A well-insulated piston-cylinder assembly is connected by a valve to an air supply at 100lbf/in.2 and 80°F. The air inside the cylinder is initially at 14.7 lbf/in² and 80°F, and occupies a volume of 0.1 ft³. Initially, the piston face is located at d=0 and the spring exerts no force on the piston. The atmospheric pressure is 14.7 lbf/in² and the area of the piston face is 0.22 ft². The valve is opened, and air is admitted slowly until the volume of the air inside the cylinder is 0.4 ft³. During the process, the spring exerts a force on the piston that varies according to F = kd, where k = 700 lbf/ft. There is no friction between the piston and the cylinder wall. Using the ideal gas model, determine for the air inside the cylinder:

(a) The final pressure

(b) The final temperature