How Does Piston Movement Affect Pressure in a Closed System?

[BuddyJim]

Hi,

I have a closed system of fixed volume with an piston pump attached. The medium is air and the initial environmental condition are at standard atmospheric. I would like to know the formulas to use that would provide me with the new pressure when the piston is at top dead center (i.e. traveled a full stroke). Would I be correct in assuming that temperature is negligible when no heat (or fuel) is supplied to the system during the cycle?

Thanks

 

[aroc91]

If you know the initial volume and pressure, you would use P₁V₁=P₂V₂, where P₁ and V₁ are the initial pressure and volume and the other side of the equation is the pressure and volume after the piston has moved.

I would also say that temperature is negligible. It would change slightly, but it's not relevant because it's a result of the pressure change.

 

[Bob S]

If you know the initial volume and pressure, you would use P₁V₁=P₂V₂, where P₁ and V₁ are the initial pressure and volume and the other side of the equation is the pressure and volume after the piston has moved.

I would also say that temperature is negligible. It would change slightly, but it's not relevant because it's a result of the pressure change.

Actually, air heats up as it is compressed, like in a diesel engine. Specifically for adiabatic compression, T·V ^γ-1 = constant, where γ = 7/5 for air. There is a similar relation for the pressure increase. See http://en.wikipedia.org/wiki/Adiabatic_process

 

[aroc91]

Actually, air heats up as it is compressed, like in a diesel engine. Specifically for adiabatic compression, T·V ^γ-1 = constant, where γ = 7/5 for air. There is a similar relation for the pressure increase. See http://en.wikipedia.org/wiki/Adiabatic_process

I know. I just meant that, from the description of the problem, temperature wasn't relevant, not that didn't occur.

 

[gmax137]

If you know the initial volume and pressure, you would use P₁V₁=P₂V₂, where P₁ and V₁ are the initial pressure and volume and the other side of the equation is the pressure and volume after the piston has moved.

I would also say that temperature is negligible. It would change slightly, but it's not relevant because it's a result of the pressure change.

We can't say whether the temperature change is 'slight' unless we know the relative volumes between piston down and piston up, which the OP failed to mention.