Final answer:
The entropy change when 3,500 J is transferred from the Sun to the Earth is calculated using the formula for entropy change, ∆S = Q/T. Energy transfer results in a decrease in entropy for the Sun and an increase for the Earth, with overall system entropy increasing.
Step-by-step explanation:
The student asks about the entropy change when 3,500 J of energy is transferred by heat from the Sun to the Earth. The Sun has a surface temperature of approximately 5,900 K, and the Earth's surface temperature is approximated at 295 K. To calculate the entropy change, we use the formula ∆S = Q/T, where ∆S is the change in entropy, Q is the heat transferred, and T is the temperature.
When heat is transferred from the Sun to the Earth, there will be entropy loss at the Sun and entropy gain at the Earth. The change of entropy for the Sun, ∆S_sun, is -Q/T_sun, and for the Earth, ∆S_earth is Q/T_earth. Therefore, the total change in entropy is the sum of these values:
- ∆S_sun = -3,500 J / 5,900 K
- ∆S_earth = 3,500 J / 295 K
By calculating these values, we find that the Sun's entropy decreases while the Earth's entropy increases, and the overall entropy change of the system (Sun and Earth) is positive, expressing the second law of thermodynamics where the total entropy of an isolated system can never decrease over time.