Which of the following is path dependent

Options

A. U
B. PdV
C. P
D. V

Answer

To determine which of the given options is path dependent, we need to understand the difference between state functions and path functions.

### Step-by-Step Solution:

1. **Define State Functions and Path Functions**:
- State functions are properties that depend only on the initial and final states of a system, regardless of the path taken to get from one state to another. Examples include internal energy (U), pressure (P), and volume (V).
- Path functions, on the other hand, depend on the specific path taken during a process. An example of a path function is work done (W).

2. **Analyze the Given Options**:
- The options provided are U (internal energy), P (pressure), V (volume), and PDB (which represents work done).
- U, P, and V are all state functions because they only depend on the state of the system and not on how the system arrived at that state.

3. **Identify the Path Dependent Quantity**:
- PDB, which represents work done, is a path function. The work done by or on a system depends on the specific path taken during the process. For example, if the volume changes against a constant pressure, the work done can be calculated using the area under the curve in a pressure-volume diagram, which varies with the path taken.

4. **Conclusion**:
- Among the options given, the only path dependent quantity is PDB (work done).

### Final Answer:
The path dependent quantity is **PDB (work done)**.

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