Question

1. One kilogram of water at 300°C expands against a piston in a cylinder until it reaches ambient pressure, 100 kPa, at which point the water has a quality of 90%. Assume the expansion is reversible and adiabatic. a) What was the initial pressure in the cylinder? b) How much work was done by the water (in kJ)?

Please answer both parts of the question

Answer 1

solution Given mass of water m. lkg Initial temperature TF 300°C final Pressure P2 = 100 kPa - quality a=0.go en expansin is reversible and adiabatic. → Reversible - adiabatic process is I sentropic process (8o Entropy remains constant) from saturated steam table at 100 kPa y specific entropy of saturated liquid (stad and saturated vaper (Sg2) Sf2 = 1:3028 kJ/kgik Sg2 = 73589 kolega y specific ) enthalpy a saturated vapar and Saturated Liquid Chez hfz = 417.51 kilkg ng2 = 2675 kilig Therefore specific entropy of find mixture S2 = Sft X₂ (Sg 2 - Sk) → Sz = 1.3028 +0.9 67.3589-1-3028) kJ » Sa = 6-75325) Tehoten

L since process is Isentropic 8. S, - S2 Si= 6.75325 KI from saturated steam table at 300°C, specific entropy of saturated vaper = 5.7059 kg But our entropy is 675329 KI Our 0 į Now od Initial steam is supenheated steam 300 C from superheated steam table we can find temperche Pressure at which entropy is 6.75329 at 300€ so After sebelo several trials we find Pressure PSSV - 2061-67 & Also Specific enthalpy at - [P, = 2066 167 kPa - 6 Answes o Initical pressure I specific enthalpy at P = 206 167 kPa The = 3022.399 | KI Specific enthalpy of final mixture h = hfz + x₂ (nga-ha) h = 417.51 +0.9 (2675-47.51) Kolke => [h2 = 2449.251 kilks 8 Work done by the water Answer & W = 573.148 k3 Wam Chichz) = (3022-399 - 2449.291)