`1mol` of an ideal gas at `400K` and `10atm` is allowed to expand, adiabatically, against `2.0atm` external pressure. Find the final temperature of the gas. [Use: `C_(v) = (5)/(2)R]`

Explanation

To solve the problem of finding the final temperature of an ideal gas undergoing adiabatic expansion, we can follow these steps:

### Step 1: Identify Given Values
We have:
- Initial temperature, \( T_1 = 400 \, K \)
- Initial pressure, \( P_1 = 10 \, atm \)
- External pressure, \( P_{ext} = 2 \, atm \)
- Moles of gas, \( n = 1 \, mol \)
...