Final answer:
The question requires using thermodynamic principles and steam tables to calculate the final temperature and mass of the saturated water vapor in a tank after pressure equalization with high-pressure steam.
Step-by-step explanation:
The question involves determining the final temperature and mass of saturated water vapor in a tank after it is connected to another vessel with steam at a higher pressure and temperature. This is a typical thermodynamics problem that falls under the subject of Engineering, specifically thermodynamics. We'll need to apply the laws of thermodynamics and properties of steam to find the solution.
First, we would find the state properties of saturated water vapor at 3.5 bar, which can be obtained from steam tables. Since the tank is rigid and insulated, the process is adiabatic, which implies no heat transfer. When the valve is opened, steam at 15 bar and 320°C will flow into the tank until the pressures equalize. Throughout the process, the temperature and mass of the steam in the tank will change.
After pressure equilibration at 15 bar, we must determine whether the contents of the tank are superheated vapor or a mixture of liquid and vapor. This can be ascertained by comparing the initial specific volume of the tank's contents with the specific volume of steam at 15 bar from the steam tables. If it is less, the steam remains superheated, and the final temperature can be found from superheated steam tables; otherwise, the final temperature is the saturation temperature at 15 bar.
Finally, to determine the final mass in the tank, we can use the final specific volume (obtained from steam tables) and the volume of the tank. The mass is calculated by dividing the total volume by the specific volume of the steam at the final state.
Thus, by using steam tables and applying thermodynamic principles, we can find the final temperature and mass of the steam in the tank after the process.