A certain amount of water of mass m, at a temperature `T_(2)` cools.to temperature `T_(1).` The heat given out by the water is absorbed by n mole of an ideal gas. The gas expands at constant temperature T and changes its volume from `V _(i) ` to `V _(f)` What is its initial volume ?

Explanation

To find the initial volume \( V_i \) of the ideal gas that absorbs the heat given out by the cooling water, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Heat Lost by Water**:
The heat lost by the water as it cools from temperature \( T_2 \) to \( T_1 \) can be calculated using the formula:
\[
Q = mc(T_2 - T_1)
...