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Консультация № 198753
26.05.2020, 18:01
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Температура абсолютно чёрного тела изменяется от 237 ⁰С до 1158⁰С. Во сколько раз увеличивается при этом полное количество излучаемой ежесекундно энергии?
Температура абсолютно чёрного тела изменяется от 237 ⁰С до 1158⁰С. Во сколько раз увеличивается при этом полное количество излучаемой ежесекундно энергии?
Обсуждение
28.05.2020, 18:16
общий
это ответ
Здравствуйте, tanuiha_77@mail.ru!
Условие : t1 = 237°С , t2 = 1158°С .
Вычислить отношение излучаемой ежесекундно энергии при указанных температурах.
Решение : Переводим заданные в Условии температуры в абсолютные : T1 = t1 + 273 = 510 °K
T2 = t2 + 273 = 1431 °K
Излучаемая ежесекундно энергия - это излучаемая мощность.
По определению Энергетическая светимость Rэ = P / S
Здесь P - мощность (поток) излучения, S - площадь излучаемой поверхности.
Отсюда излучаемая мощность P = Rэ·S
По закону Стефана-Больцмана энергетическая светимость абсолютно-чёрного тела
Rэ(T) = σ·Т4.
где T - термодинамическая температура (по Кельвину),
σ = 5,67·10-8 Вт/(м2·К4) - постоянная Стефана-Больцмана.
Тогда искомое отношение мощностей:
Р2 / P1 = Rэ(T2)·S / [Rэ(T1)·S] = (σ·T24) / (σ·T14) = T24 / T14 = (T2 / T1)4 = (1431 / 510)4 = 2,8064 = 62,0
Ответ : в результате увеличения температуры количество излучаемой ежесекундно энергии увеличится в 62 раза.
Решение похожих задач: rfpro.ru/question/197725 , rfpro.ru/question/196925 .
Условие : t1 = 237°С , t2 = 1158°С .
Вычислить отношение излучаемой ежесекундно энергии при указанных температурах.
Решение : Переводим заданные в Условии температуры в абсолютные : T1 = t1 + 273 = 510 °K
T2 = t2 + 273 = 1431 °K
Излучаемая ежесекундно энергия - это излучаемая мощность.
По определению Энергетическая светимость Rэ = P / S
Здесь P - мощность (поток) излучения, S - площадь излучаемой поверхности.
Отсюда излучаемая мощность P = Rэ·S
По закону Стефана-Больцмана энергетическая светимость абсолютно-чёрного тела
Rэ(T) = σ·Т4.
где T - термодинамическая температура (по Кельвину),
σ = 5,67·10-8 Вт/(м2·К4) - постоянная Стефана-Больцмана.
Тогда искомое отношение мощностей:
Р2 / P1 = Rэ(T2)·S / [Rэ(T1)·S] = (σ·T24) / (σ·T14) = T24 / T14 = (T2 / T1)4 = (1431 / 510)4 = 2,8064 = 62,0
Ответ : в результате увеличения температуры количество излучаемой ежесекундно энергии увеличится в 62 раза.
Решение похожих задач: rfpro.ru/question/197725 , rfpro.ru/question/196925 .
5
Благодарю, Вас, Владимир Николаевич! Ваш ответ очень помог. Желаю Вам прекрасного дня!
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