Question 398: Properties of Matter

Question

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

Choose the correct answer: