Question

An electric heater of power $1\text{kW}$ emits thermal radiations. The surface area of the heating element of the heater is $200{\text{cm}}^2$. If this heating element is treated like a black body, find the temperature at its surface. Assume its temperature is very much higher than its surroundings.
[$\sigma =5.67\times {10}^{-8}{\text{W m}}^{-2}{\text{K}}^{-4}$]

• A. $969\text{K}$
• B. $1056\text{K}$
• C. $576\text{K}$
• D. $872\text{K}$

Answer 1

The correct option is A $969\text{K}$

Since the filament temperature is very high as compared to the temperature of surroundings, we can ignore the amount of heat absorbed by the filament from the surroundings.
Power radiated by the heating element
$P=\sigma A{T}^4$
$\Rightarrow 1000=5.67\times {10}^{-8}\times 0.02\times T^4$
$\Rightarrow T^4=8818.34\times {10}^8$
$\Rightarrow T\approx 969.3\text{K}$
Thus, option (a) is the correct answer.