The pressure-volume work for an ideal gas can be calculated by using the expression `W=-int_(V_(i))^(V_(f))P_(ex)dV.` The work can also be calculated from the pV - plot by using the area under the curve within the specified limits. When an ideal gas is compressed (i) reversibly or (ii) irreversibly from volume `V_(i)` to `V_(f)`. Choose the correct option.

Options

A. `W_("reversible")=W_("irreversible")`
B. `W_("reversible")ltW_("irreversible")`
C. `W_("reversible") gt W_("irreversible")`
D. `W_("reversible")=W_("irreversible")+P_(ex)DeltaV`

Explanation

To solve the problem regarding the work done on an ideal gas during reversible and irreversible compression, we can follow these steps:

### Step 1: Understand the Work Done Expression
The work done on an ideal gas during compression can be expressed mathematically as:
\[ W = -\int_{V_i}^{V_f} P_{ex} \, dV \]
Where:
- \( W \) is the work done,
- \( V_i \) is the initial volume,
- \( V_f \) is the final volume,
- \( P_{ex} \) is the external pressure.

### Step 2: Analyze the PV Diagram
Draw a Pressure-Volume (PV) diagram for both reversible and irreversible compression.
- For reversible compression, the process is carried out slowly, allowing the system to remain in equilibrium. The curve will be smooth and continuous.
- For irreversible compression, the process occurs rapidly, and the path taken will be different, typically resulting in a steeper curve.

### Step 3: Identify the Areas Under the Curves
In the PV diagram:
- The area under the curve for reversible compression represents the work done \( W_{reversible} \).
- The area under the curve for irreversible compression represents the work done \( W_{irreversible} \).

### Step 4: Compare the Work Done
Since both processes start at the same initial volume \( V_i \) and end at the same final volume \( V_f \):
- The area under the curve for irreversible compression is generally larger than that for reversible compression due to the higher external pressure acting over a larger volume change.
- Thus, we can conclude that:
\[ W_{irreversible} > W_{reversible} \]

### Step 5: Choose the Correct Option
Based on the analysis, the correct option is:
- **W irreversible is more than W reversible.**

### Final Answer
The correct option is **W irreversible > W reversible.**

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