Question
400 kJ of energy is produced by a system at 100 K. What is the change in entropy of the surroundings?
Group of answer choices
- 4 kJ/K
The change in enthalpy of the surroundings must be known to do the calculation.
+ 4 kJ/K
0 kJ/K. The entropy change is to the system, not the surroundings.
Flag question: Question 4
Question 41 pts
Which of the following is a reason that the calculation of change in entropy of the surrounding would be incorrect?
Group of answer choices
kJ for energy and J for entropy are not reconciled
the reversed sign is not accounted for
The temperature used is Celsius instead of Kelvin
All the responses are reasons for an incorrect answer
Group of answer choices
- 4 kJ/K
The change in enthalpy of the surroundings must be known to do the calculation.
+ 4 kJ/K
0 kJ/K. The entropy change is to the system, not the surroundings.
Flag question: Question 4
Question 41 pts
Which of the following is a reason that the calculation of change in entropy of the surrounding would be incorrect?
Group of answer choices
kJ for energy and J for entropy are not reconciled
the reversed sign is not accounted for
The temperature used is Celsius instead of Kelvin
All the responses are reasons for an incorrect answer
Answers
GPT-4o mini
To calculate the change in entropy of the surroundings (\(\Delta S_{\text{surroundings}}\)), you can use the formula:
\[
\Delta S_{\text{surroundings}} = -\frac{Q}{T}
\]
Where:
- \(Q\) is the heat exchanged (in joules, so convert \(400 \text{ kJ}\) to \(400,000 \text{ J}\))
- \(T\) is the temperature in Kelvin
Given that \(Q = 400 \text{ kJ} = 400,000 \text{ J}\) and \(T = 100 \text{ K}\), we can calculate:
\[
\Delta S_{\text{surroundings}} = -\frac{400,000 \, \text{J}}{100 \, \text{K}} = -4000 \, \text{J/K} = -4 \, \text{kJ/K}
\]
Now looking at your answer choices for the first question:
1. **- 4 kJ/K**: This is correct, as we determined that the change in entropy of the surroundings is \(-4 \, \text{kJ/K}\).
2. **The change in enthalpy of the surroundings must be known to do the calculation**: This is incorrect for entropy calculations in this context.
3. **+ 4 kJ/K**: This is also incorrect as the value should be negative.
4. **0 kJ/K. The entropy change is to the system, not the surroundings**: This is incorrect because the change in entropy of the surroundings can indeed be calculated.
**Correct answer**: **- 4 kJ/K**.
---
For the second question about reasons that the calculation of change in entropy of the surrounding would be incorrect:
1. **kJ for energy and J for entropy are not reconciled**: This could lead to incorrect units if not properly converted, though it's not a primary issue here since we converted kJ to J.
2. **the reversed sign is not accounted for**: This is important as the surroundings absorb heat loss as negative.
3. **The temperature used is Celsius instead of Kelvin**: Temperature must be in Kelvin for thermodynamic calculations.
4. **All the responses are reasons for an incorrect answer**: This is a broad claim, and while some individual points may cause issues, the fundamental problem in the scenario presented was the sign for the surroundings' entropy change.
**Correct answer**: **All the responses are reasons for an incorrect answer**.
\[
\Delta S_{\text{surroundings}} = -\frac{Q}{T}
\]
Where:
- \(Q\) is the heat exchanged (in joules, so convert \(400 \text{ kJ}\) to \(400,000 \text{ J}\))
- \(T\) is the temperature in Kelvin
Given that \(Q = 400 \text{ kJ} = 400,000 \text{ J}\) and \(T = 100 \text{ K}\), we can calculate:
\[
\Delta S_{\text{surroundings}} = -\frac{400,000 \, \text{J}}{100 \, \text{K}} = -4000 \, \text{J/K} = -4 \, \text{kJ/K}
\]
Now looking at your answer choices for the first question:
1. **- 4 kJ/K**: This is correct, as we determined that the change in entropy of the surroundings is \(-4 \, \text{kJ/K}\).
2. **The change in enthalpy of the surroundings must be known to do the calculation**: This is incorrect for entropy calculations in this context.
3. **+ 4 kJ/K**: This is also incorrect as the value should be negative.
4. **0 kJ/K. The entropy change is to the system, not the surroundings**: This is incorrect because the change in entropy of the surroundings can indeed be calculated.
**Correct answer**: **- 4 kJ/K**.
---
For the second question about reasons that the calculation of change in entropy of the surrounding would be incorrect:
1. **kJ for energy and J for entropy are not reconciled**: This could lead to incorrect units if not properly converted, though it's not a primary issue here since we converted kJ to J.
2. **the reversed sign is not accounted for**: This is important as the surroundings absorb heat loss as negative.
3. **The temperature used is Celsius instead of Kelvin**: Temperature must be in Kelvin for thermodynamic calculations.
4. **All the responses are reasons for an incorrect answer**: This is a broad claim, and while some individual points may cause issues, the fundamental problem in the scenario presented was the sign for the surroundings' entropy change.
**Correct answer**: **All the responses are reasons for an incorrect answer**.