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Задать вопрос экспертам

Консультация № 196925

01.11.2019, 12:51

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Образование

Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Мощность потока энергии, излучаемой из смотрового окна мартеновской печи, Р = 2,17 кВт. Площадь смотрового
окошка S = 6 см2. Определите температуру печи.

Обсуждение

давно

Алексеев Владимир Николаевич

Мастер-Эксперт
259041
7459

03.11.2019, 16:41

общий

это ответ

Здравствуйте, Polnolyniay!
Дано : Р=2,17кВт=2170 Вт; S=6 см² = 6·10^-4 м² .
Вычислить температуру Т в печи.

Решение: Мартеновскую печь считаем моделью абсолютно черного тела, т.к. смотровое окошко мало по сравнению с размером полости печи. Применим законы излучения абсолютно черного тела. По определению энергетическая светимость
R_э = P/S
Здесь P - мощность (поток) излучения, S - площадь излучаемой поверхности.
По закону Стефана-Больцмана энергетическая светимость абсолютно-чёрного тела
R_э = [$963$]·Т⁴
где T - термодинамическая температура (по Кельвину),
[$963$] = 5,67·10^-8 Вт/(м²·К⁴) - постоянная Стефана-Больцмана.
Тогда Р/S= [$963$]·Т⁴
Т⁴ = Р/(S·[$963$]) = 2170 / (6·10^-4·5,67·10^-8) = 2170·10¹²/(6·5,67) = 63,786·10¹² К⁴
T = 2826 К , округляем до 2х значащих цифр.
Ответ: Т=2800K.

Решение похожей задачи см mydocx.ru/1-57379.html

5

спасибо большое за решение, оно очень мне помогло. главное, что все очень понятно и сделано согласно правилам. так еще и пояснения дали. просто СУПЕР!!!

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