First slide

Radiation

Question

A black body with surface area 0.001 m² is heated up to a temperature 400 K and is suspended in a room temperature 300 K .The initial rate of loss of heat from the body to room is

Moderate

A

10 W
B

1 W
C

0.1 W
D

0.5 W

Solution

The rate of heat emission, $u = σ A T^{4}$
At room temperature, the rate of absorption is $u_{0} = σ A T_{0}^{4}$
The net rate of heat loss, $u - u_{0} = σ A (T^{4} - T_{0}^{4})$
Given, $A = 0.001 m^{2}$
$T = 400 K and T_{0} = 300 K$
Thus, $u - u_{0} = 5.67 \times 10^{- 8} \times 0.001 \times [(400)^{4} - (300)^{4}]$
$= 0.99 W \approx 1 W$

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