Engineering Thermodynamics has been the core course of many science and engineering majors around the world, including energy and power, mechanical engineering, civil engineering, aerospace, cryogenic refrigeration, food engineering, chemical engineering, and environmental engineering, among which gas power cycle is one of the important contents. However, many Engineering Thermodynamics textbooks focus only on evaluating the thermal efficiency of gas power cycle, while the important concept of specific cycle work is ignored. Based on the generalized temperature-entropy diagram for the gas power cycles proposed by the authors, an ideal Otto cycle and an ideal Miller-Diesel cycle are taking as examples for the thermodynamic analyses of gas power cycles. The optimum compression ratio (or the pressure ratio) for the maximum specific cycle work or the maximum mean effective pressure is analyzed and determined. The ideal Otto and the ideal Miller-Diesel cycles, and also other gas power cycles for movable applications, are concluded that the operation under the maximum specific cycle work or the maximum mean effective pressure, instead of under the higher efficiency, is more economic and more reasonable. We concluded that the very important concept, i.e., the optimum compression (or pressure) ratio for the gas power cycles, should be emphasized in the Engineering Thermodynamics teaching process and in the latter revised or the newly edited textbooks, in order to better guide the engineering applications.