A thin square metal sheet of side is placed in deep space where the background…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A thin square metal sheet of side

0.50\,\text{m}

is placed in deep space where the background temperature may be taken as

0\,\text{K}

. Both faces of the sheet are identical and have emissivity

\varepsilon = 0.60

. A heater attached to the sheet supplies a constant power of

1.0\,\text{kW}

. Take

\sigma = 5.67\times10^{-8}\,\text{W\,m}^{-2}\,\text{K}^{-4}

. (i) Write an expression for the total power radiated by the sheet when its temperature is

T

. (ii) Hence determine the steady temperature

T

(in kelvin) at which the sheet will settle.