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Консультация № 146181
06.10.2008, 12:54
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Определить силу тока I, протекающего по вольфрамовой проволоке диаметром d=0.8 мм, температура которой поддерживается равной 3070 К. Поверхность проволоки считать серой с коэффициентом поглощения к=0.343, удельное сопротивление вольфрама p=0.92*10^-6 Ом*м. обратным излучением окружающих тел пренебречь.
Обсуждение
07.10.2008, 06:55
общий
это ответ
Здравствуйте, Салатов!
Прежде всего определяем мощность P1м, излучаемую одним метром длины проволоки, для чего слегка преобрауем "Закон Стефана - Больцмана для не абсолютно чёрного тела" P = S*σ*T4*к (1), где S - площадь поверхности, σ = 5.67*10-8 Вт/(м2*К4) - постоянная Стефана - Больцмана, T - температура тела. Поскольку для одного метра длины проволоки площадь поверхности S1м = π*d, (1) приобретает вид: P1м = π*d*σ*T4*к (2). Мощность P1м д.б. равна мощности Pв1м, выделяемой в сопротивлении R1м одного метра длины проволоки прохождением тока I. По закону Джоуля-Ленца: Pв1м = I2*R1м (3), причём R1м = ρ/q (4), где q = π*d2/4 (5) - площадь поперечного сечения проволоки. После приравнивания (3) и (2) и решения полученного уравнения относительно I с учётом (4) и (5) и сокращений с целью большего удобства вычислений получаем: I = (π/2)*(T/1000)2*√((d3/ρ)*σ*к*1012) = (π/2)*3.072*√((0.83/0.92)*5.67*0.343*10) = 48.7 А.
Прежде всего определяем мощность P1м, излучаемую одним метром длины проволоки, для чего слегка преобрауем "Закон Стефана - Больцмана для не абсолютно чёрного тела" P = S*σ*T4*к (1), где S - площадь поверхности, σ = 5.67*10-8 Вт/(м2*К4) - постоянная Стефана - Больцмана, T - температура тела. Поскольку для одного метра длины проволоки площадь поверхности S1м = π*d, (1) приобретает вид: P1м = π*d*σ*T4*к (2). Мощность P1м д.б. равна мощности Pв1м, выделяемой в сопротивлении R1м одного метра длины проволоки прохождением тока I. По закону Джоуля-Ленца: Pв1м = I2*R1м (3), причём R1м = ρ/q (4), где q = π*d2/4 (5) - площадь поперечного сечения проволоки. После приравнивания (3) и (2) и решения полученного уравнения относительно I с учётом (4) и (5) и сокращений с целью большего удобства вычислений получаем: I = (π/2)*(T/1000)2*√((d3/ρ)*σ*к*1012) = (π/2)*3.072*√((0.83/0.92)*5.67*0.343*10) = 48.7 А.
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