Question

How do you calculate the radiation constant?

Answer 1

Radiation constant:

The constant is related to the total energy radiated by a blackbody (i.e., the Stefan-Boltzman Law), and is defined as:

$$\begin{gathered} \mathrm{a}=\frac{4\mathrm{\sigma }}{\mathrm{c}} \\ \mathrm{a}=\frac{8{\mathrm{\pi }}^5{\mathrm{k}}^4}{15{\mathrm{c}}^3{\mathrm{h}}^3}\left(\because \mathrm{\sigma }=\frac{2{\mathrm{\pi }}^5{\mathrm{k}}^4}{15{\mathrm{c}}^2{\mathrm{h}}^3}\right) \end{gathered}$$

where,

$$\begin{gathered} \mathrm{\sigma }=\mathrm{Stefan}-\mathrm{Boltzman}\mathrm{Constant} \\ \mathrm{c}=\mathrm{speed}\mathrm{of}\mathrm{light} \\ \mathrm{k}=\mathrm{Boltzman}\mathrm{constant} \\ \mathrm{h}=\mathrm{Planck}\text{'}\mathrm{s}\mathrm{constant} \end{gathered}$$

Numerically, the value of radiation constant is:

$$\begin{gathered} \mathrm{a}=7.567\times {10}^{-15}\mathrm{erg}/{\mathrm{cm}}^3{\mathrm{K}}^4 \\ \mathrm{a}=7.567\times {10}^{-16}\mathrm{J}/{\mathrm{m}}^3{\mathrm{K}}^4 \end{gathered}$$