An ideal gas is taken from an initial state i to a final state f in such a way that the ratio of the pressure to the absolute temperature remains constant. What will be the work done by the gas ?

Explanation

To solve the problem, we need to analyze the situation where an ideal gas is taken from an initial state (i) to a final state (f) while maintaining a constant ratio of pressure (P) to absolute temperature (T).

### Step-by-Step Solution:

1. **Understanding the Given Condition**:
We are given that the ratio of pressure to absolute temperature remains constant. This can be mathematically expressed as:
\[
\frac{P}{T} = k
...