re: Is there proof that CO2 causes warming?

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I may be off here, but isnt this why you introduce z (compressibility factor) into the equation, which becomes the real gas law rather than ideal to account for the changing density at different P&Ts?

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Z is determined empirically for different gases as basically a correction factor in the IGL to achieve accurate results. Air works perfectly in the IGL model. Other gases need a factor based on temperature and pressure to predict outcomes using the IGL.