Basics of Thermodynamics: Otto and Diesel Air Standard Cycles

Otto Air Standard Cycle

• Four processes:
  • Process 1-2: Isentropic compression
  • Process 2-3: Constant volume heat addition
  • Process 3-4: Isentropic expansion
  • Process 4-1: Constant volume heat rejection

P-V and T-S Diagrams for Otto Cycle

• P-V diagram: rectangular shape with four corners representing the four processes
• T-S diagram: four processes plotted with temperature on the y-axis and entropy on the x-axis

Diesel Air Standard Cycle

• Four processes:
  • Process 1-2: Isentropic compression
  • Process 2-3: Constant pressure heat addition
  • Process 3-4: Isentropic expansion
  • Process 4-1: Constant volume heat rejection

P-V and T-S Diagrams for Diesel Cycle

• P-V diagram: rectangular shape with four corners representing the four processes
• T-S diagram: four processes plotted with temperature on the y-axis and entropy on the x-axis

Efficiency of Otto Air Standard Cycle

• Efficiency is a function of compression ratio (r)
• Efficiency = 1 - (1/r)^(γ-1), where γ is the adiabatic index

Problem 1: Otto Cycle with Given Conditions

• Given conditions: compression ratio (r) = 8.7, initial state (P1, T1) = (1 kp/cm2, 1 c°), heat added (Q) = 870 kcal/kg
• To determine:
  • Pressure, volume, and temperature at the beginning of each process
  • Net work (W)
  • Thermal efficiency (η)

Problem 2: Diesel Cycle with Given Conditions

• Given conditions: compression ratio (r) = 15, initial conditions (P1, T1) = (1 kp/cm2, 20 c°), maximum temperature (Tmax) = 3300 c°
• To determine:
  • Heat added per kilogram (Q)
  • Heat rejected per kilogram (Q_rej)
  • Net work (W)
  • Thermal efficiency (η)
  • P-V and T-S diagrams

Problem 3: Air Standard Cycles with Given Conditions

• Two cycles:
  • Diesel cycle: compression ratio (r) = 20, cut-off ratio (ρ) = 8, maximum temperature (Tmax) = 1700 K°
  • Otto cycle: compression ratio (r) = 8, maximum pressure (Pmax) = 60 kp/cm2 abs
• To determine:
  • Thermal efficiency (η) and temperature at each corner for both cycles

Problem 4: Internal Combustion Engine on Otto Cycle

• Given conditions: compression ratio (r) = 8, power produced (P) = 12 horsepower
• To determine:
  • Rate of heat added (Q_dot) and rate of heat rejected (Q_rej_dot)

Problem 5: Air Standard Diesel Cycle

• Given conditions: compression ratio (r) = 12, maximum temperature (Tmax) = 1500 K°, temperature at beginning of compression (T1) = 300 K°, temperature at end of expansion (T4) = 700 K°
• To determine:
  • Thermal efficiency (η) and P-V diagram for the cycle