A simple piston–cylinder engine operates using a sequence of three processes:1-2 Compression at constant temperature, maintained by heat transfer to the environment.2-3 Expansion at constant pressure, maintained by heating from flames.3-1 Cooling at constant volume back to the initial state 1.Using the ideal gas property information in (and following the format of) the Detailed heat pump cycle analysis example of Section 2.8 , derive expressions for the energy transfer as work and heat for each process.Express the efficiency of the cycle, η ≡ W_{net output}/Q_{input from flames,} as a function of the compression ratio r_V = V₁/V₂. Plot the efficiency over the r_V range 1–20, for γ = 7/5. Does this look like a promising engine cycle?

Detailed heat pump cycle analysis We will do one final example in which we look in  more detail at the thermodynamic analysis of a proposed heat pump. This example will use most of the ideas introduced in this chapter and will give you a look at what one can do with simple thermodynamic analysis. An inventor proposes to make a heat pump using a simple piston–cylinder system in which the contained gas is put through a repetitive series of four processes shown in Figure 2.7. We want to determine the performance of this design as a function of some key design parameters.