A gas expands under constant pressure P from volume `V_(1)` to`V_(2)`The work done by the gas is

Options

A. `P(V_(2)-V_(1))`
B. `P(V_(1)-V_(2))`
C. `P(V_(1)^(lambda)-V_(2)^(lambda))`
D. `P(V_(1)V_(2))/(V_(2)-V_(1))`

Answer

To find the work done by a gas expanding under constant pressure from volume \( V_1 \) to \( V_2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Process**: The gas is expanding at constant pressure \( P \). This means that throughout the expansion, the pressure remains the same.

2. **Identify the Initial and Final Volumes**: The initial volume of the gas is \( V_1 \) and the final volume is \( V_2 \).

3. **Use the Formula for Work Done**: The work done \( W \) by the gas during an expansion at constant pressure can be calculated using the formula:
\[ W = P \Delta V \]
where \( \Delta V \) is the change in volume.

4. **Calculate the Change in Volume**: The change in volume \( \Delta V \) is given by:
\[ \Delta V = V_2 - V_1 \]

5. **Substitute the Change in Volume into the Work Formula**: Now, substituting \( \Delta V \) into the work formula, we get:
\[ W = P (V_2 - V_1) \]

6. **Final Expression for Work Done**: Therefore, the work done by the gas during the expansion from volume \( V_1 \) to \( V_2 \) at constant pressure \( P \) is:
\[ W = P (V_2 - V_1) \]

### Final Answer:
The work done by the gas is \( W = P (V_2 - V_1) \).

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