What is the relation for work done (i) reversibly and (ii) irreversibly for the isothermal expansion of an ideal gas from volume `V_(1)` to `V_(2)` at temperature T?

Explanation

To find the relation for work done during the isothermal expansion of an ideal gas from volume \( V_1 \) to \( V_2 \) at temperature \( T \), we will derive the expressions for both reversible and irreversible processes.

### Step-by-Step Solution:

#### (i) Work Done Reversibly

1. **Start with the definition of work done (dW)**:
\[
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