The state of the atmosphere is significantly affected by greenhouse gaseous pollutants. The respective thermodynamic parameters that describe the state of the atmosphere are its pressure, temperature and volume. Anthropogenic gases with a greenhouse effect influence these parameters and especially the average global temperature of the atmosphere. As a result of comparing the temperature records and the concentrations of pollutants such as carbon dioxide, which has the highest ratio from all green house gases, it is concluded that there is a quantitative expression based on the laws of thermodynamics between the temperature values recorded over time and the concentration values. As a result of the application of the laws of thermodynamics of the atmospheric state, the quantitative expressions are obtained that allow calculating the adiabatic constant of atmospheric air. By the application of the temperature gradient as a function of the altitude, the following fact is found that the absolute value of the gradient increases over time, a fact that leads to a slow instability of the atmosphere with values of the adiabatic constant that decrease slowly over time. As a manner of the validation of the suggested method, the numerical value of the universal gas constant is re-calculated. Another important obtained result is about specifical thermal capacity of atmospheric air. This value is decresaing slowly over time together with the decreasing of the value of adiabatical constant. The slowly decreasing of both parameters leads to the increasing of the speed of winds which are more frequent last time. The importance of the suggested method of the paper consists in the fact that the parameters that are contained in the expressions allows to calculate the speed of winds and hurricanes which are increasing over time.