| align="center" |154,199.48 | align="center" |0.00143 | align="center" | | align="center" |270.65 | align="center" |0.0 | align="center" |0.0 |- | align="center" |5 | align="center" |51 000 | align="center" |167,322.83 | align="center" |0.00086 | align="center" | | align="center" |270.65 | align="center" |-0.0028 | align="center" |-0.00085344 |- | align="center" |6 | align="center" |71 000 | align="center" |232,939.63 | align="center" |0.000064 | align="center" | | align="center" |214.65 | align="center" |-0.002 | align="center" |-0.0006096 |} Derivation The barometric formula can be derived using the ideal gas law: Assuming that all pressure is hydrostatic: and dividing the by the expression we get: Integrating this expression from the surface to the altitude z we get: Assuming linear temperature change and constant molar mass and gravitational acceleration, we get the first barometric formula: Instead, assuming constant temperature, integrating gives the second barometric formula: In this formulation, R* is the gas constant, and the term R*T/Mg gives the scale height (approximately equal to 8.4 km for the troposphere). (For exact results, it should be remembered that atmospheres containing water do not behave as an ideal gas''. See real gas or perfect gas or gas for further understanding.) See also Hypsometric equation NRLMSISE-00 Vertical pressure variation References Atmosphere Vertical position Pressure