題的簡化對數式。\n\n公式的結構值得記牢：括號內分子 (T_g−T_a) 是熱氣相對環境的溫升驅動力，分母 (T_g−T_act) 是熱氣相對作動點的剩餘溫差。若熱氣溫度 T_g 不高於作動溫度 T_act，分母為零或負值，代表元件永遠達不到標示溫度，數學上對數發散、物理上就是不會作動——這是概念題常出的變化。溫差比愈大，對數值愈大，作動愈慢；反之熱氣溫度愈高，分母縮小，作動反而愈快。\n\n易混淆對照：本式用的是天花板噴流的溫度與速度，不是火羽流軸心值，也不是室內平均溫度；探測器的作動時間同樣採此模型，只是把標示溫度換成探測器的動作溫度，定溫式可直接套用，差動式則要改用溫升率的判準。延伸考點常結合火羽流與天花板噴流的溫度衰減式，先求出撒水頭位置的 T_g 與 u，再代入本式求作動時間。",true,[28,32,36,40,44,48],{"webId":29,"stem":30,"number":31,"year":11,"session":12},"fire-109-1-fire-science-031","建築物火災在閃燃發生後之全盛期火災的特性，不包括下列何者？",31,{"webId":33,"stem":34,"number":35,"year":11,"session":12},"fire-109-1-fire-science-033","乙醇之燃燒化學反應式為下列何者？ 9 3",33,{"webId":37,"stem":38,"number":39,"year":11,"session":12},"fire-109-1-fire-science-030","海龍替代滅火藥劑中，下列何者在大氣之滯留時間最久？",30,{"webId":41,"stem":42,"number":43,"year":11,"session":12},"fire-109-1-fire-science-034","BLEVE 的發生，下列敘述何者錯誤？",34,{"webId":45,"stem":46,"number":47,"year":11,"session":12},"fire-109-1-fire-science-029","有關防火塗料敘述，下列何者錯誤？",29,{"webId":49,"stem":50,"number":51,"year":11,"session":12},"fire-109-1-fire-science-035","有關引火性液體的敘述，下列何者正確？",35,[53,57,61,65,69],{"webId":54,"year":55,"stem":56,"number":13},"fire-113-1-fire-science-032",113,"可燃物在大氣中僅因受熱致使溫度升高而引發燃燒的最低溫度稱為：",{"webId":58,"year":59,"stem":60,"number":13},"fire-112-1-fire-science-032",112,"將大塊的木頭切碎為小片的木屑時，下列敘述何者錯誤？",{"webId":62,"year":63,"stem":64,"number":13},"fire-111-1-fire-science-032",111,"下列何者非油槽火災發生沸溢或濺溢的主要因素？",{"webId":66,"year":67,"stem":68,"number":13},"fire-110-1-fire-science-032",110,"有關爆炸性物質之特性，下列何者正確？",{"webId":70,"year":71,"stem":72,"number":13},"fire-108-1-fire-science-032",108,"下列有關防止靜電災害的方法中，何者錯誤？",1785129967387]