The work done by one mole of a monatomic ideal gas `( gamma = 5 //3` ) in expanding adiabatically is 825 J . The initial temperature and volume of the gas are 393 K and 0.100 `m^3` obtain the final temperature of the gas .

Explanation

To find the final temperature of the gas after it has expanded adiabatically, we can use the relationship derived from the first law of thermodynamics and the properties of an ideal gas. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Work done (W) = 825 J
- Initial temperature (T1) = 393 K
- Initial volume (V1) = 0.100 m³
- Number of moles (n) = 1 mole
- Gas constant (R) = 8.314 J/(mol·K)
...