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 $\sigma=5.67 \cdot 10^{-8} W M^{-2}K^{-4}$.