The entropy change at a given temperature is expressed as:
`q = T DeltaS`
`DeltaS = q//DeltaT`
`DeltaS = q - T`
`S = q//T`

Options

A. `q = T DeltaS`
B. `DeltaS = q//DeltaT`
C. `DeltaS = q - T`
D. `S = q//T`

Explanation

To solve the question regarding the expression for entropy change at a given temperature, we will analyze each of the provided equations step by step.

### Step-by-Step Solution:

1. **Understanding the Concept of Entropy (S)**:
- Entropy is a measure of the disorder or randomness in a system. It is a state function, meaning it depends only on the initial and final states of the system, not on the path taken.

2. **Analyzing the Given Equations**:
- We have four equations to evaluate:
1. \( q = T \Delta S \)
2. \( \Delta S = \frac{q}{\Delta T} \)
3. \( \Delta S = q - T \)
4. \( S = \frac{q}{T} \)

3. **Evaluating Each Expression**:
- **Equation 1: \( q = T \Delta S \)**:
- This equation relates heat (q) to temperature (T) and the change in entropy (\(\Delta S\)). It is a correct expression for reversible processes.

- **Equation 2: \( \Delta S = \frac{q}{\Delta T} \)**:
- This equation suggests that the change in entropy is equal to the heat added divided by the change in temperature. This is not a standard expression for entropy change and is incorrect.

- **Equation 3: \( \Delta S = q - T \)**:
- This equation does not correctly represent the relationship between heat and entropy. It is incorrect.

- **Equation 4: \( S = \frac{q}{T} \)**:
- This equation represents the entropy of a system in terms of the heat added and the temperature. It is a valid expression but is not the standard form for change in entropy.

4. **Identifying the Correct Expression**:
- The most appropriate expression for the change in entropy (\(\Delta S\)) during a reversible process is derived from the first equation:
\[ \Delta S = \frac{q_{\text{rev}}}{T} \]
- This means that the correct answer to the question is the first equation \( q = T \Delta S \).

### Conclusion:
The correct expression for the entropy change at a given temperature is:
\[ \Delta S = \frac{q_{\text{rev}}}{T} \]