Calculate pressure and temperature at remaining three states

Question

An engine operates on an ideal, cold air-standard Otto cycle with a compression ratio of 8 (r = v₁/v₂). Heat transfer to the engine is from a high-temperature reservoir at 1273 K, and heat transfer from the engine is to the surroundings at 293 K. At the beginning of the isentropic-compression process, the pressure and the temperature of the working fluid are P₁ = 110 kPa and T₁ = 323 K. At the end of the combustion process the temperature is T₃ = 1173  K.

Use: k_air = 1.4, c_v,air = 0.717 J/g.K, c_p,air =1.004 J/g.K, M_air = 28.97 g/mol,

(a) Calculate the pressure and temperature at the remaining three states of the Otto cycle: P₂, T₂, P₃, T₃, P₄, T₄.

(b) Calculate the thermal efficiency of the cycle.

(c) Calculate the thermal efficiency of a Carnot cycle operating between the same high- and low-temperature reservoirs. Explain why it is different from (b).