properties of air under pressure.... question 3

[billdedman]

If a volume of a gas (say, ambient atmospheric air) is reduced in a sealed container, to 1/2 of its original volume, doesn't it follow that the pressure would double?

Is this phenomenon linear in nature, all the way up to say, a 10:1 reduction in volume?

If it's NOT linear, why not? Would the rise in temperature due to compression have any effect on the pressure increase?

Thanks much for any information.
Bill Dedman in Hayward, CA
(billdedman@hotmail.com

 

[insideman]

It would double IF the temperature remained the same. But usually you will not have isothermal compression. It will be more nearly adiabatic (no heat lost or gained).

Dig up a temperature-entropy diagram for air.
The perfect adiabatic process will be represented by a straight vertical line on the diagram.

 

[butelja]

If the air is compressed isothermally, then it will very nearly be linear. At extreme pressures, a compressibility factor comes into play.

It the air is compressed isentropically, the the pressure volume relationship will be P*V^k = constant. This occurs with a 100% efficient compression process and zero heat transfer. For air, k=1.4.

Most real processes will be a polytropic process, where P*V^n = constant. n will vary between 1 and k depending upon the process.

 

[fareast]

I thought that boyles/charles law applied in these cases (there are one or two exceptions)

Simply P1V1T1=P2V2T2 therefore if the change in volume is slow enough to allow the heat liberated to dissipate then you can apply boyles law and state that should the volume be reduced by half then the pressure will double.

 

[GregLocock]

You (fareast) are right, but so is butelja, and he's righter! Your statement is true for a lump of ideal gas, in whatever conditions, whereas butelja takes a further step. Combining both equations allows you to find the temperature once it has reached a particular point on the pv^gamma curve. Cheers

Greg Locock