How much energy does a bar of iron radiate after losing 8.0 × 10^6J?

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SUMMARY

A bar of iron measuring 0.5m x 0.2m x 0.1m, with a density of 7900 kg/m³ and an initial temperature of 600K, radiates energy at a rate of 220 W after losing 8.0 × 106 J. The emissivity of the bar is assumed to be 0.8. To calculate the energy radiation, one must apply the Stefan-Boltzmann law, taking into account the temperature drop resulting from the energy loss. The discussion highlights the importance of considering temperature distribution and cooling dynamics in thermal radiation calculations.

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physics123
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A bar of iron is 0.5m long, 0.2m wide and 0.1m high (which means its volume is 1.0 × 10−2m3 and its surface area is 3.4 × 10−1m2 ). Iron has a density of 7900 kg m3 , a heat capacity of 400 J kg◦C , and a coefficient of linear expansion of 1.2 × 10−5 . The bar of iron is initially at 600K.

Assuming that the emissivity e = 0.8, what is the rate at which iron radiates energy after it has lost 8.0 × 106J?I know the answer is 220 W, but how do I get that answer? Thanks!
 
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physics123 said:
A bar of iron is 0.5m long, 0.2m wide and 0.1m high (which means its volume is 1.0 × 10−2m3 and its surface area is 3.4 × 10−1m2 ). Iron has a density of 7900 kg m3 , a heat capacity of 400 J kg◦C , and a coefficient of linear expansion of 1.2 × 10−5 . The bar of iron is initially at 600K.

Assuming that the emissivity e = 0.8, what is the rate at which iron radiates energy after it has lost 8.0 × 106J?I know the answer is 220 W, but how do I get that answer? Thanks!
A thorough analysis would consider the uneven temperature distribution that would develop within the bar as it cools. It involves Fourier transforms. I shall guess you are not expected to allow for that.
What would be the temperature drop in losing that much energy?
 
Hint: Figure temperature after cooling, then go with Stefan-Boltzmann law, appropriately scaled. I would ignore the expansion coeff. - but, whatever.
 

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