A long metal sheet that can be approximated as a blackbody is being conveyed
through a water bath to be cooled. In order to prevent thermal burn on people
handling the sheet, it must exit the water bath at a temperature below
\(45^{\circ} \mathrm{C}\). A radiometer is placed normal to and at a distance of
\(0.5 \mathrm{~m}\) from the sheet surface to monitor the exit temperature. The
radiometer receives radiation from a target area of \(1 \mathrm{~cm}^{2}\) of
the metal sheet surface. When the radiometer detects that the metal sheet
temperature is not below \(45^{\circ} \mathrm{C}\), an alarm will go off to warn
that the sheet is not safe to touch. Determine the irradiation on the
radiometer that the warning alarm should be triggered.