Question

A piston-cylinder device has two stops; a lower set and an upper set, that constrain the cylinder. When the piston is on the lower stops, the volume is 0.4 liters. When the piston reaches the upper stops, the volume is 0.6 liters. The piston-cylinder initially contains water at 100 kpa and a quality of 20%. The water is heated until it is completely transformed to steam. Additionally, the mass of the piston requires a pressure of 300kpa to raise it. When the piston hits the upper stops:
Determine the final pressure in the cylinder

Determine heat input

Determine work for the overall process

Hint: there are 4 states. Think about the process involved

Answer 1

Answer:

2080kJ

Explanation:

m(U4 - U1) = Q4 - W4

If P is less than 300kpa, then V = 0.4L

If P is greater than 300kpa, then V = 0.6L

If P is equal to 300kpa, then 0.4L < V < 0.6L

At 100kpa, vf = 0.001043m/kg and vg = 1.693m³/kg

Level 1

v1 = 0.001043 + 0.2 x 1.693 = 0.33964

m = V1/v1 ⇔ 0.4/0.33964

m = 1.178kg

u1 = 417.36 + 0.2 x 2088.7 = 835.1kJ/kg

Level 3

v3 = 0.6/1.178 = 0.5095 < vG = 0.6058 at P3 is equal to 300kpa

NOTE: Piston does reach upper stops to reach saturated vapor

Level 4

v4 = v3 = 0.5095m³/kg = vG at P4

P4 = 361kpa, u4 = 2550.0kJ/kg

1W4 = 1W2 + 2W3 + 3W4 = 0 + 2W3 + 0

1W4 = P2 (V3 - V2) = 300 x (0.6 - 0.4) = 60kJ

1Q4 = m(u4 -u1) + 1W4 = 1.178(2550.0 - 835.1) + 60 = 2080kJ