I made the following attempt to solve this question.However I don't know how to find final pressure.I don't know how to find final temperature for both sides.Can you give me a hint?
The total volume is constant. The air compression takes place adiabatically and reversibly, so you know the relationship between its pressure and its volume.
You are told the initial volume of the water container, the mass fractions of liquid water and water vapor, and the temperature of the saturated mixture. From this, you can determine the mass of the water in the container. What value do you get? This doesn't change.
You are told that the final state of the water is 100% saturated vapor and 0 % liquid water. So, from the steam tables, for any given pressure, you can determine the specific volume. And, since you know the mass of water, you can determine the actual volume. If you guessed the final pressure correctly, then the pressures of the water and air on the two sides of the piston must match and the sum of their volumes must add up to the original total volume. This is how you determine the final pressure and temperature of the water vapor.
No work is done on the combined system, so, knowing the final states of both the water and air, you can calculate the change in internal energy for each of them. The sum is then equal to the amount of heat added.