we are asked to determine the power irradiated by a star given its area and temperature.
To do that we will use the following formula:
[tex]P=\sigma AT^4[/tex]Where:
[tex]\begin{gathered} P=power \\ A=\text{ area} \\ T=\text{ temperature} \\ \sigma=\text{ constant} \end{gathered}[/tex]The constant sigma is equivalent to:
[tex]\sigma=5.7\times10^{-8}Wm^{-2}K^{-4}[/tex]Now, we substitute the values:
[tex]P=(5.7\times10^{-8}Wm^{-2}K^{-4})(6.29\times10^{18}m^2)(7005K)^4[/tex]Solving the operations:
[tex]P=8.63\times10^{16}W[/tex]And thus we get the power of the start.
