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Question
Compare the rate of radiation of metal bodies at 727 °C and 227 °C.
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Solution
Given:
T1 = 727 °C = 727 + 273 = 1000 K,
T2 = 227 °C = 227 + 273 = 500 K
To find: Ratio of radiation `[((dQ)/dt)_1/((dQ)/dt)_2]`
Formula:
`(dQ)/dt = σAeT^4`
Calculation:
From formula,
`((dQ)/dt)_1 = σAeT_1^4` ...............(1)
`((dQ)/dt)_2 = σAeT_2^4` ...............(2)
Dividing equation (1) by (2),
`((dQ)/dt)_1/((dQ)/dt)_2 = (σAeT_1^4)/(σAeT_2^4) = (T_1/T_2)^4`
= `(1000)^4/(500)^4 = 16`
The rate of radiation of the metal sphere at 727 °C and 227 °C is 16:1.
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