Carbon Dioxide (CO2), which is generally associated with green house effect and damage to the environment, can be used in the fight against ozone depletion. CO2(R744) is a practical replacement to existing fluoro-carbon based refrigerants. Although R744 has a global warming potential (GWP) of 1, it is about 1000-3000 times lower than the GWP of most other commonly used refrigerants. This paper follows a theoretic approach to compare the performance of R744 with other natural refrigerants, employing the first law of thermodynamics, i.e., using coefficient of performance (COP). It shows the optimized pressure plots of a R744 compressor and sketches the effect of compressor performance on the COP of the refrigeration system.Units: SI