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Консультация № 199588
13.11.2020, 14:30
0.00 руб.
0
2
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Солнце излучает как абсолютно чёрное тело с температурой Т⊙ = 5800 К. В космосе на орбите Земли находится зачернённый шар. Найти его установившуюся температуру Т(°С), если угловой размер Солнца с Земли γ = 32'.
Подсказка. Шар поглощает энергию от Солнца своим сечением, а излучает всей поверхностью.
Солнце излучает как абсолютно чёрное тело с температурой Т⊙ = 5800 К. В космосе на орбите Земли находится зачернённый шар. Найти его установившуюся температуру Т(°С), если угловой размер Солнца с Земли γ = 32'.
Подсказка. Шар поглощает энергию от Солнца своим сечением, а излучает всей поверхностью.
Обсуждение
18.11.2020, 14:10
общий
это ответ
Здравствуйте, dar777!
При решении предыдущей задачи было установлено, что для сферического источника излучения (в данном случае - Солнца) с температурой T[sub]0[/sub] и радиусом R на расстоянии r от него выполняется соотношение
где [$963$] = 5.67[$183$]10[sup]-8[/sup] Вт/(м[sup]2[/sup][$183$]К[sup]4[/sup]) - постоянная Стефана, I - интенсивность излучения. Тогда
или, с учётом того, что R/r = tg [$947$]/2,
Тогда на поперечное сечение шара радиуса R площадью S = [$960$]R[sup]2[/sup] будет приходиться излучение мощностью
поглощаемое шаром. Если считать шар абсолютно чёрным телом (поглощающим всё излучение), то при температуре T мощность его излучения составит
а равновесная температура определится из условия
откуда
и
В данном случае для T[sub]0[/sub] = 5800 K и [$947$] = 32' получим
При решении предыдущей задачи было установлено, что для сферического источника излучения (в данном случае - Солнца) с температурой T[sub]0[/sub] и радиусом R на расстоянии r от него выполняется соотношение
где [$963$] = 5.67[$183$]10[sup]-8[/sup] Вт/(м[sup]2[/sup][$183$]К[sup]4[/sup]) - постоянная Стефана, I - интенсивность излучения. Тогда
или, с учётом того, что R/r = tg [$947$]/2,
Тогда на поперечное сечение шара радиуса R площадью S = [$960$]R[sup]2[/sup] будет приходиться излучение мощностью
поглощаемое шаром. Если считать шар абсолютно чёрным телом (поглощающим всё излучение), то при температуре T мощность его излучения составит
а равновесная температура определится из условия
откуда
и
В данном случае для T[sub]0[/sub] = 5800 K и [$947$] = 32' получим
5
Спасибо за заказ! Это самое лучшее решение)))
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