An SI engine operates on a modified ideal gas standard Otto cycle in which the isentropic expansion process (process 3-4) is replaced with a polytropic process with n = 1.5 (i.e. pv^1.5 = constant) as shown in Fig 1. The cylinder pressure at state 1, pr = 1 bar, and the temperature, T = 300 K, and the compression ratio is 10. The amount of heat added during the constant volume process is 1800 kJ per kg of working fluid (i.e. q23 = 1800 kJ/kg). The specific heat ratio, y = cp/cv = 1.3, cp = 1.00 kJ/kgK, and pv^1.5 = constant. s = 0.
Figure 1: Modified Ideal Gas Standard Otto Cycle
Assuming the working fluid is an ideal gas and has constant specific heats, determine:
(a) Heat and work transfer per unit mass of working fluid for each process in the modified Otto cycle.
(b) Gross indicated thermal efficiency of the cycle.
Hint: Use specific quantities such as specific volume, specific work, etc. pv = RT, and pv^1.5 = constant.
