Pressure At Surface And Scale Height

In summary, the person is trying to calculate the scale height of an atmosphere with given values for atmospheric pressure at different heights. They rearrange the formula for pressure at a certain height and set it equal to the relative pressure at the two known heights. However, they encounter an issue with the cancellation of λ and need advice on their calculations.
  • #1
bobbles22
17
0
Please can someone tell me if my thinking here is right...

I've got a planet with an atmospheric pressure at 6km of 0.5 P0 and at 8km of 0.4 P0 (P0 = pressure at the surface).

I want to work out the scale height of the atmosphere.

Given scale height = λ

and for height above surface = z

P(z)=P(0)e(-z/λ)

I could rearrange to show the pressure at the surface as:

P(0)=P(z)/e(-z/λ)

I could then use the relative pressure, assume P(0)=1 (as it will cancel out shortly) and height from each of the know quantities and set them equal to each other like this:

0.4/e(-8000/λ) = 0.5/e(-6000/λ)

A little mutliplication...

0.4 e(-6000/λ) = 0.5 e(-8000/λ)

Take the Log of both sides...

(-6000/λ) log 0.4 = (-8000/λ) log 0.5

But know I'm left with the λ cancelling out if I multiply both sides by λ. I'm sure I've gone wrong here somewhere. Probably something very simple. Can anyone advise? Have I made a simple mistake in my working or have I gone completely off the reservation and need to start again? I just need to end up with λ = xxx metres.

Thank you.
 
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  • #2
hi bobbles22! :smile:
bobbles22 said:
0.4 e(-6000/λ) = 0.5 e(-8000/λ)

Take the Log of both sides...

(-6000/λ) log 0.4 = (-8000/λ) log 0.5

nooo :wink:

(-6000/λ) + log 0.4 = (-8000/λ) + log 0.5 :smile:
 

Related to Pressure At Surface And Scale Height

What is pressure at the Earth's surface?

Pressure at the Earth's surface refers to the force exerted by the weight of the atmosphere above a particular point on the Earth's surface. It is measured in units of force per unit area, such as pounds per square inch or pascals.

How is pressure at the Earth's surface affected by altitude?

As altitude increases, the pressure at the Earth's surface decreases. This is because the weight of the atmosphere above a given point decreases as altitude increases. This relationship between pressure and altitude is known as the barometric formula.

What is the scale height of the Earth's atmosphere?

The scale height of the Earth's atmosphere is the average vertical distance over which the atmospheric pressure decreases by a factor of e (approximately 2.718). For the Earth's atmosphere, the scale height is approximately 8.5 kilometers.

How does temperature affect pressure at the Earth's surface?

Temperature and pressure are directly related at the Earth's surface. As temperature increases, the molecules in the atmosphere have more energy and move faster, resulting in a higher pressure. Conversely, as temperature decreases, the pressure decreases as well.

What is the relationship between pressure at the Earth's surface and weather?

The pressure at the Earth's surface plays a crucial role in weather patterns. High pressure systems are associated with clear, dry weather, while low pressure systems are associated with cloudy, stormy weather. Changes in pressure also drive winds and influence the movement of weather systems.

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