9.22. Consider a cold air-standard Diesel cycle. At the beginning of compression, p = 14.0 Ibffin. and 7; = 520°R. ‘The mass of air is 0.145 Ib and the compression ratio is 17. The ‘maximum temperature in the cycle is 4000°R. Determine (a) the heat addition, in Bru. (b) the thermal efficiency, (c) the cutoff ratio, KNOWN: An air-standard Diesel cycle has a known compression ratio and a specified state at the beginning of compression. The mass and the maximum cycle temperature are given. FIND: Determine (a) the heat addition, (b) the thermal efficiency, and (c) the cutoff ratio. SCHEMATIC AND GIVEN DATA: m=0.145 Ib eee = 140 Ibffin? 7, = 520°R r=VlVa=17 ENGINEERING MODEL: See Example 9.2. ANALYSIS: Begin by fixing each principal state of the cycle (Table A-22E), State 1: 7) = 520°R + m = 88.62 Btullb, va = 158.58 State 2: For the isentropic compression va = (Val i)-va = (1/17)(158.58) = 9.3282 Thus, interpolating in the table: 72 = 1534.5°R, fy = 378,32 Buullb State 3: 7 = 4000°R — hy = 1088.3 Btu/lb, v3 = 0.4518 State 4: For the isentropic expansionProblem 9.22 (Continued) ~ Page 2 (Vdb¥V3) = (Vila) (Vals) = Wl Vay T/T) * (17-(1534.5/4000) = 6.522 and va = (ViVi = 2.9466 Thus, interpolating in the table: 7, = 2253.7°R, 14 = 421.25 Btw/lb (a) ‘The heat addition is determined from an energy balance on Process 2-3, as follows. Q2s = (us — ua) + Way = mus — un) + mpa(vy ~ v2) = mths ~ hn) Inserting values Qa = (0.145 1b)(1088.3 ~ 378,32) Bru/lb = 102.9 Btu (b) To determine the thermal efficiency, first evaluate the net work of the cycle. Weyce = Qeyste = Ors ~ Our = Qas ~ (us — m1) = 102.9 — (0.145)(421.25 — 88.62) = 54.67 Btu Thus, the thermal efficiency is 1 = WeyalQas = 54,67/102.9 = 0.531 (53.1%) (c) Since p:= ps, the cutoff ratio is re= ValVy = 5/7, = 4000/1534.5 = 2.619.26 Consider an air-standard Diesel cycle. Operating data at principal states in the cycle are given in the table below. ‘The states are numbered as in Fig. 9.5. Determine (a) the cut-off ratio. (b) the heat addition per unit mass, in Btu/Ib. (c) the net work per unit mass, in Buw/lb. (d) the thermal efficiency. State TCR) p(ibiin.”) wu (Bulb) fh (Btu/lby 1 320 142 88.62_ 124.27 2 1502.5 657.8 266.84 369.84 3 3000 657.8 585.04 790.68 4 1527.1 418 271.66 376.36 29.26 KNOWN: An air-standard Diesel cycle operates with property data given at principal states. FIND: Determine (a) the cut-off ratio, (b) the heat addition per unit mass, (c) the net work per unit mass, and (d) the thermal efficiency. SCHEMATIC AND GIVEN DATA: ENGINEERING MODEL: 1. Air, modeled as an ideal gas, is the system. 2. The compression and expansion processes are adiabatic, 3. Kinetic and potential energy effects are negligible. ANALYSIS: (a) The cut-off ratio can be determined as follows. For the constant pressure process, p2 = ps. Noting that for an ideal gas, p = RTIvProblem 9.26 (Continued) ~ Page 2 Since r. = vy/vy 3000°R__ 9 49 a | hase = (b) The heat addition occurs during process 2-3. Thus, noting that I= mp(vs— v2) mus — ta) = Ors — Was = Qos — mp v3 ~ v2) Thus Qasim = (us ~ Ua) + ps ~ V2) = ha In Inserting values Ge 5, -h, = 750.68 369. sabe 420.84 Btu/tb, (©) The net work per unit mass can be determined from the net heat transfer per unit mass Weyce Oz On Applying the closed system energy balance to process 4-1 tg, = 271 oR 98 ot 183.04 Btuilb Solving for net work per unit mass gives #208451 s018 237.80 Bru/lb (d) Thermal efficiency is W. Qr5 1m tm