Piston & Cylinder Thought Experiment

[Robert11]

Hello,

 

Lets say you have a theoretically perfect piston in a cylinder.

No leaks around clearances, etc.

Hypothetically perfect.

 

The piston is at the top of the cylinder; no space left; none..

 

Now, I slowly withdraw the piston:

 

a. Irrespective of whether I withdraw it a very small amount, or a substantial amount,

the minute there is any clearance established, that volume is a "perfect vacuum"

True ?

 

b. The force required to withdraw the piston stays constant as it is moved.

True ?    

 

Just a bigger volume that is a perfect vacuum is established.  True ?

 

Thanks,

Bob

[exchemist]

Hello,

 

Lets say you have a theoretically perfect piston in a cylinder.

No leaks around clearances, etc.

Hypothetically perfect.

 

The piston is at the top of the cylinder; no space left; none..

 

Now, I slowly withdraw the piston:

 

a. Irrespective of whether I withdraw it a very small amount, or a substantial amount,

the minute there is any clearance established, that volume is a "perfect vacuum"

True ?

 

b. The force required to withdraw the piston stays constant as it is moved.

True ?    

 

Just a bigger volume that is a perfect vacuum is established.  True ?

 

Thanks,

Bob

If the seal is perfect then you have almost a perfect vacuum. Any solid however still has a very small residual vapour pressure above absolute zero, so there will be a handful or so of gaseous atoms, released from the material of which the piston and cylinder surfaces are made. This will generally be so small as to be completely negligible. But it would not be strictly accurate to call it a "perfect vacuum, unless you also specify some sort of idealised material with zero vapour pressure.

 

The force needed to withdraw the piston will be the ambient pressure on the other side of the piston, multiplied by its surface area. Assuming you envisage this being atmospheric pressure, then approx 10^5 Pa area in m2 will give the force in N.

 

Yes, this force will remain constant as the piston is withdrawn, as it is due solely to the atmospheric pressure, which is obviously not changed by the act of moving the piston.   

Edited June 1, 2018 by exchemist

[DaveC426913]

If you did this in deep space, not only would you not have to worry about any force to extract the piston, but you wouldn't need to have a theoretically perfect seal, since there are too few atoms in hard vacuum to make their way past the seal.

[exchemist]

If you did this in deep space, not only would you not have to worry about any force to extract the piston, but you wouldn't need to have a theoretically perfect seal, since there are too few atoms in hard vacuum to make their way past the seal.

Indeed. In fact the interesting question in that situation would be whether the vapour pressure of the materials of the piston and cylinder would eventually push the piston out!