An unspecified quantity of an ideal gas has an initial pressure of 5 atm and temperature of `30^@C` . The gas is expanded at `30^@C` until the volume has increased by 60% of the initial value. Next, the quantity of the gas in the vessel is increased by 20% of the initial value while the volume is maintained constant. Finally the temperature is adjusted at constant volume until the gas pressure is again 5 atm. What is the final temperature?

Explanation

To solve the problem step by step, we will use the ideal gas law and the relationships between pressure, volume, and temperature.

### Step 1: Initial Conditions and Expansion
1. **Given Initial Conditions**:
- Initial Pressure, \( P_1 = 5 \, \text{atm} \)
- Initial Temperature, \( T_1 = 30^\circ C = 303 \, \text{K} \)
- Let the initial volume be \( V_1 = V \).

...