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Консультация № 184760
12.12.2011, 16:30
59.15 руб.
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Вследствие изменения температуры тела максимум его спектральной энергетической светимости переместился с длины волны λ1=2,5 мкм до λ2=0,125 мкм. Считая тело абсолютно черным определить, во сколько раз изменилась: а) температура тела; б) максимальное значение спектрально энергетической светимости; в) интегральная энергетическая светимость.
Вследствие изменения температуры тела максимум его спектральной энергетической светимости переместился с длины волны λ1=2,5 мкм до λ2=0,125 мкм. Считая тело абсолютно черным определить, во сколько раз изменилась: а) температура тела; б) максимальное значение спектрально энергетической светимости; в) интегральная энергетическая светимость.
Обсуждение
13.12.2011, 08:51
общий
это ответ
Здравствуйте, Олег!
Длина волны, соответствующая максимуму спектральной энергетической светимости абсолютно чёрного тела, определяется законом смещения Вина:
где b = 2.898·10[sup]-3[/sup] м·К - постоянная Вина. Другими словами, длина волны обратно пропорциональна температуре.
Максимум спектральной плотности энергетической светимости абсолютно чёрного тела определяется законом излучения Вина:
где C = 1.29·10[sup]-5[/sup] Вт/(м[sup]3[/sup]·К[sup]5[/sup]) - вторая постоянная Вина (максимум пропорционален пятой степени температуры).
Интегральная энергетическая светимость абсолютно чёрного тела определяется законом Стефана-Больцмана:
где [$963$] = 5.67·10[sup]-8[/sup] Вт/(м[sup]2[/sup]·К[sup]4[/sup]) - постоянная Стефана-Больцмана (светимость пропорциональна четвёртой степени температуры).
В данном случае длина волны, соответствующая максимуму спектральной энергетической светимости, уменьшилась в [$955$][sub]1[/sub]/[$955$][sub]2[/sub] = 2.5/0.125 = 20 раз. Следовательно, температура тела увеличилась также в 20 раз, максимальное значение спектрально энергетической светимости увеличилось в 20[sup]5[/sup] = 3200000 раз, а интегральная энергетическая светимость - в 20[sup]4[/sup] = 160000 раз.
Длина волны, соответствующая максимуму спектральной энергетической светимости абсолютно чёрного тела, определяется законом смещения Вина:
где b = 2.898·10[sup]-3[/sup] м·К - постоянная Вина. Другими словами, длина волны обратно пропорциональна температуре.
Максимум спектральной плотности энергетической светимости абсолютно чёрного тела определяется законом излучения Вина:
где C = 1.29·10[sup]-5[/sup] Вт/(м[sup]3[/sup]·К[sup]5[/sup]) - вторая постоянная Вина (максимум пропорционален пятой степени температуры).
Интегральная энергетическая светимость абсолютно чёрного тела определяется законом Стефана-Больцмана:
где [$963$] = 5.67·10[sup]-8[/sup] Вт/(м[sup]2[/sup]·К[sup]4[/sup]) - постоянная Стефана-Больцмана (светимость пропорциональна четвёртой степени температуры).
В данном случае длина волны, соответствующая максимуму спектральной энергетической светимости, уменьшилась в [$955$][sub]1[/sub]/[$955$][sub]2[/sub] = 2.5/0.125 = 20 раз. Следовательно, температура тела увеличилась также в 20 раз, максимальное значение спектрально энергетической светимости увеличилось в 20[sup]5[/sup] = 3200000 раз, а интегральная энергетическая светимость - в 20[sup]4[/sup] = 160000 раз.
5
Спасибо!
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