A piston-cylinder apparatus contains 4 kg of saturated liquid water at 35C. The
ID: 950103 • Letter: A
Question
A piston-cylinder apparatus contains 4 kg of saturated liquid water at 35C. The piston’s cross sectional area is 0.06 m2 , and initially it is resting on stops, enclosing a volume of 0.03 m3 . To raise the piston, a pressure of 300kPa has to be applied. Heat is transferred until the volume is 0.075 m3 , at which point the piston encounters a linear spring. To deflect the spring 1 m, a force of 360 kN is required. More heat is transferred until the final pressure is 7 MPa. How much work is done in the process? How much heat is required?
Explanation / Answer
W = W1 + W2
P1 = 300000 Pa
V1 = 0.03 m3
V2 = 0.075 m3
W1 = P1* (V2-V1) = 300000 * (0.075 - 0.03) = 13500 J
For spring:
P2 = 7 x 106 Pa
A = 0.06 m2
ks = 360000 N/m
x = (P2 - P1) * A / ks = 7 x 106 * 0.06 / 360000 = 1.12 m
W2 = 1/2 * ks * x2 = 224450 J
Total work done = W1 + W2 = 13500 + 224450 = 237950 J
From steam table for saturated liquid water:
Initial intenal energy, U1 = 146.67 * 1000 * 4 = 586680 J
Final specific volume = (V2 + A * x)/M = (0.075 + 0.06 * 1.12)/4 = 0.0356 m3/kg
Final temperature = 270 oC (from steam table for the calculated saturated vapor specific volume)
Final intenal energy, U2 = 2593.7 * 1000 * 4 = 10374800 J
U = U2 - U1 = 10374800 - 586680 = 9788120 J
Q = U + W
Total heat required, Q = 9788120 J + 237950 J = 10026070 J
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