finalmidterms1 - 1 Michael G. Castro 02-38595 1) A well...

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1 Michael G. Castro 02-38595 1) A well insulated tank contains 1 lb m of steam at 20.4082 atm and 644.261 K. The tank is connected to a frictionless piston-cylinder device via well-insulated pipe with a valve. Initially the cylinder is empty. Then the valve is opened and some of the steam from the tank is allowed to flow into the cylinder until the condition of the tank is 5170.07 mmHg and 900°R. How much steam remains in the tank at this point? What is the final temperature of the steam in the cylinder if it assumes the final pressure within the tank? Schematic Diagram: Well insulated Tank valve valve Frictionless piston-cylinder Frictionless piston-cylinder System 1 System 2 Well insulated Tank 1 lb m of steam at 20.4082 atm 644.261 K. Mf=? 5170.06 mmHg 900 °R Tf=? 5170. 06 mmHg Solution: m out + mf = m 1 = 1 lb m System 1 20.4082atm = 300psia 644.261K=700°F System 2 5170.07 mmHg=100psia 900R=440°F v i =2.226 ft 3 / lb m v i =5.2 ft 3 / lb m Note: v i =2.226 ft 3 / lb m and v i =5.2 ft 3 / lb m were found on the steam tables. For the case of v i =5.2 ft 3 / lb m, iteration was performed. (440-420)/(450-440) = (x-5.068)/(5.266-x) 20(5.266-x) =10(x-5.068) 105.32-20x = 10x-50.68 156 = 30x x= 5.2 ft 3 / lb m Since the volume of the tank is constant it can be considered that: m i v i =m f v f m i = 1 lb m v i =2.226 ft 3 / lb m v i =5.2 ft 3 / lb m m f = m i v i /v f = (1 lb m )( 2.226 ft 3 / lb m )/( 5.2 ft 3 / lb m ) Michael G. Castro 02-38595 T V (°F) V V (ft 3 / lb m ) 420 5.068 440 x 450 5.226 m f =0.4280769 lb m
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1 m out = 1 - m f m out = 0.5719231 lb m Using the First Law: d(mU) I /(dt) + Δ[m(H + 1/2v 2 + zg)] fs = Q’ + Ws Assume: No change in elevation. No change in flow velocity. No shaft work. No heat loss. d(mU)pc/(dt) + Δm(H) = 0 m f U f - m i U i + m out H out – m in H in = 0 m f U f - m i U i + m out H out = 0 From the steam tables: U i = 1245.3 Btu/ lb m at 300psia and 700°F U f = 1152.23 Btu/ lb m at 100psia and 440°F Note: U f is obtained from iteration.
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finalmidterms1 - 1 Michael G. Castro 02-38595 1) A well...

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