Question

A solar collector is placed in direct sunlight where it absorbs energy at the rate of 892 J/s for each square meter of its surface. The emissivity of the solar collector is

e = 0.77. What equilibrium temperature does the collector reach? Assume that the only energy loss is due to the emission of radiation.

Answer 1

According to Stefan-Boltzmann Law, The energy per unit time per unit area _{$\small j$} is;

$\small j=e\sigma T^{4}$

Here _{$\small j$} = 892 J/s for each square meter, e = 0.77 emissivity, $\small \sigma$ = 5.67 $\small \times$ 10^-8 Wm^-2K^-4 is Stefan-Boltzmann constant and T is temperature. Thus;

   $\small \Rightarrow T=\sqrt[4]{\frac{j}{e\sigma }}$

   $\small \Rightarrow T=\sqrt[4]{\frac{892}{0.77\times 5.67\times 10^{-8}}} =378\: K$