[{"data":1,"prerenderedAt":73},["ShallowReactive",2],{"q-fire-113-1-fire-science-022":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-113-1-火災學概要-022","fire-113-1-fire-science-022",113,1,22,"一物體在 27℃時輻射出的能量為 E，則當溫度升高到 627℃時輻射出的能量變為多少？",{"A":16,"B":17,"C":18,"D":19},"9E","81 E","300 E","600 E","B",null,[],false,"本題考點：史蒂芬－波茲曼定律，輻射能與絕對溫度的四次方成正比。\n【正解理由】依史蒂芬－波茲曼定律，物體表面單位面積的輻射放射能 E＝εσT⁴，其中 T 必須採絕對溫度。27℃ 換算為 300 K，627℃ 換算為 900 K，兩者的絕對溫度比為三倍，輻射能比即為三的四次方等於八十一倍，故溫度升高後的輻射能為 81E。故選 B。\n【逐項排除】\n(A) 9E 係把四次方誤取為二次方，三的二次方為九，指數用錯。\n(B) 81E 為三的四次方，符合輻射能與絕對溫度四次方成正比的關係，為正解。\n(C) 300E 恰為 27℃ 換算後的絕對溫度數值 300 K，係把溫度數值本身誤當成能量倍率；絕對溫度比為三，其一、二、三、四次方分別為三、九、二十七、八十一，均無法得到 300。\n(D) 600E 恰為 627℃ 與 27℃ 的溫度差 600 度，同樣是把溫度差誤當成能量倍率，與四次方關係無關。\n【演算步驟】E＝εσT⁴；T₁＝27＋273＝300 K；T₂＝627＋273＝900 K；E₂／E₁＝(900 K／300 K)⁴＝3⁴＝81；E₂＝81E。\n【記憶點】先把攝氏換成絕對溫度，再取四次方；溫度三倍就是輻射八十一倍。","史蒂芬－波茲曼定律 E＝εσT⁴ 描述物體表面單位面積的輻射放射能，σ 為史蒂芬－波茲曼常數，約 5.67×10⁻⁸ 瓦每平方公尺每四次方絕對溫度，ε 為放射率，黑體為一、灰體介於零與一之間。式中溫度必須採絕對溫度，原因在於輻射源自分子熱運動的絕對強度，只有以絕對零度為起點的溫標才能反映能量的絕對量；若誤以攝氏度數相除，627 除以 27 約為二十三倍，四次方後偏差可達數十萬倍，這正是本題設計的主要陷阱。\n四次方的威力是火災學的重點。溫度提高到三倍，輻射熱就成長八十一倍，這說明為何閃燃前後輻射熱通量會急遽跳升，也說明為何輻射是建築物之間延燒的主要熱傳途徑。常用的判準是地板面受熱通量達到約 20 kW 每平方公尺時，室內可燃物幾乎同時被引燃，此為閃燃的判定條件之一。\n三種熱傳方式可一併對照記憶：傳導依傅立葉定律，熱流與溫度梯度成正比，靠介質分子的接觸傳遞；對流依牛頓冷卻定律，熱流與溫差成一次方正比，靠流體流動傳遞；輻射依史蒂芬－波茲曼定律，與絕對溫度的四次方成正比，且不需介質，可在真空中傳遞。低溫時對流佔優勢，高溫時輻射迅速主導，這是火場熱傳的基本圖像。\n延伸考點：輻射熱通量隨受體與火源距離的平方成反比衰減，鄰棟延燒與安全隔離距離的題型即由此推導；另一常見變化是改問放射率或受體角度因子的影響。此處有一個常見誤解值得澄清：放射率 ε 與常數 σ 只影響輻射能的絕對量，本題求的是同一物體在前後兩個狀態下的能量比值，ε 與 σ 在相除時完全相消，因此無論該物體是黑體或灰體，倍率都仍是八十一倍。",true,[28,32,36,40,44,48],{"webId":29,"stem":30,"number":31,"year":11,"session":12},"fire-113-1-fire-science-021","依建築物火災 t2 成長理論，若釋熱率達 1 MW 需時間 100 秒，則釋熱率達 4 MW 所需時間為多少秒？",21,{"webId":33,"stem":34,"number":35,"year":11,"session":12},"fire-113-1-fire-science-023","根據 Burgess-Wheeler 定理，若丙烷的燃燒下限為 2.2%，其燃燒熱約為多少 kcal\u002Fmole？",23,{"webId":37,"stem":38,"number":39,"year":11,"session":12},"fire-113-1-fire-science-020","依據「滅火器認可基準」對於火災分類之內容，下列物質燃燒時，何者屬於 A 類火災？",20,{"webId":41,"stem":42,"number":43,"year":11,"session":12},"fire-113-1-fire-science-024","木材加熱到引火溫度時，可燃性氣體析出量迅速增加，木材的引火溫度約為多少℃？",24,{"webId":45,"stem":46,"number":47,"year":11,"session":12},"fire-113-1-fire-science-019","所謂通風控制燃燒，其燃燒速度受下列何因素決定？",19,{"webId":49,"stem":50,"number":51,"year":11,"session":12},"fire-113-1-fire-science-025","容器內氣體受到壓縮造成內部溫度升高，進而發火，此現象稱為？",25,[53,57,61,65,69],{"webId":54,"year":55,"stem":56,"number":13},"fire-112-1-fire-science-022",112,"兩種可燃性氣體以等比例混合，其燃燒下限分別為 1.5%、4.5%，則該混合氣體的燃燒下限約為多少%？",{"webId":58,"year":59,"stem":60,"number":13},"fire-111-1-fire-science-022",111,"連棟式木造建築物引發火災，消防隊射水同時拆除未受火勢波及的房屋，請問其採取的滅火方法係下列何者？",{"webId":62,"year":63,"stem":64,"number":13},"fire-110-1-fire-science-022",110,"火災中所產生的輻射熱量與下列何者成正比？",{"webId":66,"year":67,"stem":68,"number":13},"fire-109-1-fire-science-022",109,"預防過氧化丁酮之火災爆炸時，下列何種原則正確？",{"webId":70,"year":71,"stem":72,"number":13},"fire-108-1-fire-science-022",108,"物體在 327℃時的輻射強度為 E，則當溫度升高到 927℃時的輻射強度為何？",1785129966301]