Consider the Otto cycle described in Problem 4.51. The initial state (state 1) temperature, pressure, and volume are 90 F, 14.7 psia, and 40 in³, respectively. The compression ratio, V_max/ V_min, is 8.5. The maximum temperature is 4500 F (state 3). Assume the specific heat ratio is constant with a value of 1.4. Determine the work transfer associated with each process and the net work for the cycle.

Problem 4.51

An air-standard Otto cycle is often used as a very simplified model of a spark ignition engine. The following sequence of processes applied to a fixed mass of air in a piston–cylinder assembly constitutes the Otto cycle:

Process 1–2: Isentropic compression from the maximum volume V_max to the minimum volume Vmin. Note: This process can be described as PV^γ = constant, where γ is the specific-heat ratio.

Process 2–3: Constant-volume heat addition to a peak cycle temperature T₃.

Process 3–4: Isentropic expansion from V_min to V_max. See the note for process 1–2.

Process 4–1: Constant-volume heat rejection to return to the initial state.

A. Sketch this cycle in P–V coordinates and label each state point (1, 2, 3, and 4).

B. The following properties are associated with a particular execution of the Otto cycle. The initial state (state 1) temperature, pressure, and volume are 320 K, 120 kPa, and 0.001 m³, respectively. The compression ratio, V_max/ V_min, is 9.0. The maximum temperature is 3000 K (state 3). Assume the specific heats can be treated as constants with the following values: c_p = 1.008 kJ/kgK, and c_v = 0.721 kJ/kg K. Determine the work transfer associated with each process and the net work for the cycle.