Barometric formula and height ratios

[shyguy79]

Homework Statement

Starting from the barometric formula for a thin, isothermal atmosphere, show that the ratio of the pressure P(z2) at height z2 to the pressure P(z1) at height z1 is given by

P(z2)/P(z1) = e(-(z2-z1)/y) where y is the scale height

Homework Equations

Barometric formula: P(z) =P(0) e(-z/y)

The Attempt at a Solution

looks easy but i just can see how?

 

[Simon Bridge]

If it looks easy, then you should be able to see how.
Have you tried writing P(z1) and P(z2) in the barometric formula and just dividing them?

aside: on notation:

P(z)=P(0).exp(-z/y) ... in plain text, or, in LaTeX (worth learning)
$$P(z)=P_0 e^{-z/y}$$

 

[shyguy79]

I'm afraid my algebra is a little rusty, how do you divide e(-z2/y) by e(-z1/y)?

 

[Simon Bridge]

property of powers
$$x^a x^b = x^{a+b}$$... it's the same for the exponential function.

 

[shyguy79]

got it... just clicked

 

[Simon Bridge]

:) I get blind spots like that sometimes.

 

[shyguy79]

Yeah, thanks for the memory jog :-)