Homework No 3 soln eml 3100 2010

Homework No 3 soln eml 3100 2010 - Homework No 3 Assuming...

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Homework No. 3 Assuming cold air standard assumptions 1.The compression ratio for an Otto Cycle is 9.2. At the beginning of the compression stroke the pressure is 100kPa and the temperature is 22 deg C. The heat transfer to the cycle is 2100 kJ/kg a. determine the temperature and pressure at the end of each process in the cycle b. determine the thermal efficiency a. P1 = 100 kPa T1 = 22 deg C = 295K T2 = T1 *(V1/V2)^(k-1) = 295*(9.2)^.4=716.7 K P2 = P1*(V1/V2)^k = 100*(9.2)^1.4= 2235 kPa Qin = Cv (T3-T2) therefore T3 = Qin/Cv + T2 = 2100/.717 + 716.7 = 3645 K T3/T2 = P3/P2 or P3 = (T3/T2)*P2 = (3645/716.7)*2235= 11367 kPa T3/T4 = (V4/V3)^(k-1) therefore T4 = 3645/(9.2^0.4)= 1500K P3/P4 = (V4/V3)^k = 9.2^1.4=22.351 therefore P4 = 11367/22.351= 509 kPa b. thermal effic = 1 – 1/(r k-1 )= 1 – (1/9.2^0.4) = 0.59 or 59% 2. For the cycle above, assume that the engine consumes 3.75 gallons of gasoline per hour and that the heating value of the gasoline is 125,000 btu/ gallon. What is the theoretical power output of this cycle in Hp? Hint: you already calculated an efficiency…review the lecture on efficiencies. Q in = 3.75 gal/h * 125,000 btu/gal = 468750 btu/h Wnet = Qin * effic = 468750*.588=275625btuh or 108 Hp
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