The Barometric Formula

If the atmospheric pressure at ground level is P0 = mmHg = inHg = kPa and the temperature is uniform at K = °C then the pressure at an altitude of h = m = ft is Ph = mmHg = inHg = kPa This calculation uses m = amu M = kg/mol. 如果地面处的大气压为 P₀ = mmHg = inHg = kPa，温度均匀为 K = °C，那么在高度为 h = m = ft 处的气压为 P_h = mmHg = inHg = kPa。此计算使用 m = amu，M = kg/mol。 中文译文中的待填/计算数值依次对应：1：pmm 2：pin 3：pk 4：t 5：tc 6：h 7：hc 8：pmh 9：pih 10：pph 11：ms 12：mb。实际数值以上方原输入框为准。

Note that the model calculation assumes a uniform temperature, and is therefore not a realistic model of the atmosphere. The temperature tends to decrease with height, so the model calculation will overestimate the pressure at a given height.

The Barometric Formula

Starting at some point in midair, the change in pressure associated with a small change in height can be found in terms of the weight of the air. The change in pressure depends on density, but ρ depends on the pressure as follows: The solution for the change from the ground ( P0) to height h ( Ph ) gives Calculation 计算 Details of solution 解题细节 从接地（P₀）到高度h（P_h）的变化解为 从空中某一点开始，小高度变化引起的压力变化可以表示为空气重量的函数。压力变化取决于密度，但密度ρ与压力的关系如下：

The development of the barometric formula makes use of a number of concepts from kinetic theory, such as the ideal gas law and the associated molecular constants. In the exponential, the two terms have the units of energy. The numerator mgh is gravitational potential energy and the term kT is thermal energy.

The Barometric Formula

Having shown that the rate of change of pressure with height has the form it is necessary to take the limit as the change in height approaches zero, putting it in the form of a derivative. This type of equation can be solved for P by making a substitution of the type fitting the boundary conditions gives 已证明压力随高度变化的速率具有这种形式，因此需要将高度变化趋近于零作为极限，将其表示为导数的形式。这种类型的方程可以通过一种适合边界的替换来求解P。

The Barometric Formula

The equation for the variation of barometric pressure with height has the form which has the formal solution 其形式解为 Substituting the solution gives 代入解得 Since this equation must be valid for all values of h, forcing the solution to fit the physical boundary conditions yields: 由于该方程对所有h的值都必须成立，因此迫使解符合物理边界条件： 气压随高度变化的方程形式为

Atmospheric Pressure, Selected Heights

Compared to the standard Atmospheric pressure at sea level, 760 mmHg = 760 torr, the pressure at some heights above the earth are:

These pressures are considerably below those predicted by the barometric formula, which can be used to calculate variations in barometric pressure with height near the earth. (The predicted pressures above used temperature 300K and pressure 760 mmHg.) Though the pressure decreases rapidly, even at 200 km (124 mi) there is enough residual atmospheric pressure to gradually slow a satellite, limiting its lifetime.

Constituents of the Air

The constituents of dry air can be expressed as volume percentages, which will translate to the partial pressures out of the total atmospheric pressure