A masslesss piston divides a closed thermallyy insulated cylinder into two equal parts. One part contains M = 28 g of nitrogen. At this temperature, one-third of molecules are dissociated into atoms and the other part is evacuated. The piston is released and the gas fills the whole volume of the cylinder at temperature `T_(0)`. Then, the piston is slowly displaced back to its initial position. calculate the increases in internal energy of the gas. Neglect further dissociation of molecules during, the motion of the piston.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the number of moles of nitrogen gas.
Given:
- Mass of nitrogen, \( M = 28 \, \text{g} \)
- Molar mass of nitrogen \( N_2 = 28 \, \text{g/mol} \)

Using the formula for moles:
...