Homework Help: Barometric formula and height ratios

1. Jan 16, 2012

shyguy79

1. The problem statement, all variables and given/known data
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

2. Relevant equations
Barometric formula: P(z) =P(0) e(-z/y)

3. The attempt at a solution
looks easy but i just can see how?

2. Jan 16, 2012

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)
$$P(z)=P_0 e^{-z/y}$$

Last edited: Jan 16, 2012
3. Jan 16, 2012

shyguy79

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

4. Jan 16, 2012

Simon Bridge

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

5. Jan 16, 2012

shyguy79

got it... just clicked

6. Jan 16, 2012

Simon Bridge

:) I get blind spots like that sometimes.

7. Jan 16, 2012

shyguy79

Yeah, thanks for the memory jog :-)