Question

PROBLEM-4 (50%) One kg of air is in a piston-cylinder assembly. Air is modeled as an ideal gas with a constant specific heat ratio, k = 1.4. The air undergoes a power cycle consisting of four processes in series: Process 1-2: Constant-temperature expansion at 600 K from P1 = 0.5 MPa to P2 = 0.4 MPa Process 2–3: Polytropic expansion with n=k to P3 = 0.3 MPa Process 3–4: Constant-pressure compression to V4 = V1 Process 4–1: Constant-volume heating. (a) Sketch the cycle on P-v and T-v diagrams. (10 points) (b) Determine the work and heat transfer for each process, in kJ. (30 points) (c) Show that Wcycle Qcycle by calculations. (10 points)

Answer 1

essembly with constant Problem-4 mo Givens mans of air malkg piston lincher casse cylinder specific Heats 2) Processes 1-23) 77600k const expansion P1 =O 5mparto P2=o.umpa Process polyfropic processes n=kzty to P3= 0-3 Process 3-4 = constant pressure compression Vuori Process-u-las a) p-x diagram tudiagram I coreempa 2-3 =) v=Ć Heating T P 2 q 2 u 3 3 Yusri 2) volume via mirti 1x0.2878403x600 Pi Oi5xcob => V= o.sunum² = vu Tizbook, Pizogmpa P. = PzUz formace छ 0.5 x 0.3uut va a) Vză 0.4305m3 LookT Ou 23 for 2-3 2.lt 1.4 boy xo.u305 - PLX P3 Vyk :) lich .

Die LE2 i T3 x 600 T2 E2 3-4. 0.5287 Vu SIF R Oozunu TH T Tч 552-655 Q2 V₂ 2) 0.4305 o. Burn 22 271 Wzu -55° 29 kJ 27 V 0.528773 P3 Tzz P2 T3-552.6556 a) for ?? Tu= 360k b) for processe 1-2 T2 >> to za Work wo, z = Qiz = Per in 2 Mzz Qiz: 0.5x16x0.3444 in in W 2²Q 2 = 38.425kJ =) Work & seal bology system Heat gained transfer in 1-2 for process 2-3 it is adiabatic proces 27 Q2-3²0 -z- I co z = CBCT E-T₂) = 1005 ( 600-5520655 2.2.-3= 158 kJ 33.99 for process 34 Pec 2). Work clone Wzu = par 20.3810 (Vu-V3) 20.3x10° (0.3uclu - 0.5287) 2) Louk done on system. Woo - 0.718 2) W₂-3 C fo 2) Wzu the

2) Qsu CECTET3) & W34 2) Qzu= 0.7180 360 -552-655) = 55.29 ₂2 Qout -193161629KT for processes til jac work done wellso due to w=cas dr=o 2) Heat transfer Q2. C CT, -Tu) 721 Q2 172032465 =) Heat L 22 Q: 0.718C600-360) gained c) 2 total sum of woo ookldone for cycle is Waycle wirt Wezt us but win 33.99 5•2 bcycle & post (Wayete 2 17.12871 KS totait sum of Heat transfer for cojeleis Qcycle = QiztQzz tabut Que 38.425+ 358 -55• 29 to 22 3001t5T - z 38-425+ 0 p - 193.61629 + 172.32 Qcycle = 17.128 71 kJ 2) Quijele Wcycle z proved