Problem 1 (60 Points) A frictionless piston-and-cylinder device initially contains 17 kg of a vapor-liquid mixture of methane with quality w = 0.118. The top is open to the atmosphere, and piston and the surroundings exert a total pressure of 1 MPa on the fluid. Then, 10 MJ of heat is slowly added to the fluid over a given time period. There are no heat losses from the fluid. The cylinder has a cross-sectional area of 0.79 m2. A pin that is attached to the inner wall of the cylinder 1 m from the bottom will limit how much the piston can move up (see diagram). a. What will be the final state of the system after all the heat is added? Note that if you specify two intensive variables for the system, its state is specified. b. Extra credit (10 points): what will be final the temperature and pressure of the fluid after the heat is added? This step will involve some trial-and-error procedure. Hint: If the amount of heat added is large enough, the piston will first move up at constant pressure until it hits the pin, and then the fluid will continue to get heated at constant volume afterwards. In such a scenario, your overall process will have two stages in it: before hitting the pin, and after hitting the pin. To determine if this is indeed the case, first find out the amount of