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Q.

A black body at a temperature of $227^{0} C$ radiates heat at the rate of $20 {calm}^{- 2} s^{- 1}$ . When its temperature rises to $727^{0} C$ the heat radiated will be

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a

40 units

b

160 units

c

320 units

d

640 units

answer is C.

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Detailed Solution

Heat radiated by black body

$E = σ {AT}^{4} \Rightarrow E α T^{4} or \frac{E_{1}}{E_{2}} = \frac{T_{1}^{4}}{T_{2}^{4}} or \frac{20}{E_{2}} = {(\frac{500}{1000})}^{4} = {(\frac{1}{2})}^{4} = \frac{1}{16} \Rightarrow E_{2} = 16 \times 20 {calm}^{- 2} s^{- 1} = 320 {calm}^{- 2} s^{- 1}$

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