- #1
mklein
- 43
- 0
Dear all
I am a secondary and sixth form teacher in London and I have come across a
puzzling situation involving a piston.
Imagine you can set up a piston of known mass resting on a gas beneath. The
piston will come to rest at a certain height from the bottom of the tube.
We can work out at what height the piston will rest by considering the
weight of the piston (w), the area of the piston(a) and the pressure (p) of
the gas inside.
w=pa , pv=nRT
w=(nRT/v)a -------> w=nRt/h
------------
h = nRT/w (this is the height the piston will rest at)
------------
Of course, I have ignored atmospheric pressure(call this A), which creates
an additional downwards force which depends on the area of the piston
(downwards force = Aa). Factoring in atmospheric pressure we find that the
height the piston will rest at is:
--------------
h=nRT/(w+Aa)
--------------
What I don't understand is the first equation (no atmospheric pressure).
This has NO DEPENDENCE on the area of the piston. Surely if we set up
different area pistons with the same number of moles of gas and the same
weight on top they would settle at different heights? I appreciate that if
this were carried out in a cylinder sealed at the top then as the piston
tried to move a vacuum would be created at the top which would affect the
results. BUT what if the basic experiment were tested on the moon? Common
sense says that in a wider cylinder the piston would settle at a lower
height, and in a narrower cylinder it would settle higher up (same volume of
gas?)
I find it hard to believe that the area ONLY has an affect on the height in
which the piston settles in a situation where there is an atmosphere
I would really appreciate people's thoughts on this
Regards
Matt Klein
I am a secondary and sixth form teacher in London and I have come across a
puzzling situation involving a piston.
Imagine you can set up a piston of known mass resting on a gas beneath. The
piston will come to rest at a certain height from the bottom of the tube.
We can work out at what height the piston will rest by considering the
weight of the piston (w), the area of the piston(a) and the pressure (p) of
the gas inside.
w=pa , pv=nRT
w=(nRT/v)a -------> w=nRt/h
------------
h = nRT/w (this is the height the piston will rest at)
------------
Of course, I have ignored atmospheric pressure(call this A), which creates
an additional downwards force which depends on the area of the piston
(downwards force = Aa). Factoring in atmospheric pressure we find that the
height the piston will rest at is:
--------------
h=nRT/(w+Aa)
--------------
What I don't understand is the first equation (no atmospheric pressure).
This has NO DEPENDENCE on the area of the piston. Surely if we set up
different area pistons with the same number of moles of gas and the same
weight on top they would settle at different heights? I appreciate that if
this were carried out in a cylinder sealed at the top then as the piston
tried to move a vacuum would be created at the top which would affect the
results. BUT what if the basic experiment were tested on the moon? Common
sense says that in a wider cylinder the piston would settle at a lower
height, and in a narrower cylinder it would settle higher up (same volume of
gas?)
I find it hard to believe that the area ONLY has an affect on the height in
which the piston settles in a situation where there is an atmosphere
I would really appreciate people's thoughts on this
Regards
Matt Klein