Plot the atmospheric pressure as a function of elevation (0-20000 m) at a location where the gr

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Plot the atmospheric pressure as a function of elevation...

Plot the atmospheric pressure as a function of elevation $(0-20000 \mathrm{~m})$ at a location where the ground pressure is $100 \mathrm{kPa}$ at $500 \mathrm{~m}$ elevation. Use the variation shown in Problem 1.64.

Key Concepts

Data Representation in Atmospheric Studies

Plotting atmospheric pressure versus elevation is a common method used in atmospheric sciences to visualize how pressure decreases with height. Such graphs help researchers and students understand the underlying exponential relationship and analyze the impact of variables like temperature and gravitational acceleration on atmospheric pressure.

Barometric Formula

The barometric formula provides a way to compute atmospheric pressure as a function of altitude. Under the assumption of, for example, an isothermal atmosphere, it shows that pressure decreases exponentially with height. This formula combines the principles of hydrostatic equilibrium with the ideal gas law, yielding an expression where pressure is given in terms of a reference pressure and the exponential of the negative altitude divided by a characteristic scale height.

Hydrostatic Equilibrium

This concept explains that within a fluid at rest, the pressure decreases with height due to the weight of the fluid above. It is mathematically expressed as the balance between the pressure gradient and the gravitational force acting on the fluid, typically written as dP/dz = -?g. This forms the foundational basis for determining how atmospheric pressure changes with elevation.

Atmospheric Scale Height

Atmospheric scale height is a key concept that represents the altitude over which the atmospheric pressure decreases by a factor of e (approximately 2.718). It is derived from the properties of the atmosphere, including temperature and the mean molecular weight of the air, typically expressed as H = RT/(Mg). This parameter is crucial for quantitatively relating changes in pressure with changes in elevation.

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