(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Homework question for a graduate level atmospheric science course:

A mercury barometer of height h has an imperfect vacuum above its mercury column so

that it measures a surface pressure of 29.80 inches Hg when the true surface pressure is

29.90 inches Hg, and it measures a surface pressure of 29.72 inches Hg when the true

surface pressure is 29.80 inches Hg.

What will this barometer measure when the true pressure is 29.7 inches Hg?

2. Relevant equations

p=rho*g*z

3. The attempt at a solution

This question seems easy but I just cannot seem to get to an answer. I've tried using the hydrostatic equation to set up some sort of ratio, but in the end I get 2 unknowns and I can't figure out how to fix it.

I set up the equations for the first 2 cases as such:

p_actual = g((rho_mercury*z_mercury)+(rho_air*z_air))

So, for the first case:

29.90 in = 101,253 Pa = (9.81 m/s^2)(13,594 kg/m^3)(29.80 in = 0.7569 m) + (9.81 m/s^2)(1.2 kg/m^3)(z_air)

And then I solved for z_air, getting 26.758 m.

Doing the 2nd case, I got z_air = 21.747 m.

I then calculated dp/dz for the two cases as such:

(p_actual-p_mercury)/(z_air-z_mercury)

So, for the first case:

315 Pa/(26.758 m - 0.7569 m )= 12 Pa/m

And I got pretty much the same value for the 2nd case, so I'm assuming I have to use this somehow... But for the third case, I end up with two unknowns: the height of the mercury, and the pressure measured by the mercury barometer, and I don't know what to do from here. Any help would be greatly appreciated... Thanks!

**Physics Forums - The Fusion of Science and Community**

# Question about a mercury barometer with an imperfect vacuum

Have something to add?

- Similar discussions for: Question about a mercury barometer with an imperfect vacuum

Loading...

**Physics Forums - The Fusion of Science and Community**