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Консультация № 199587
13.11.2020, 14:30
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Интенсивность излучения Солнца на Земле I = 1,4 кВт/м2, а его угловой размер с Земли γ = 32'. Считая Солнце абсолютно чёрным телом, определить температуру его поверхности Т⊙.
Интенсивность излучения Солнца на Земле I = 1,4 кВт/м2, а его угловой размер с Земли γ = 32'. Считая Солнце абсолютно чёрным телом, определить температуру его поверхности Т⊙.
Обсуждение
18.11.2020, 13:31
общий
это ответ
Здравствуйте, dar777!
Интенсивность излучения определяется выражением
где d[$934$][sub]e[/sub] - поток энергии через элемент dS поверхности. В случае Солнца она одинакова во всех точках сферы радиуса r, поэтому на всю поверхность сферы будет приходиться излучение мощностью
С другой стороны, мощность излучения Солнца как абсолютно чёрного тела, имеющего форму сферы радиуса R, равна
где [$949$][sub]T[/sub] - энергетическая светимость абсолютно чёрного тела с температурой T, определяемая законом Стефана-Больцмана:
([$963$] = 5.67[$183$]10[sup]-8[/sup] Вт/(м[sup]2[/sup][$183$]К[sup]4[/sup] - постоянная Стефана). Приравнивая, получаем
откуда
или, с учётом того, что r/R = ctg [$947$]/2,
В данном случае I = 1400 Вт/м[sup]2[/sup], [$947$] = 32' и
Интенсивность излучения определяется выражением
где d[$934$][sub]e[/sub] - поток энергии через элемент dS поверхности. В случае Солнца она одинакова во всех точках сферы радиуса r, поэтому на всю поверхность сферы будет приходиться излучение мощностью
С другой стороны, мощность излучения Солнца как абсолютно чёрного тела, имеющего форму сферы радиуса R, равна
где [$949$][sub]T[/sub] - энергетическая светимость абсолютно чёрного тела с температурой T, определяемая законом Стефана-Больцмана:
([$963$] = 5.67[$183$]10[sup]-8[/sup] Вт/(м[sup]2[/sup][$183$]К[sup]4[/sup] - постоянная Стефана). Приравнивая, получаем
откуда
или, с учётом того, что r/R = ctg [$947$]/2,
В данном случае I = 1400 Вт/м[sup]2[/sup], [$947$] = 32' и
5
Это самое лучшее решение!
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