If `w_(1), w_(2), w_(3)` and `w_(4)` for an ideal gas are magnitude of work done in isothermal, adiabatic, isobaric and isochoric reversible expansion processes, the correct order will be :

Options

A. `w_(1) gt w_(2) gt w_(3) gt w_(4)`
B. `w_(3) gt w_(2) gt w_(1) gt w_(4)`
C. `w_(3) gt w_(2) gt w_(4) gt w_(1)`
D. `w_(3) gt w_(1) gt w_(2) gt w_(4)`

Explanation

To solve the problem of determining the correct order of work done (W1, W2, W3, W4) for an ideal gas in various reversible expansion processes (isothermal, adiabatic, isobaric, and isochoric), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Work Done in Different Processes:**
- The work done (W) in a thermodynamic process is represented by the area under the PV (Pressure-Volume) curve.
- The types of processes we are considering are:
- **Isothermal (W1)**: Constant temperature.
- **Adiabatic (W2)**: No heat exchange.
- **Isobaric (W3)**: Constant pressure.
- **Isochoric (W4)**: Constant volume.

2. **Analyze Each Process:**
- **Isothermal Process (W1)**: The work done is significant because the gas expands at a constant temperature, and the area under the curve is relatively large.
- **Adiabatic Process (W2)**: The work done is less than in isothermal because the gas does not exchange heat with the surroundings, leading to a steeper curve.
- **Isobaric Process (W3)**: The work done is the largest among these processes because the pressure remains constant while the volume changes, leading to a significant area under the curve.
- **Isochoric Process (W4)**: No work is done since the volume does not change (W = 0).

3. **Determine the Order of Work Done:**
- From the analysis, we can conclude:
- W3 (Isobaric) > W1 (Isothermal) > W2 (Adiabatic) > W4 (Isochoric)
- Therefore, the correct order of work done is:
- **W3 > W1 > W2 > W4**

### Final Answer:
The correct order of work done is:
**W3 > W1 > W2 > W4**