Answer :
To solve this problem, we will calculate the entropy for both cases, remembering that the concept of entropy is the relationship between the heat released / gained and the temperature. After calculating the entropy in the sun and on the earth we will find the difference between the two. So that,
Entropy at Sun
[tex]S_1 = \frac{Q}{T_1}[/tex]
[tex]Q= 4500 J[/tex]
[tex]T_1 = 5200 K[/tex]
Replacing,
[tex]S_1 =\frac{4500}{5200}[/tex]
[tex]S_1 = 0.86 J \cdot K^{-1}[/tex]
The entropy at Earth,
[tex]S_2 = \frac{Q}{T_2}[/tex]
The values are,
[tex]T_2 = 290K[/tex]
[tex]Q = 4500J[/tex]
Replacing at the equation,
[tex]S_2 = \frac{4500}{290}[/tex]
[tex]S_2 = 15.51J \cdot K^{-1}[/tex]
Then the total change in entropy will be,
[tex]\Delta S = S_2 -S_1[/tex]
[tex]\Delta S = 15.51-0.86[/tex]
[tex]\Delta S = 14.65 J \cdot K^{-1}[/tex]
Therefore the entropy change is [tex]14.65J \cdot K^{-1}[/tex]