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**Help please -- Change in temperature over altitude**

## Homework Statement

Combine the equations dP/dT=-Î¼gp/RT and the vapor pressure to find the rate dT/dz (use the chain rule).

## Homework Equations

dP/dT=-Î¼gp/RT, Î¼ is the molecular weight

dT/dz

## The Attempt at a Solution

My textbook says the definition of vapor pressure is p=p

_{0}e

^{(-L/RT)}. However, to get there they used the Clausius-Clapeyron equation and one of the intermediate steps is 1/p(dp/dT)=L/RT

^{2}. This is the equation I used. Applying the chain rule, dT/dz=(dp/dz)(dT/dp) I found dT/dz=-Î¼gT/L. However, when asked to find an actual value of dT/dz, I am given the L and Ï (density) to plug into the equation. Does Î¼ have something to with the density? And what would I use for T. I think I may have done something wrong. I tried working out the equation in a different way using the original Clausius-Clapeyron equation for the vapor pressure: dP/dT=L/TÎ”V and found dT/dz=-Î¼gpÎ”V/RL, but am not sure how to use density, Ï, and L, latent heat, with this equation either. Am I using the right equation for vapor pressure? Missing a step? How can I account for Ï and L? Thanks for any of your help!