Question

A spring-loaded piston/cylinder contains water at 500°C, 3 MPa. The setup is such that pressure is proportional to volume, P = CV. It is now cooled until the water becomes saturated vapor. Sketch the P-v diagram and find the final pressure.

Answer 1

State 1: v1 = 0.11619 m3/kg

Process: m is constant and P = C0V = C0m v = C v

P = Cv ⇒ C = P1/v1 = 3000/0.11619 = 25820 kPa kg/m3

State 2: x2 = 1 & P2 = Cv2 (on process line)

Trial & error on T2sat or P2sat: Here

at 2 MPa vg = 0.09963 ⇒ C = 20074 (low)

2.5 MPa vg = 0.07998 ⇒ C = 31258 (high)

2.25 MPa vg = 0.08875 ⇒ C = 25352 (low)

Interpolate to get the right C ⇒ P2 = 2270 kPa