Otto Cycle

The Otto cycle is the idealized thermodynamic cycle for spark-ignition (SI) internal-combustion engines. In the air-standard Otto cycle the working fluid is modelled as air (ideal gas) undergoing four internally reversible processes: 1-2 isentropic (adiabatic, reversible) compression, 2-3 constant-volume heat addition (combustion), 3-4 isentropic expansion (power stroke), and 4-1 constant-volume heat rejection. Key assumptions: ideal gas with constant specific heats, no friction or pumping losses, and heat transfer only during constant-volume processes. Important performance characteristics include thermal efficiency (depends only on compression ratio and specific-heat ratio), specific work per cycle, and mean effective pressure.

Governing FormulaCommon relations for the ideal Otto cycle (air-standard, constant specific heats): - Compression ratio r = V1 / V2. - Isentropic temperature relations: T2 = T1 * r^{(γ-1)}, T4 = T3 / r^{(γ-1)} (γ = c_p/c_v). - Heat added: Q_in = m c_v (T3 - T2). - Heat rejected: Q_out = m c_v (T4 - T1). - Net work: W_net = Q_in - Q_out = m c_v [(T3 - T2) - (T4 - T1)]. - Thermal efficiency (ideal Otto): η = 1 - 1 / r^{(γ-1)} (independent of heat addition amount). - Mean effective pressure (m.e.p.): p_me = W_net / (v1 - v2) where v1 and v2 are specific volumes at states 1 and 2 (per unit mass).

Knowledge Check

10 Questions

1.Which ordered sequence of processes correctly describes the ideal Otto cycle?

2.What is the ideal Otto-cycle thermal efficiency for an engine with compression ratio r and specific-heat ratio γ?

3.Calculate the thermal efficiency of an ideal Otto cycle with compression ratio r = 8.0 and γ = 1.4 (assume constant specific heats).

4.Air at state 1 is at T1 = 300 K. For an ideal Otto cycle with r = 10 and γ = 1.4 (constant specific heats), what is the temperature after isentropic compression (T2)?

5.For an ideal Otto cycle with γ = 1.4, compression ratio r = 9 and peak temperature after heat addition T3 = 2200 K, what is T4 after isentropic expansion?

6.One kilogram of air (use c_v = 0.718 kJ·kg^{-1}·K^{-1}, constant) is used in an ideal Otto cycle. Given T1 = 300 K, compression ratio r = 8, and the heat-addition raises the cycle to T3 = 2000 K, what is the net specific work output W_net (kJ/kg)?

7.An Otto-cycle working fluid delivers W_net = 500 kJ per kg of fuel-air mixture per cycle. The specific volume at state 1 is v1 = 0.85 m^3/kg and the compression ratio is r = 8.0. What is the indicated mean effective pressure p_me (kPa)?

8.For an ideal Otto cycle (constant γ), if the compression ratio r is increased while all other parameters remain the same, how does the thermal efficiency change?

9.Compute the ideal Otto-cycle efficiency for compression ratio r = 10 when γ = 1.3 (use constant specific heats).

10.In the ideal Otto cycle which state corresponds to the maximum instantaneous temperature in the cycle?