## ME 300 Summer 2015 â Homework 5

## ME 300 Summer 2015 â Homework 5

ME 300 Summer 2015 â Homework 51. A piston-cylinder device contains 0.8 kg of steam at 320Â°C and 1 MPa. Steam is cooled at constantpressure until half of the mass condenses.ABCShow the process on a T-v diagramFind the final temperatureDetermine the final volume change2. The gage pressure of an automobile tire is measured to be 210 kPa before a trip and 220 kPa afterthe trip at a location where the atmospheric pressure is 92 kPa. Assuming the volume of the tireremains constant at 0.035 m3, determine the percent increase in the absolute temperature of the airin the tire.3. A mass of 5 kg of saturated water vapor at 310 kPa is heated at constant pressure until thetemperature reaches 240Â°C.ABCCalculate the work done by the steam during this process.Sketch the process on a well labeled T-v diagramCalculate the total heat transferred to the steam.4. A piston-cylinder device contains 0.2 m3 of air at 400 kPa and 60Â°C. Heat is transferred to the air inthe amount of 40 kJ as the air expands isothermally. Determine the amount of boundary work doneby the air in this process.5. An unknown mass of iron at 90Â°C is dropped in an insulated tank that contains 80 L of water at 20Â°C.At the same time, a paddle wheel driven by a 200 W motor is activated to stir the water. Thermalequilibrium is established after 25 min with a final temperature of 27Â°C. Determine the mass ofiron. Neglect energy stored in the paddle wheel, and assume water density to be 1000 kg/m3.6. A piston-cylinder device initially contains steam at 220 kPa, 240Â°C and 0.5 m3. At this state, a linearspring (F = k Â· dx) is touching the piston in static equilibrium (i.e. no force is exerted). Heat is thenslowly transferred to the system, causing the pressure and the volume to rise to 260 kPa and 0.7 m3,respectively.AShow the process on a P-v diagram with respect to thesaturation linesBDetermine the final temperatureCDetermine the work done by the systemDDetermine the total heat transferred7. An ideal gas undergoes two processes in a piston-cylinder device as follows:Process 1-2 is polytropic compression from T1 and P1 with a polytropic exponent n, and compressionratio of r = V1 / V2.Process 2-3 is constant pressure expansion at P3 = P2 until V3 = V1.ASketch the process on a single P-v diagram.BObtain an expression in variable form for the ratio of compression-to-expansion work asa function of n and r.CFind the value of this ratio for n = 1.4 and r = 5.

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