12.6 Heat Loss by Radiation

All warm bodies lose heat energy by emitting long-wave thermal radiation according to the Stefan-Boltzmann law: \[\begin{equation} R_\_=\varepsilon A_h\sigma T_h^4 \tag{12.16} \end{equation}\] Here \(T_h\) is the absolute (Kelvin) temperature of the surface of the body in our case, the fleece tips of the sheep, \(\sigma\) is the Stefan-Boltzmann constant, and \(\varepsilon\) is the emissivity of the body. Total heat energy lost this way by the sheep is then \(R_\_ = (\pi dL)(\varepsilon\sigma T_h^4)\).

To obtain a rough estimate of heat loss by radiation, we substitute the following parameter values \(dL=0.5\cdot 1.0\), \[R_\_=(\pi \cdot 0.5 \cdot 1)(1 \cdot 5.67 \cdot 10^{-8} \cdot 293^4)= 656 W,\] assuming \(\varepsilon=1\) and \(T_h\)= 293K and using \(\sigma=5.67 \cdot 10^{-8} W M^{-2}K^{-4}\).