Question

A thin brass rectangular sheet of sides $15.0\text{cm}$ and $12.0\text{cm}$ is heated in a furnace to ${527}^{\circ }\text{C}$ and taken out in vacuum. Find the electric power needed to maintain the sheet at this temperature, given that its emissivity is $0.250$.
(Take $\sigma =5.67\times {10}^{-8}{\text{W/m}}^2-{\text{K}}^4$)

• A. $300\text{W}$
• B. $209\text{W}$
• C. $250\text{W}$
• D. $400\text{W}$

Answer 1

The correct option is B $209\text{W}$

Area of both the sides of the plate
$A=2\times \left(15.0\right)\times \left(12.0\right)\times {10}^{-4}{\text{m}}^2=3.60\times {10}^{-2}{\text{m}}^2$
The energy radiated by the plate
$=ϵ\sigma A{T}^4$
$=0.250\times 5.67\times {10}^{-8}\times 3.60\times {10}^{-2}\times (527+273{)}^4$
$=5.10\times {10}^{-10}\times (800{)}^4\approx 209\text{W}$