The optimization of a gas power cycle can be thermodynamical, techno-economical, thermo-economical and so on but, in general, the thermodynamic modeling is mandatory to solve the problem. Once the thermodynamic model is established the properties of the gases present in the cycle must be evaluated and the simplifications made for this evaluation could lead to inaccurate and even misleading results. In this paper the effect of using the perfect gas model in the optimization of the Specific Fuel Consumption (SFC) of the open simple cycle gas turbine has been analyzed. The results are obtained for compressor and turbine inlet temperatures (CIT and TIT) between 260 K-320 K and 1200 K-1800 K respectively. The optimization yields the minimum of SFC but also the corresponding values of compressor pressure ratio and specific power. In this work the optimization is first performed with a highly accurate ideal gas modeling approach in order to generate benchmark results. Afterward, the optimization is performed with a perfect gas modeling approach using four different methods (named A, B, C and D) to evaluate the constant value needed of the isobaric heat capacity. It is found that the optimization results can depend strongly on the method or rule used to evaluate the heat capacity. As an example, the uncertainty in the optimal value of SFC is between 8.5% and 14.9% with method C and below 3.2% with method D. In general, huge deviations in the compressor pressure ratio are found. Values higher than 160/0 for CIT below 300 K regardless the TIT value are found with methods A, B and C. In the worst case this deviation can be even higher than 100%. In general, this uncertainty gives rise to higher deviations in the specific power than in optimal SFC values. For example, with the method B and a TIT of 1800 K the ranges of the relative error are 56%-112%, 4.9%-6.2% and 17.8%-26.7% in the compressor pressure ratio, optimal SFC and specific power respectively. With respect to the CIT and TIT dependence the deviations in the compressor pressure ratio and specific power increase for high TIT and low CIT. This work is an extension of a previous paper publish by the author where the detailed development of the modeling approaches used in this work can be consulted.