Question

The temperature at the surface of the Sun is approximately 5,300 K, and the temperature at the surface of the Earth is approximately 293 K. What entropy change of the Universe occurs when 6.00 103 J of energy is transferred by radiation from the Sun to the Earth?

Answer 1

The entropy change of the Universe that occurs is 19.346 J/K

Step-by-step explanation:

Given;

temperature of the sun,
`T_s` = 5,300 K

temperature of the Earth,
`T_E` = 293 K

radiation energy transferred by the sun to the earth, E = 6000 J

The sun loses Q of heat and therefore decreases its entropy by the amount

`\delta S_(sun) = (-Q)/(T_s)`

The earth gains Q of heat and therefore increases its entropy by the amount

`\delta S_(Earth) = (-Q)/(T_E)`

The total entropy change is:

`\delta S_(Earth) + \delta S_(sun) = (Q)/(T_E) -(Q)/(T_S) \\\\ = Q((1)/(T_E) -(1)/(T_S) )\\\\= 6000((1)/(293) -(1)/(5300) )\\\\=6000(0.0032243)\\\\= 19.346 \ J/K`

Therefore, the entropy change of the Universe that occurs is 19.346 J/K