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I'm trying to come up with a question, be it a simple one, where a mass of ideal gas (Oxygen) is bound in a cylindrical tube and has a circular piston applied to it - so that the gas becomes pressurised. Once the gas has been pressurised it will gain a certain temperature, which is the objective of the question I'm trying to compose.

If we imagine some mass of oxygen inside a cylindrical tube that is compressed by a circular piston then the volume of the enclosed space and thus the volume of the gas is given by:

[tex]V_{compressed}=\pi r^2h[/tex]

Where 'r' is the radius of the circular piston and 'h' is the height of the compressed volume.

Applying some force to this piston causes the compression and pressure, the pressure from this force is given by:

[tex]F_{compressed}=\frac{P}{A}=\frac{P}{\pi r^2}[/tex]

Where F is the force applied by the piston and A is the cross-sectional area of the circular piston.

Using these equations and the ideal gas equation:

[tex]PV=nRT\: ,\: \frac{F}{\pi r^2}\times \pi r^2h=PV[/tex]

We find the product of PV is independent of the radius of the piston and only dependent on the force F and the height h. So resolving the ideal gas equation for temperature we find

[tex]\frac{Fh}{nR}=T[/tex]

Now, I believe and hope this is all right so far... Provided it is I want to determine some reasonable values for 'F', 'h' and the mass of the oxygen such that it satisfies the ideal gas conditions - those being high temperature and low pressure.

I'm not really sure what qualifies as high temperature and low pressure, I'm not sure what a 'high' temperature is? I think it's just when the kinetic energy of the particles is much greater than the interaction energy between the particles - but once again I'm not sure for what temperature this would be.

Thanks for any help,

SK