Which of the following expressions regarding entropy is not correct?

Options

A. `DeltaS_("system")=(q)/(T)`
B. `DeltaS_("system")=DeltaS_("total")+DeltaS_("surrounding")`
C. `DeltaS=DeltaS_("final")-S_("initial")`
D. `DeltaS_("total")=DeltaS_("system")+DeltaS_("surrounding")`

Answer

To solve the question regarding which expression about entropy is incorrect, we will analyze the provided equations and options step by step.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Entropy (S) is a measure of the disorder or randomness in a system.
- The change in entropy (ΔS) can be defined in various ways, depending on the context.

2. **Review the Given Equations**:
- **Equation 1**: \( S_{\text{system}} = \frac{Q}{T} \) (where Q is the heat added and T is the temperature).
- **Equation 2**: \( \Delta S = S_{\text{final}} - S_{\text{initial}} \).
- **Equation 3**: \( \Delta S_{\text{system}} = \Delta S_{\text{total}} - \Delta S_{\text{surroundings}} \).

3. **Rearranging Equation 3**:
- From Equation 3, we can rearrange it to find \( \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} = \Delta S_{\text{total}} \).
- This indicates that the total change in entropy is the sum of the changes in the system and surroundings.

4. **Analyzing the Options**:
- **Option A**: \( \Delta S_{\text{system}} = \frac{Q}{T} \) (Correct).
- **Option B**: \( \Delta S_{\text{system}} = S_{\text{total}} + S_{\text{surroundings}} \) (Incorrect).
- **Option C**: \( \Delta S = S_{\text{final}} - S_{\text{initial}} \) (Correct).
- **Option D**: \( \Delta S_{\text{total}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} \) (Correct).

5. **Identifying the Incorrect Expression**:
- The incorrect expression is found in **Option B**: \( \Delta S_{\text{system}} = S_{\text{total}} + S_{\text{surroundings}} \). This is not a correct representation of the relationship between the changes in entropy.

### Final Answer:
The expression regarding entropy that is not correct is **Option B**: \( \Delta S_{\text{system}} = S_{\text{total}} + S_{\text{surroundings}} \).