Question

7. The principal states in a cold air-standard Diesel cycle are given below. The mass of air is 1 kg. The Cv of air is 0.7 kJ/kg.K and k = 1.4. Determine: (a) the heat addition and work done in each process, in kJ. (b) the net work output, in kJ. (c) the thermal efficiency. State 1: p= 100 kPa; T = 300 K State 2: p = 2000 kPa State 3: T= 1100 K

Answer 1

Diesel cycle : process 1-2 ; Adiabatic compression 2-3; const pressure heat addition " 3-4 Adiabatic expansion constant Volume Heat Rejection I-s Diagram P-N Diagram T P a supplied P= constant → WE 2 3 소 para const Veconst & Rejected es Ikg T = 300k Given At 1 p=100 kpa > 0.7 kJ/kgk 2!- k= 1.4 p= 2000 kpa 1100 kpa T- 3 - Y =) P vir = P₂ V process pur= constant 12 1.4 2000 P. 100 pi - 8.497 CS Scanned with CamScanner

K- 6) ( 8.497) 1.4-1 Tz 300 TL=706.06 k a As is know that process Adiabatic compression (Heat supplied (da) = 0 dQ= dut dew (1st law of thermodynamics) mcv (T₂ -T.) + dw -mar(T₂ -T.) -IX 0.7 * ( 706,06-300) dw = -284.24 KJ Heat supplied dw in OKJ 1-2 work done - process 2-3 dQ= mcp (T3-T2) 1-4X0.7 -0.98 cp к (p = kx(y = v do 3 1x 0.98 ( 1100- 706.06) In 2-3 process Heat Addition da = 386.06 kJ du= marc T3-72) 0.7 ( 1100-706.06) IX du = 275.758 kJ (1st law) da = dut de 386.06 2.75.758 + dw 2-3 process in work done dwa 110.302 kJ 2-3 3-4 In process ; we know that T P2 P3 V3 sv 15 (or) 706.06 کم [ کا 1100 She lot vyu) and 8.497 x 706.06 Too ICS Scanned with CamSanner

= 5.4532 į alls 51 sm K-1 3-4 process; (5:45) Vy Ty 1.4-1 1100 |тч 558.09 K dq=ol Adiabatic process da = dut dw dw= du E-mxcv( Ty-T3) -1X0.7 (558.09-1100) dw 2 379.33 kJ - In 3-4 I work done = 379.33 kJ process =OKJ Heat addition dwzo 4-1 Const volume process : dQ - mx y *(-) " X 0.7* ( 300-558.09) dQ2 180.66 kJ I work done = ok] In 4-1 process 180.66 kJ Heat Released - + Wyrl output Net work out H1-2+ H2-3 +43-4 - 284.24 + 110.302 + 379-33 to 205.392 kJ Net Work Net work Net work Thermal Efficiency Heat supplied Q2-3 205-392 2 = 0.53 (XY)2 = 53 %. 386.06 cs Scanned with CamScanner