Pressure volume (PV) work done by an ideal gas system at constant volume is

Options

A. `-(DeltaP)/P`
B. Zero
C. `-V/(DeltaP)`
D. `-DeltaV`

Answer

To solve the question regarding the pressure-volume (PV) work done by an ideal gas system at constant volume, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Work Done in Thermodynamics**:
- The work done (W) by a gas during expansion or compression can be expressed as:
\[ W = -P \Delta V \]
where \( P \) is the pressure and \( \Delta V \) is the change in volume.

2. **Identifying Conditions**:
- The question specifies that the process occurs at constant volume. This means that the volume of the gas does not change during the process.

3. **Determining Change in Volume**:
- Since the volume is constant, the change in volume (\( \Delta V \)) is:
\[ \Delta V = V_{\text{final}} - V_{\text{initial}} = 0 \]

4. **Substituting into the Work Formula**:
- Substituting \( \Delta V = 0 \) into the work formula gives:
\[ W = -P \times 0 = 0 \]

5. **Conclusion**:
- Therefore, the work done by an ideal gas system at constant volume is:
\[ W = 0 \]

### Final Answer:
The pressure-volume (PV) work done by an ideal gas system at constant volume is **zero**.

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