How Does Temperature Constancy Affect Atmospheric Pressure with Altitude?

[calculusisrad]

Ideal Gas Law Problem (Please help!)

Show that if the temperature in the atmosphere is independent of altitude, then the pressure as a function of altitude y is

p=(p initial)e^(-mgt/kT)

Where m is the average mass per molecule of air.

I really have no idea where to start. Please help! Thank you so much!

I thought maybe you use the ideal gas law and manipulate the variables to get it to match. I tried, but I couldn't get anywhere. Thanks

 

[conquest]

Try deriving a differential equation for P by using the ideal gas law and calculating the pressure from above and below for a slither of air

Also in the function you gave p is constant as a function of y (fix this and try using h instead of y this might trigger something)

 

[calculusisrad]

Thank you for your response, but I still can't figure out what to do. Find the rate of change of pressure with respect to h, right? doesn't that wind up as a constant if I'm using p=p+gy? That probably makes no sense lol, but I thought I'd show that I attempted to figure it out. I would really appreciate some more help and/or directly what I need to do to get started please!