A metal ball of surface area 200 ;c m^2 and temperature 527^o C i… - Vidyadip

MCQ

A metal ball of surface area $200\;c{m^2}$ and temperature ${527^o}C$ is surrounded by a vessel at ${27^o}C$. If the emissivity of the metal is $0.4$ , then the rate of loss of heat from the ball is .......... $joules $ approx. $(\sigma = 5.67 \times {10^{ - 8}}J/{m^2}\; - s - {k^4})$

A
$108$
B
$168$
✓
$182$
D
$192$

✓

Answer

Correct option: C.

$182$

c
(c) Rate of heat loss $E = \sigma \,eA({T^4} - T_0^4)$

$ = 5.67 \times {10^{ - 8}} \times 0.4 \times 200 \times {10^{ - 4}}\times [{(273 + 527)^4} - {(273 + 27)^4}]$

$ = 5.67 \times {10^{ - 8}} \times 0.4 \times 200 \times {10^{ - 4}}\times {(800)^4} - {(300)^4}$ $=182J/sec$

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