Name: atmospheric pressure and altitude
Uploaded: 2025-05-22T09:06:09.000Z
Duration: 1 min 18 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Earth and Environmental Science

Earth's Systems

ESS.EES.2.5

Variation of Atmospheric Pressure

The earth is enveloped by layers of air, known as the atmosphere. It is pulled down toward the surface by gravity, and exerts a pressure known as atmospheric pressure.
Atmospheric pressure changes with height and can be given in terms of the weight or density of air. However, from the ideal gas law, density also depends on pressure.
Assuming that the air temperature and the acceleration due to gravity remain constant with height and by substituting the expression for density and rearranging the equation, the rate of change of pressure with height can be obtained.
Here, the constant quantities inside the parentheses are termed alpha.
The equation is then integrated from sea level and solved to obtain the relation for pressure with height&#8212;the Barometric formula.
By considering nitrogen molecules at 300 kelvin, one can obtain an approximate value of one over alpha, a characteristic length known as pressure scale height. 
The atmospheric pressure drops exponentially by a factor of one over e for every 8,800 meters above sea level.

variation of atmospheric pressure

Change in atmospheric pressure with height is particularly interesting. The decrease in atmospheric pressure with increasing altitude is due to the decreasing gravitational force per unit area as we move away from the surface of the earth.
Assuming the air temperature is constant at a given altitude and that the ideal gas law of thermodynamics describes the atmosphere to a good approximation, one can find the variation of atmospheric pressure with height.
Let p(y) be the atmospheric pressure at height y. The density &#961; at y, the temperature T in the Kelvin scale (K), and the mass m of a molecule of air are related to the absolute pressure by the ideal gas law, in the form:
<img alt="Ideal gas law formula diagram, showing density equation &#961;=mp/kBT, educational reference." src="/files/ftp_upload/14711/14711_Equation_1.svg" style="text-align: center; height: 38px;" data-altupdatedat="1754904545000" data-alt="Ideal gas density equation \(&#961; = \frac{mp}{kT}\), formula illustration for thermodynamics concepts." />
Using density from the ideal gas law, the rate of variation of pressure with height is integrated from sea level, and the final expression is obtained as:
<img alt="Exponential decay equation: p(y) = p&#8320;exp(-&#945;y), mathematical formula." src="/files/ftp_upload/14711/14711_Equation_2.svg" style="text-align: center; height: 17px;" data-altupdatedat="1754904545000" data-alt="Probability distribution formula p(y)=poexp(-&#945;y), mathematical equation." />
where,
<img alt="Thermal equilibrium equation diagram: 1/&#945; = kBT/mg, educational physics formula." src="/files/ftp_upload/14711/14711_Equation_3.svg" style="text-align: center; height: 38px;" data-altupdatedat="1754904545000" data-alt="Equation showing balance of forces, 1/&#945; = kBT/mg, for physical equilibrium analysis." />
Atmospheric pressure drops exponentially with height, since the y-axis points up from the ground, and y has positive values in the atmosphere above sea level. The pressure drops by a factor of 1/e when the height is 1/&#945;, which gives us a physical interpretation for &#945;. The constant 1/&#945; is a length scale that characterizes how pressure varies with height and is often referred to as the pressure scale height.

Change in atmospheric pressure with height is particularly interesting. The decrease in atmospheric pressure with increasing altitude is due to the ...

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Education

JoVE Core

Physics

Unit 1

Fluid Mechanics

KEY TERMS AND CONCEPTS

atmospheric pressure and altitude

Atmospheric pressure and altitude are closely linked. As height increases, atmospheric pressure decreases. This happens because the gravitational force per unit area becomes smaller as we move away from Earth’s surface.

To describe this change, the atmosphere is treated with a constant air temperature at a given altitude. The ideal gas law of thermodynamics is also used as a good approximation for the air. Let p(y) be the atmospheric pressure at height y. The density ρ at y, the temperature T in Kelvin, and the mass m of an air molecule are related to absolute pressure by the ideal gas law.

Using the density from the ideal gas law, the rate of change of pressure with height can be integrated from sea level. The result shows that atmospheric pressure drops exponentially with height. Since the y-axis points upward from the ground, y has positive values above sea level in the atmosphere.

The pressure drops by a factor of 1/e when the height reaches 1/α. This gives a physical meaning to α. The constant 1/α is a length scale that describes how pressure changes with height, and it is often called the pressure scale height.

Atmospheric Pressure and Altitude

characteristics of fluids

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Atmospheric pressure and altitude are closely linked. As height increases, atmospheric pressure decreases. This happens because the gravitational force per unit area becomes smaller as we move away from Earth’s surface. To describe this change, the atmosphere is treated with a constant air temperature at a given altitude. The ideal gas law of thermodynamics is also used as a good approximation for the air. Let p(y) be the atmospheric pressure at height y. The density ρ at y, the temperature T...

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bernoulli's principle

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bernoulli's principle: applications

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key terms and concepts

See how atmospheric pressure decreases with altitude, why the drop is exponential, and what the pressure scale height tells us about the atmosphere.

Atmospheric Pressure and Altitude | JoVE K12

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Atmospheric Pressure and Altitude

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