HW_8_Soln

HW_8_Soln - ME 309 Fall 2008 Section 2 (Merkle) Homework #...

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ME 309 Fall 2008 Section 2 (Merkle) Homework # 8 Due Mon 15 Sep 2008 Problem 8-1 A frictionless 3000- N piston maintains a gas at constant pressure in a cylinder. The cross-sectional area of the piston is 5200 mm 2 and the atmospheric pressure acting on this area is 0.1 MPa . A process occurs in which a paddle wheel transfers 6800 N · m of work to the gas, 10 kJ of heat is transferred from the gas, and the internal energy of the gas decreases by 1 kJ . Determine the distance ( mm ) moved by the piston. Solution : Known : piston = 3000 N, p=0.1Mpa (const), A = 05200 mm 2 , Paddle wheel work— 6800 n m Q=10 kJ Δ U=1 kJ . Find: Distance piston moves ( mm ) Sketch : Assumptions : Perfect gas, all work input to paddle goes into fluid; no change in pe or ke Analysis : Note : 1 N-m = 1 J P gas = 100,000 + 3000/5.2e-3 = 676,900 N/m 2 Energy equation Q – W = Δ U gas Q is removed—sign is negative: Q = -10,000 J Work done on system by paddle = 6800 N-m (= J ) Work done by piston against ambient pressure (force times distance) Note : Fluid inside piston pushes against both the piston weight and the ambient pressure, so the pressure acting is the pressure inside the cylinder. = p cyl A * d = N-m Energy equation: -10,000 + 6800 + 676,900*5.2e-3*d = -1000 J Solve for distance traveled by piston: = 0.625 m Piston Travel : 625 mm Problem 8-2 A well-insulated, 0.3028 m 3 (80-gal), electric hot-water heater initially contains water at 322 K (120 F). Hot water is withdrawn from the tank at 1.893e-4 m 3 /s (3 gal/min) while cold water at 283 K (50 F) enters to keep the tank full. The cold water mixes completely with the water in the tank at each instant. Because of a power outage,
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there is no energy input to heat the incoming cold water. Estimate the time required for
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HW_8_Soln - ME 309 Fall 2008 Section 2 (Merkle) Homework #...

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