Graphically show the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from `(p_(i), V_(i))` to `(p_(f), V_(f))`. With the help of a pV plot compare the work done in the above case with that carried out against a constant pressure `p_(f)`.

Explanation

To solve the problem of graphically showing the total work done in an expansion of an ideal gas that changes reversibly and isothermally from \((p_i, V_i)\) to \((p_f, V_f)\), we will follow these steps:

### Step 1: Draw the p-V Diagram
1. **Set up the axes**: Draw a Cartesian coordinate system where the y-axis represents pressure (P) and the x-axis represents volume (V).
2. **Plot the isothermal curve**: Since the process is isothermal for an ideal gas, the curve will be a rectangular hyperbola. This curve represents the relationship between pressure and volume for an ideal gas at constant temperature.

### Step 2: Mark Initial and Final States
1. **Identify the initial and final states**: Mark the initial state \((p_i, V_i)\) on the curve and the final state \((p_f, V_f)\). Ensure that \(V_i < V_f\) since it is an expansion.
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