Both q & w are __________ function & q + w is a ___________ function :-

Options

A. State, Path
B. State, State
C. Path, State
D. Path, Path

Answer

To solve the question, we need to identify the nature of the functions involved: heat (q) and work (w), and their sum (q + w).

### Step-by-Step Solution:

1. **Identify the Nature of q and w:**
- Heat (q) and work (w) are both forms of energy transfer. They depend on the specific path taken during a process. This means that the values of q and w can change based on how the system transitions from one state to another.
- Therefore, both q and w are classified as **path functions**.

2. **Identify the Nature of q + w:**
- The sum of heat and work (q + w) corresponds to the change in internal energy (ΔU) of the system. The change in internal energy is a property that depends only on the initial and final states of the system, not on how the system reached those states.
- Hence, q + w is classified as a **state function**.

3. **Fill in the Blanks:**
- Based on the analysis above, we can fill in the blanks in the question:
- Both q & w are **path functions**.
- q + w is a **state function**.

### Final Answer:
Both q & w are **path functions** & q + w is a **state function**.

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