A cylindrical log 15cm in diameter and 68cm long is glowing red hot in a fireplace. If it 's emitting radiation at the rate of 38kW, what is its temperature? the log's emissivity e=1.

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Mathematics

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13 October, 06:19

A cylindrical log 15cm in diameter and 68cm long is glowing red hot in a fireplace. If it 's emitting radiation at the rate of 38kW, what is its temperature? the log's emissivity e=1.

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Gauge Gibson · Answer 1

T = (P / e S A) ^ (1/4)

P = 38 kW = 38,000 W

e = 1

S (sigma) = 5.67 * 10^ (-8)

A = 2 r² π + 2 r π h = 2 * (0.075) ² * 3.14 + 2 * 0.075 * 3.14 * 0.68

A = 0.355605 m²

T = (38,000 / (1 * 5.67 * 10^ (-8) * 0.355605)) ^ (1/4) =

= (3.8 * 10^ (12) / 2.0162803) ^ (1/4) =

= 1.172 * 10^3 = 1,172 K