Air volume under pressure 3

[Artisi]

My turn to ask a question for once.
If I compress 1 cubic foot of air at atmospheric pressure to 20 psi (gauge)what volume do I end up with.
Thanks guys and girls

Naresuan University
Phitsanulok
Thailand

 

[quark]

That depends upon what process you follow. For adiabatic compression(where there is no heat transfer to and from the air undergoing compression) the formula is P1V1^k = P2V2^k where k is the ratio of specific heats(1.4 for diatomic gases).

If you maintain constant temperature of air through out the compression process then the isothermal formula will be P1V1 = P2V2.

However, when you use a compressor to do the work, you can approximately use the adiabatic process and thus the volume will be 14.7 x 1^1.4 = (20+14.7)xV2^1.4.
Thus, V2 = 0.541cu.ft (this is called actual cu.ft)

Check these two informative threads
thread403-7556
thread798-106556

Regards,

 

[Artisi]

Thanks for quick response - I used P1V1 = P2V2 to come up with the answer - then questioned myself if I was correct -brain is getting a bit fuzzy with age I guess.

Naresuan University
Phitsanulok
Thailand

 

[25362]

In the EOS pV=f (T) one needs two parameters to determine the third. In this case, knowing the final pressure, temperature would be necessary and sufficient.

If the compression path is fully identified one could estimate the other macroscopic properties, given the final pressure, for example:

P1V1=P2V2 refers to an isothermic process, while
P1V1^[γ] = constant, to an adiabatic process.

BTW, compression can follow a variety of paths, e.g., isothermic, adiabatic, even isochoric. We can compress a gas at constant volume (!) by the addition of heat.

 

[sailoday28]

25362 (Chemical)Your statement"BTW, compression can follow a variety of paths, e.g., isothermic, adiabatic, even isochoric. We can compress a gas at constant volume (!) by the addition of heat"
is interesting. Why not include the paths of constant enthalpy, internal energy, etc,?
In fact compression for two phase, one component could include constant volume and temp.
I think you are stating that compression is any process in which the pressure is changed.

 

[25362]

Sailoday28, you are right. I should have said pressurizing rather than compressing, since the latter involves, by definition, a reduction in volume. This is a frequent error probably stemming from the fact that we call compressed air, air that is subjected to pressures above atmospheric. For that clarification you merit a star.