Question

Problem # 2 135 Points Polytropic Processes A piston-cylinder undergoes a constant pressure expansion process followed by an adiabatic compression. The adiabatic compression can be modeled as a polytropic process PVn constant with a volume exponent n 1.4. At state 1 the pressure of the system is P1 60 psi, the volume is Vi 8.868 ft3 and the internal energy U 1630.6 BTU. The work output during the constant pressure process is W2-75.2 BTU and the heat transfer input for this process is 1Q2- 687.4 BTU. The final system pressure is P3 100 psi. Neglecting kinetic and potential energy effects sketch the processes on a P-y diagram and determine final system volume V3 in ft3 and the final internal energy U3 in BTU = Find: 12 Points Given: [3 Points] System Energy Diagram 12: 14 Points Assume = Pdv wP-Pvil-n w Pvi In vvil AU Q-W-m-(q - w) 1 Btu 778 ft-lb 1 ft144 in w System Energy Diagram 2 3: 14 Points] Process Diagram: 14 Points]

Answer 1

Ansas Given tat polytoopic poocess pv^: constant Volume ex porent System P 60 psi Volume V 8 868 43 Totesnal eresqy U,- 1630 6 BTU の。:73-2BTU 68. BTU ca syptem pessuze P 1o0 psi The Prsocess-1 > Isbarsic cxpansien pxocess 2-1 (n4) paocess 2-» adiabatic Compeession P2 o0 isobosic ex pansion' PP60 Psi PCAV)

N2 P() 5.2 60 (8.868) 8.868 G168 - V - 8-863 (-u,) G8.4 3. +(U2- l630.6) 2242 8 BTU U adiabatic compression' 1-Y Compoession adiabatic 60x 15.636 81-86 = \o 8S wo - usk done in Compseasion proceas 100 X1O. 85 - 60 x15:636 : 368.55

ニ 368.85x5.4 - 68.25 BTU 2 U-U2 +W,- 3 Q330adiobatic ( 8-8)68-2s) Paocess wz-Ve becaux Ug = 2311 05 BTU iis input toyste= Find Syotem volume Va : Totesnal enesqy Ua = 231| . 0S BTU