Question

A piston-cylinder apparatus contains 4 kg of saturated liquid water at 35˚C. 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?

Answer #1

W = W1 + W2

P1 = 300000 Pa

V1 = 0.03 m^{3}

V2 = 0.075 m^{3}

W1 = P1* (V2-V1) = 300000 * (0.075 - 0.03) = 13500 J

For spring:

P2 = 7 x 10^{6} Pa

A = 0.06 m^{2}

k_{s} = 360000 N/m

Δx = (P2 - P1) * A / k_{s} = 7 x 10^{6} * 0.06 /
360000 = 1.12 m

W2 = 1/2 * ks * Δx^{2} = 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 * Δx)/M = (0.075 + 0.06 *
1.12)/4 = 0.0356 m^{3}/kg

Final temperature = 270 ^{o}C (from steam table for the
calculated saturated vapor specific volume)

Final intenal energy, U2 = 2593.7 * 1000 * 4 = 10374800 J

ΔU = U2 - U1 = 10374800 - 586680 = 9788120 J

Q = ΔU + W

**Total heat required, Q = 9788120 J + 237950 J = 10026070
J**

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