In a change from state `A` to state `B`

Options

A. `q` depends only on the initial and final state
B. `w` depends only on the initial and final state
C. `DeltaE` depends only on the initial and final state
D. `DeltaE` depends upon the path adopted by `A` to change into `B`.

Explanation

To solve the question regarding the change from state A to state B in terms of thermodynamics, we need to analyze the properties of heat (Q), work (W), and internal energy change (ΔE) in relation to state functions and path functions.

### Step-by-Step Solution:

1. **Understanding State Functions and Path Functions**:
- A **state function** is a property that depends only on the state of the system, not on how it got there. Examples include internal energy (ΔE), enthalpy, and pressure.
- A **path function** is a property that depends on the specific path taken to reach a particular state. Examples include heat (Q) and work (W).

2. **Analyzing the Options**:
- **Option 1**: "Q depends only on the initial and final state."
- This statement is **incorrect**. Heat (Q) is a path function and depends on the specific process taken to go from state A to state B.

- **Option 2**: "Work depends only on the initial and final state."
- This statement is also **incorrect**. Work (W) is a path function and depends on the path taken during the process.

- **Option 3**: "ΔE depends only on the initial and final state."
- This statement is **correct**. The change in internal energy (ΔE) is a state function and depends only on the initial and final states of the system, regardless of the path taken.

- **Option 4**: "ΔE depends upon the path adopted by A to change into B."
- This statement is **incorrect**. Since ΔE is a state function, it does not depend on the path taken.

3. **Conclusion**:
- The correct option is **Option 3**: "ΔE depends only on the initial and final state."