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This might be the answer you are looking for, but I made some mistake (the result seems unreal, please comment to tell me the wrong part. I just wanted to show the direction that may be correct): By the equation for pressure lapse: $$P=P_0\cdot e^{-\frac{z}{H}}$$ where $H=8 km=8000 m$ (scale height) and $z$ is the height above the surface. We differentiate ...