Answer
a) $16,000,00E_{EARTH}$
b) $193, 067,034,0(E_{EARTH})$
Work Step by Step
a) As per the given problem, we have:
$E=kT^4$
Here, $k$ is defined as constant of proportionality
$\dfrac{E_{SUN}}{E_{EARTH}}=\dfrac{kT^4_{SUN}}{kT^4_{EARTH}}$
Plug the given data in the above expression, we get
This gives: $E_{SUN}=16,000,00E_{EARTH}$
b) As per the given problem, we have:
$E'=kAT^4$
Here, $k$ is defined as constant of proportionality
$\dfrac{E'_{SUN}}{E_{EARTH}}=\dfrac{kA_{SUN}T^4_{SUN}}{kA_{EARTH}T^4_{EARTH}}$
Plug the given data in the above expression, we get
This gives: $E_{SUN}=(\dfrac{6000}{300})^4\dfrac{kA_{SUN}T^4_{SUN}}{kA_{EARTH}T^4_{EARTH}}=193, 067,034,0(E_{EARTH})$