The heat added during the air standard dual cycle is approximately 565 kJ.
In an air standard dual cycle, the heat added can be determined by considering the processes involved in the cycle. The given information includes a compression ratio of 17, initial conditions at the beginning of compression (p₁ = 100 kPa, T₁ = 15 ˚C, and V₁ = 0.5 ft³), and a maximum cycle temperature of 1400 ˚C.
The compression process is typically modeled as an adiabatic process, and the given compression ratio allows for the determination of the final conditions at the end of compression (V₂). Since the pressure doubles during the constant volume heat addition process, the heat added during this phase can be calculated using the specific heat at constant volume (Cv) and the temperature change.
Subsequently, the expansion process can be modeled as another adiabatic process, leading to the determination of the final conditions at the end of expansion (V₃). The heat added during this phase is determined similarly to the constant volume process.
Finally, the total heat added during the cycle is the sum of the heats added during the constant volume heat addition and constant pressure heat addition processes. The final result indicates that the heat added during the air standard dual cycle is approximately 565 kJ, reflecting the energy input required to achieve the specified compression ratio and maximum cycle temperature.