A radiating body has a Kelvin temperature T original , and its surroundings are

Question

A radiating body has a Kelvin temperature T original , and its surroundings are at 500k (T original >500 k) If the Kelvin temperature of the radiating body is increased to 4T original, the net rate at which the body radiates increases by a factor of 450. What was the original temperature T original?

Explanation / Answer

Solved a similar question already.. with different numbers.. i put in the question and the answer.. hope it helps :) A radiating body has Kelvin temperature T, and it’s surroundings are at 500K (T > 500K). If the Kelvin temperature of the radiating body is increased to 2T, the net rate at which the body radiates increases by a factor of 39. what was the original temperature T? ANSWER : Energy radiated/sec = Q-dot = watt = k [T^4 - To^4] k = involves product of emmisivity, cross. area, sigma --------------------------- Q1-dot = k [T^4 - 500^4] Q2-dot = k [16*T^4 - 500^4] divide [Q2-dot/Q1-dot] = 39 = [16*T^4 - 500^4] / [T^4 - 500^4] T^4 [39 - 16] = 39*500^4 - 500^4 23 T^4 = 38*500^4 T^4 = [38/23]*500^4 T = [38/23]^1/4 *500 = 566.87 K

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