Question

The ideal Otto cycle, shown in the figure above, is the cycle used by gasoline engines to generate useful work. It consists of an adiabatic compression from step 1 to 2, followed by an isochoric increase in pressure from step 2 to 3, followed by an adiabatic expansion from 3 to 4, and finally an isochoric decrease in pressure from step 4 to 1.Consider an Otto cycle that works on a monoatomic ideal gas (γ= 5/3,cV= 3R/2), initially at a volume V1 and temperature T1= 298 K, by increasing its pressure from P1= 101.3 kPa to P2= 500 kPa. From step 2 to 3, the pressure increases from P2= 500 kPa to P3= 1500 kPa. From step 3 to 4, the pressure decreases from P3= 1500 kPa toP4= 600 kPa and T4= 550 K. What is the total amount of work w done by the cycle?

Answer 1

Given, Oto cycle o 1-2 2-3 3-4 4- Adliabac compression tsochox'c beat addition adiabatic expansion isochoric heat reg 130 Given 7:573 cv. 3R/2 V s initial volume Ti>293k 1013 kPa P2500kPa PA GOO IP2 14:550k Pa 21500 kPa P (1-2) 2-3) vi constant PVP pat Pula Pave? Po o Vicomprevion ato zy Tz a 1692.965 Fri 2:606 ] and 7-1 -1 TV5_ 9- 1 CS Scalined NV: TzV2 27 5/3-1 - 12, V TE: 298x(2606) II a 564.32KL

Heat supplied . ev CT3 - T2) :c9a) -3R/ C 1692.96 - 584.32) 125 rue 2 125 (1692.96-564.325 - 14108 kJ/kg : Otto cycle efficiency of ..Mittal - 51 (2.606) 0°4719 > 47.1901 a WBT Efficiency work done Heat supplied wonadone. nxqa 0.4719x 14108 665.8:12 KJ /kg