The air standard efficiency of a heat engine is defined as the ratio of the net work output to the heat input. It represents the maximum efficiency that can be achieved by a heat engine operating between two specified temperature limits, assuming no losses or irreversibilities.
The Carnot cycle is a theoretical thermodynamic cycle that describes the most efficient way to convert heat into work. It consists of four processes: two isothermal processes and two adiabatic processes. The Stirling cycle is also a theoretical thermodynamic cycle, but it uses two isothermal processes and two constant volume processes.
The air standard efficiency of the Carnot cycle is given by:
η_Carnot = 1 - (T_L/T_H)
where T_H is the higher temperature and T_L is the lower temperature of the cycle.
The air standard efficiency of the Stirling cycle is given by:
η_Stirling = 1 - (T_L/T_H) * (V_1/V_2)^γ
where γ is the ratio of specific heats, V_1 is the volume of the working fluid at the beginning of the compression process, and V_2 is the volume of the working fluid at the end of the compression process.
Comparing the two equations, it is clear that the Carnot cycle has a higher air standard efficiency than the Stirling cycle. This is because the Carnot cycle uses two isothermal processes, which are more efficient than the constant volume processes used in the Stirling cycle.
