(i) A sample of a gas initially at `27^(@)` C is compressed from 40 litres to 4 litres adiabatically and reversibly. Calculate the final temperature `(C_(v) =2.5 R)` .
(ii) Calculate the maximum work done in expanding 16 gm of oxygen at 300 K and occupying, a volume of `5 dm^(3)` isothermally until the volume becomes `25 dm^(3)`.
(iii) 10 gm of argon gas is compressed isothermally and reversibly at a temperature of `27^(@)` C from 10 litre to 5 litre. Calculate q, w`.DeltaE` and `DeltaH` for this process.

Explanation

Let's solve the questions step by step.

### Question (i):
A sample of a gas initially at `27°C` is compressed from `40 liters` to `4 liters` adiabatically and reversibly. Calculate the final temperature `(C_v = 2.5 R)`.

**Step 1: Convert the initial temperature to Kelvin.**
- \( T_1 = 27°C = 27 + 273 = 300 K \)

...