The temperature at the surface of the Sun is approximately 5,150 K, and the temperature at the surface of the Earth is approximately 285 K. What entropy change of the Universe occurs when 5.00 103 J of energy is transferred by radiation from the Sun to the Earth?

In this case, we need to use the correct expression to solve this. In thermodynamics, the expression to use that puts a relation between heat, temperature and entropy is the following:

ΔS = Q/T

To determine the entropy change of the universe, we need to sum the entropy change of Earth and the entropy of the sun.

As the sun is transfering radiation to Earth, the sun is losing energy, therefore, heat is negative, while Earth receives the heat, so it's positive. Calculating the entropy for the sun and Earth:

ΔSs = -Q/Ts

ΔSe = Q/Te

ΔSu = ΔSe + ΔSs

Let's calculate both entropies by separate:

ΔSe = 5x10^3 / 285 = 17.54 J/K

ΔSs = -5x10^3 / 5,150 = -0.971 J/K

Therefore, the entropy of universe:

ΔSu = 17.54 - 0.971

ΔSu = 16.569 J/K