# Homework Help: Under Pressure! Finding the height of compressed air!

1. Dec 7, 2011

1. The problem statement, all variables and given/known data
A 1.0--tall cylinder contains air at a pressure of 1 . A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from escaping, then mercury is slowly poured into the cylinder until no more can be added without the cylinder overflowing. Find the height of the compressed air. It recommends P1V1=P2V2 and that temperature is constant.

2. Relevant equations
P1V1=P2V2
F=mg
P=F/A

3. The attempt at a solution
P1V1=P2V2
P1A1m=P2hA
(P1*1M)/h=P2

The system is at rest so the force gravity is pulling on the Hg is balanced by the air pressure
PA=F=mg
A(P1*1M)/h=ρ(1-h)Ag
(P1*1M)/pg=h(1-h)
.76=-h^2 + h
0=-h^2 +h -.76
The answers is 76cm ( think the book is wrong) and that quadratic has answers with i in it. I'm unsure what I'm doing wrong! I asked my prof and he couldn't help me. I asked my lab instructor and he says what I did looked right. So 3 people (including me) have missed what is wrong with my work. Please help me :'(

2. Dec 7, 2011

Am I on the right track for this?

3. Dec 7, 2011

### I like Serena

I believe you are forgetting that the outside force is not just the weight of the mercury, but also the atmospheric pressure.

4. Dec 7, 2011

so then it will be:

A(P1*1M)/h = 101300A + ρ(1-h)Ag

I'll try solving this

5. Dec 7, 2011