Question 376: Properties of Matter

Question

For a black body at temperature 727oC, its radiating power is 60 watt and temperature of surrounding is 227oC. If temperature of black body is changed to 1227oC then its radiating power will be

Accepted Answer

Radiating power of a black body
$$ = {E_0} = \sigma \left( {{T^4} - T_0^4} ight)A$$
where $$\sigma $$ is known as the Stefan-Boltzmann constant, A is the surface area of a black body, T is the temperature of the black body and T
0
is the temperature of the surrounding.
$$ 	herefore $$ 60 = $$\sigma $$(1000
4
Ã¢ÂÂ 500
4
)    ...(i)
[T = 727
o
C = 727 + 273 = 1000 K, T0 = 227
o
C = 500 K].
In the second case, T = 1227
o
C = 1500 K and let E' be the radiating power.
$$ 	herefore $$ E' =  $$\sigma $$(1500
4
Ã¢ÂÂ 500
4
)    ...(ii)
From (i) and (ii) we have
$${{E'} \over {60}} = {{{{1500}^4} - {{500}^4}} \over {{{1000}^4} - {{500}^4}}} = {{{{15}^4} - {5^4}} \over {{{10}^4} - {5^4}}} = {{50000} \over {9375}}$$
$$ 	herefore $$ $$E' = {{50000} \over {9375}} 	imes 60 = 320\,W$$

Answer

304 W

Answer

320 W

Answer

240 W

Answer

120 W

Properties of Matter

For a black body at temperature 727oC, its radiating power is 60 watt and temperature of surrounding is 227oC. If temperature of black body is changed to 1227oC then its radiating power will be

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