Applying the Energy Balance Figure P3.84 shows a piston–cylinder assembly fitted...

Applying the Energy Balance

Figure P3.84 shows a piston–cylinder assembly fitted with a spring. The cylinder contains water, initially at 1000°F, and the spring is in a vacuum. The piston face, which has an area of 20 in.², is initially at x₁ = 20 in. The water is cooled until the piston face is at x₂ = 16 in. The force exerted by the spring varies linearly with x according to F_spring = kx, where k = 200 lbf/in. Friction between the piston and cylinder is negligible. For the water, determine

(a) the initial and final pressures, each in lbf/in.²

(b) the amount of water present, in lb.

(c) the work, in Btu.

(d) the heat transfer, in Btu.