Question

A piston-cylinder device initially contain 0.4 m3 of 1.8-kg saturated liquid water and steam mixture at 110 kPa. A electric heater in the device is turned on and passes a current of 1.7 A from a 120-V source. Only transfer of electrical work and boundary work exist. The piston initially rests on a set of stops, and a pressure of 200 kPa is required to move the piston. Afterwards the system continues to raise the piston and eventually reaches the temperature of 400 Celcius.

Find the initial quality of the system,initial internal energy (kj/kg), time it takes for the system to just move the piston (hours), final volume of system (m3), and total time it takes for the system to reach its final state (hours)

Answer 1

200 kPa V.0.4m² mas 1.8 kg 6 w = (1.7x120) = 204 walt initial Conditions: saturated liquid water & steam mixture. volume v=0.4m mal m = 1.8kg. and Pressu sure P= 110 kPa = 1. Ibar. specific volume 0.4 1.8 - 0.2224 at loi bar (saturated steam tables). m²/kg ut O.oulou6 m. 15492 m gola m2/kg. KJ/kg kJ/g. 428.8 hf hgfg - 2250.8

G initial quality of steam V (of + at 110 kPa. 0-2224 0.001046 + * [1.5492 -0.001046] x = 0.1428 2 initial internal Energy U = h. Po ha (x= 0.428) + CM21) = [ht + (x11 (160) @ 110kea h = 428.8 + (0.1428 x 2250.8) h = 750.6178 kJ/kg . initial internal Energy Y = hi - PV = 750.6178 - (110 x0.224) U, = 726.154 kJ/kg now, Pressure (200 kPad is required to just raise the Piston from stops. Same [ specific volume is no mars transfer. Since there is POCO x2

at 200 kpa, (2 bar) [from steam tables) VF 0.001061 m²/kg m/g va = 0.88540 ht 504.7 kJ /kg hfg 2201.6 kJ/kg (a + 22 Mfgo) e 200 kPa 20 19 2 0.2224 = 0.001061 + 2% (0.88gud - ooo 1061 1061) d2 0.2502 ho 22 [hf + a ghfg @ 200kpa. 504.7. + (0.2502 x 2201. 01.6) h₂= 1055.733 KJ/kg . Internal Evergy at stale - (P2.0) 1055733 (200 x 0.2224 KJ/kg. 10 11.253 N POCO X2

:heat required to just raise the Piston in (₂-0) 1.8 (10112 253 - 726.154) W = 513.178 KJE. Power given by electric heater 1.7 X 120 204 w. 513.178 = 204 kJ/s. 3 : time required to just raise the Piston 204 tz 2.52 seconds t,.2= 7X10-4 hrs. (400°C). (super heated - 200bos sleam) keal El. 2=0 no boot kpa V (m3/9) СО T ON POCO X2

after that, System Continues to raise the Piston and eventually reaches the temperature 400°c. 2-3 is Constant Pressure Process (200kpa). at final state ( 200kpa & 400°c). t saturation = 120.2°C. at 200 kpa, tsaturation since 400°C > it is super heated steam. tsat at 200 kpa & 400°c (from steam tables) VA 1.080 m3/kg h = 2870.5 kJ/kg u final volume of System: v=v V₂ = m. v 1.8 X 1.080 2 V3. 1.944 m ON POCO X2

6. Total time it takes for System to reach its final state T= time taken for 1-2 + time taken for 2-3 time taken for 2-3 Process total heat required from 2-3 (hz-ba) [..P=c) = 1.8 [2810.5 - 1055-733] m 3266.58 KJ time taken for 2-3 3266.58 204 t2-3 = 16.012 second total time =) T= tint toga 2-52 + 16.012 T 18. 532 secondy total time it takes for system to reach its final state 18.532 seconds 18-532 hrs 3600 T = 0.00514 hrs ON POCO X2
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