9-46 An air-standard Diesel eycle has a compression ratio of 16 and a cutoff ratio of 2 At the beginning of the e pression process, air is at 95 KPa and 27°C. Accounting for the variation of specific heats with temperature, determine (a) the temperature after the heat-addition process, (b) the thermal efficiency, and (c) the mean effective pressure. ‘Ansners: (a) 1725 K, (b} 56.3 percent, (c) 675.9 kPa 9-46. An sirstandard Diesel eycle with a compression ratio of 16 and a cuof ratio of 2 is considered. The temperature afer the heat addition process, the thermal efficiency, and the mean effective pressure ae to be determined. Assumptions 1 The airstandard assumptions are applicable. 2 Kinetic and potential enerzy changes are negligible. 3 Airis An ideal yas with variable specific heats Properties The yas constant of ait is R = 0.287 KI/kg.K. The properties of air are given in Table A-I7, Analysis (a) Process 1-2: isentropic compression. hy, =214.07KIkg, ¥, =6212, 1, =300K —> 624K 890.9 Kk, L th 7g O21 2)=38.825 — sonstant heat addition, Pos b —r Cir, =a, =(24860.4K): m4.8K — ~ hh, =1910,6-8909 = 1019. 7k, Process 3-4: isentropic expansion, 2,2 us 546) =36.37 —> u, =659.7kkg Process 4-1: v~ constant heat rejection ny ty =659.7 21407 445.63 Kika TO19.7KIKE i ~ fos = 1019.7 445.63 = 574.07 Kk (RI; _ (0.287kPa-m’/ky-K300 K) Ro OSKP 145.63 kike 56.3% 0,906 my aan STAOTIIG (kPa 2a)” oom" gh)9-48 An ideal Diesel cycle has a compression ratio of 17 and a cutoff ratio of 1.3. Determine the maximum tempera- ture of the air and the rate of heat addition to this eycle when it produces 140 KW of power and the state of the air at the beginning of the compression is 90 kPa and 57°C. Use con- tant specific heats at room temperature. 9-48 An ideal diesel eyele has a compression rato of 17 and a cutoff ratio of 1.3. The maximum temperature ofthe air and the rate of heat addition are to be determined. Assumptions 1 The ai-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Ai is ‘an ideal gas with constant specific heats. Properties The properties of ai at room temperature are ¢, 005 KIKwK, cy = 0.718 bike K, R A= 14 (Table A-2a), 287 kMawK, and, Analysis We begin by using the process types to fx the emperatures of the states, fs rhea y nf) ype he 4%, (2) =r? =G30Ky(17)*! =1025K a” 7 Ym, & ny > tow nip |-toe =aenskut) -1992K ‘Combining the first law as applied tothe various processes with the process equations gives 113 =! _o6s97 Wt Taq3—1) According o the definition ofthe thermal efficieney, 0, ~ tt. MOK og ok To 0.6597 9-49E An ideal Diesel cycle has a maximum cycle tem: perature of 2300°F and a cutoff ratio of 1.4. The state of the air at the beginning of the compression is P) = 14.4 psia and T, = 50°F. This cycle is executed in a four-stroke, eight- cylinder engine with a cylinder bore of 4 in and a piston stroke of 4 in, The minimum volume enclosed in the cylinder is 45 percent of the maximum cylinder volume, Determine the power produced by this engine when it is operated at 1800 rpm. Use constant specific heats at room temperature.{9-498 An ideal diesel eycle has a a cutot ratio of 1.4. The power produced is to be determined, Assumptions 1 The air-standard assurnptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Airis ‘an ideal gas with constant specific heats 3704 psia-t'lbm.R (Table A-1E), ¢, = 0.240 Btwlbm-R, Properties The properties of air at room temperature are ey =0.171 Biwlbm'R, and k= 1.4 (Table A-2Ea) Analysis The specific volume of the ar at the stat of the compression is Rh 4 /lom-RXSIOR) x 14.4 psia =13.128 bm ‘The total air mass taken by all 8 cylinders when they are charged is ma/2 24/1244 13.128 bm (8) =0.01774 Ibm ‘The rate at which air is processed by the engine is determined from (0.01774 Ibm cycle 1800/60 rev's) Drevieycle = 0.2661 Ibm’s=958,0 lbnvh since there are two revolutions per eyele ina four-stroke engine. The compression ratio is, ao 08s tthe end ofthe compression, the air temperature is jt = (510 Rx22.22)"" Applicaton of the frst law and work integral tothe constant pressure heat addition gives 4 =p (Ts ~Ty) = (0.240 Bulb R)(2760~1763)R =239,3Btulbm while the thermal effcieny is 1 fat aegis PT aT aay The power produced by this engine is then Wye. = 1350 =HM din 058 o1bmy0.6021239. Bao =62.1hp 9-30 An air-standard dual cycle has a compression ratio of, 14 and a cutoff ratio of 1.2. The pressure ratio during the constant-volume heat addition process is 1.5, Determine the thermal efficiency, amount of heat added, the maximum gas pressure and temperature when this cycle is operated at 80 KPa and 20°C at the beginning of the compression. Use constant specific heats at room temperature.{9-80 An ideal dual eycle has a compression ratio of 14 and cutoff ratio of 1.2. The thermal efficiency, amount of heat added, ‘and the maximum gas pressure and temperature are to be determined. Assumptions 1 The air-standard assumptions are applicable, 2 Kinetic and potential ene ‘an ideal gas with constant specific heats, Properties Tbe properties of air at room temperature are ¢y = 1.005 kkk, cy = 0.718 kitke-K, R= 0.287 kitke-K, and A= 14 (Table A-20), Analysis The spevtic volume ofthe air atthe start oF the compression is changes are neyligible, 3 Airis 7 3 RT, _ (0.287 kPa-m*/kg-K\293 K) 5 % Bf, (0287 KPa F293 951 ag 4 Ti s0kPa ie ie Cans and the specific volume atthe end of the compression is a a : roby LOSI AE yo7s08 "ag “ ° The pressure atthe end of the compression is P, =“(2] = Art = s0KPaytay =3219kPa and the maximum pressure is P= Py = ry Py = (1 SXS219KPa) = 4829KPa “The temperature atthe end of the compression is rt (203 ey(ta} 82.0K ss09KPa w= 20 7 non Sig) 120 From the definition of cutoftr 4 (1.2X(0.07508 m/kg) = 0.09010 ke “The remaining state temper 1=7,{ 2] =a20{ 202) -a516« 7 2.07508) 1-12) =ustox/ ore) =S075K 7 1051 Applying the fist law and work expression to the heat addition processes gives, in Cyl Ta) Hep (Ts ~Ty) (0.718 ky-KY1263-842.0)K +(1.005 kiiky-KX1516— = 556.5kJikg 3K ‘The heat rejected is (Ty -T) =(O.718kdikg- KXS67.5—293)K =197.LkIkg. 197.1 Kke din 5S6.5KIIKE 6469-52E._ An air-standard Diesel cycle has a compression ratio of 18.2. Air is at 120°F and 14.7 psia at the beginning of the compression process and at 3200 R at the end of the heat- addition process. Accounting for the variation of specific heats with temperature, determine (a) the cutoff ratio, (b) the heat rejection per unit mass, and (c) the thermal efficiency. 9-52E An air-standard Diesel cycle with a compression ratio of 18.2 is considered, The eutof ratio, the heat rejection per unit mass, and the thermal efficiency are to be determined. Assumptions 1 The ar-standard assumptions are applicable. 2 Kinetic and potential energy changes are ne an ideal gas with variable specific heats Properties The properties of air are given in Table A-I7E, Analysis (a) Process 1-2: isentropic compression 14, =98.90 Biullbm T= S80R aay 1, =17258R 429,56 Btwlbm 632 —> Us T_ 3200R fp TS8R =1.854 49.48 Bru/lbm o) Process 3-4: isentropic expansion. “ 1) 182 eae haw, = #82 (0958)<9,315 —9 n= 272.58 Blom rei 1.854% ass : Process 41 1= constant heat rejection doy "tty 272.58 -98.90= 173.7 Bralbom 6 ng wt fost = 1B 9 556 58.60% din 419.9 Beullbm 9-54 An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is 95 kPa and 20°C. If the maximum temperature in the cycle is not to exceed 2200 K, determine (a) the thermal efficiency and (b) the mean effec- tive pressure, Assume constant specific heats for air at room temperature. Answers: (2) 63.5 percent, (b) 933 kPa9-84 An ideal diesel engine with ar as the working fluid has a compression ratio of 20. The thermal efficiency and the mean effective pressure are to be determined, Asswmprions 1 The air-standatd assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Airis Aan ideal gas with constant specific heats Properties ‘The properties of ar at room temperature are cy = 1,005 kilky-K, ey = 0.718 kiMkg-K, R = 0.287 Kl/kg'K, and ke 14 (Table A), Analysis (a) Process 2: isentropic compression. LAK ‘ y * -(293 20/4 = Process 2:3: P= constant heat adltion, ry Tt (7) Gin = hy —hy = € (Ty ~T; )= (1.005 kivkg - KX2200-971. 1K = 1235 ki/kg. hous 4 —, Se, [Ty ~T,) = (0.718 Kilkg-K Y920.6~293)K = 450.6 KI/kg * (22687 2.265)" =n{) = (200K 22°) =920.6 (228) = er00 (228) -s206x Waaion = Fin ~4 784.4 kike 13S Kk eB, 0287KPA- Mg Kp sesmntag ers, 7 ‘OS KPa 63.5% scout 784.4 kike (a w=) o.sssmghi-120)( Ww 9-57 A four-cylinder two-stroke 24-L diesel engine that operates on an ideal Diesel cycle has a compression ratio of 22 and a cutoff ratio of 1.8. Air is at 70°C and 97 kPa at the beginning of the compression process. Using the cold-air- standard assumptions, determine how much power the engine will deliver at 3500 rpm. =v9-87 A four-eylinder ideal diesel engine with ar as the working Muid has a compression ratio of 22 and a cutoff ratio of 1.8 Te power the engine will deliver at 2300 rpm is to be determined. Assumplions 1 The cold air-standard assumptions are applicable. Kinetic and potential energy changes are negligible. 3 ‘Airis an ideal gas with constant specific heats Properties The properties of air at room temperature are cy A= 14 (Table A-2), Analysis Process 1-2: isentropic compression. 00S Kiike-K, cy =0.718 Kitky-K, R= 0.287 kikg'K, and Forthe cycle: BY, ___(97 kPay0.0024 m?) ona36ste ‘RT, (0.287 kPa-m'/kg-K)343K) H Oy = mls ~ hy = me p(T ~Tr) 0.002365 ky) 1-005 kirky K\(2216~ 118K 2.2464) Qouy = mtg — 14 )=mey (Fy —F,) (0.002365 ky 0.718 ki/ky -K(T81~ 343) O.7438KI Wyaout = Oy ~ Qouy =2-240~0.7438= 1.502 klitev Wr, (3500/60 vis) 502 KN tev) =87.6 KW Diseussion Note that for 2-stroke engines, | thermodynamic eyele is equivalent to 1 mechanical eyele (and thus revolutions), 9-59E An ideal dual cycle has a compression ratio of 15 and a cutoff ratio of 1.4. The pressure ratio during constant- volume heat addition process is 1.1. The state of the air at the beginning of the compression is P, =14.2 psia and T, = 75°F. Calculate the cycle’s net specific work, specific heat addition, and thermal efficiency. Use constant specific heats at room temperature.9-S9E. An ideal dual cycle has a compression ratio of 15 and cutoff rato of 1.4, The net work, heat addition, and the thermal elliciency are to be determined, Assumptions \ The air standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Airis ‘an ideal gas with constant specific heats. Properties The properties of ar at room temperature ate = 0.3704 psia t'bm.R (Table A-IE), ¢, = 0.240 BuullbmR, 6 =0.171 BuullbmR, and k= 1.4 (Table A-2Ea), Analysis Working around the cycle, the germane properties atthe various states are S35 RMIS) 47 580 R 14.2 psiay(15)'* = 629.2 psia 1.16292 psa) 692.1 psia 692.Lpsia (629.2psia ison 738K Applying the first law to each ofthe processes gives wy-2 =6.(7y 7) = 0.171 Balbo RY 1580~S35)R = 178.7 Biw/lbm 27.02 Bru/lbm a = 6AT, Ty) = (0.171 Bull RY(I738 1580) 4-4 =¢ (Ts —T,) =(0.240 Bullom-RX2433—1738)R = 166.8 BtwiTbm 166 8 Btullbm—(0.171 Bulb RX2433—1738)R = 47.96 Bulb, pes -6Ts-Ty 5-4 =64(T) Ty) = (0.171 Buullom RX 2433 -942.2)R = 2549 Buwllbm. The net work of the eyele is fas = Wag tog “Whoa =254.94-47.96-178.7 = 124.2Btullbm and the net heat addition is Gin = 42-4 + 9o-5 = 27.024 1668 =193.8Btu/lbm Hence, the thermal efficiene 24.2.Btu/lbm Gy 193. 8Btullbm 0.641