In order to cool the turbine blade under high temperature operating conditions, the film-cooling method is generally applied. In this study, $CO_2$ was used as working fluid and it helped the operating system to prevent the loss of compressed air. The trapezoidal diffuser shape was adopted at the cross section of hole and the characteristics of heat flow with various working fluids were numerically studied. In particular, the different mixture ratios of $CO_2$, such as various density ratios of 0.2, 0.8, and 1.0, respectively, were considered. Numerical results are graphically depicted with various conditions.