A piston cylinder contains 900 kg of water. The piston is contained between two

Question

A piston cylinder contains 900 kg of water. The piston is contained between two sets of stops. When the piston is resting on the bottom stops, the volume is 1 m3. The piston comes into contact with a linear spring, with k = 15 kN=m, when the volume reaches 2 m3. When the piston comes into contact with the top stops, the volume is 3 m3. The water is initially at 70C. Heat is added until the system becomes a single phase. (a) Sketch a p-8 and a T-8 diagram for the process. (b) Find the nal T, p, v, u, and x. (c) Find the work done by the water. (d) Find the net heat transfer for the process.

Explanation / Answer

A linear spring has a force linear proportional to displacement. F = k x, so the equilibrium pressure then varies linearly with volume: P = a + bV, with an intersect a and a slope b = dP/dV. Look at the balancing pressure at zero volume (V -> 0) when there is no spring force F = PA = PoA + mpg and the initial state. These two points determine the straight line shown in the P-V diagram. Piston area = AP = (p/4) · 0.12 = 0.00785 m2 V 0.557 a = P0 + mpg Ap = 100 + 5Ê· Ê9.80665 = 106.2 kPa intersect for zero volume. P2 = P1 + dP dV D V = 400 + 0.4Ê-Ê0 (0.557 - 0.4) = 515.3 kPa

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