Under Pressure Finding the height of compressed air

In summary, the problem involves a 1.0-meter tall cylinder containing air at a pressure of 1 and a very thin, frictionless piston at the top to prevent air from escaping. Mercury is slowly poured into the cylinder until it reaches its maximum capacity without overflowing. Using the equation P1V1=P2V2 and assuming constant temperature, the height of the compressed air is calculated to be 76 cm. However, this answer is incorrect as it does not take into account the atmospheric pressure acting on the system. By including this factor, the correct solution is obtained.
  • #1
IslandHead
10
0

Homework Statement


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.


Homework Equations


P1V1=P2V2
F=mg
P=F/A



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 :'(
 
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  • #2
Am I on the right track for this?
 
  • #3
Welcome to PF, IslandHead! :smile:

I believe you are forgetting that the outside force is not just the weight of the mercury, but also the atmospheric pressure.
 
  • #4
so then it will be:

A(P1*1M)/h = 101300A + ρ(1-h)Ag

I'll try solving this
 
  • #5
It works :D i got thanks!
 
  • #6
Cheers! :smile:
 

FAQ: Under Pressure Finding the height of compressed air

1. How does compressed air exert pressure?

Compressed air exerts pressure because it contains more molecules in a given space compared to uncompressed air. This results in the molecules colliding more frequently with the walls of the container, creating a force that we perceive as pressure.

2. How can I calculate the height of a column of compressed air?

To calculate the height of a column of compressed air, you will need to know the pressure of the air, the density of the air, and the acceleration due to gravity. You can then use the formula P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height of the column.

3. Can the height of compressed air change with temperature?

Yes, the height of compressed air can change with temperature. As the temperature increases, the molecules in the air have more energy and move faster, resulting in a higher pressure and a taller column of compressed air. Similarly, a decrease in temperature would result in a decrease in pressure and a shorter column of compressed air.

4. What factors can affect the height of compressed air?

The height of compressed air can be affected by factors such as temperature, pressure, and the density of the air. Other factors that can impact the height include the volume and shape of the container, the type of gas being compressed, and the altitude of the location where the experiment is taking place.

5. Is there a limit to the height of compressed air?

Yes, there is a limit to the height of compressed air. This limit is determined by the maximum pressure that the container can withstand before bursting. Once this pressure is reached, the compressed air will escape and the height of the column will decrease. Additionally, as the height increases, the weight of the air column will also increase, eventually reaching a point where it collapses under its own weight.

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