Heat Flow for Isothermal Compression

[triage]

The work (W) required per unit mass to compress Isothermally
an ideal gas from a low pressure P1 to a higher pressure P2 is shown as:

W=RTLn(P2/P1)

It is my understanding that this equation represents the absolute work referenced to a pressure of 0 and that if P1 is greater than ambient Pa, and the compression is being completed within the natural atmosphere, the acutal net work would subtract the ambient pressure work component:

Wnet=RTLn(P2/P1) - Pa (V1-V2)

where: Pa is ambient pressure
V1 is the volume of the unit mass at P1
V2 is the volume of the unit mass at P2

If the above is correct, my question is relating to the amount of heat Q, which must be removed during compression from P1 to P2.

My text indicates that the amount of heat Q is equal to the absolute work W, but common sense tells me that is should be equal to the net work Wnet.

Can someone tell me which is correct?

 

[zdas04]

I calculate the heat load on a compressor (which is never isothermal) as

T2=T1(P2/P1)^((k-1)/k) and

Q = mc(T2-T1)

I don't know that you can't approach it from a work viewpoint, but I've never done it that way. Your Wnet seems to be subtrating a total work (ft-lbf, for example) from specific work (ft-lbf/lbm, for example) so you might take a look at that prior to going much further.



David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[25362]

The system presented by triage shows, as it were, two compressors acting on the gas simultaneously: the piston's (net) work, "helped" by the surrounding expanding air work contribution at the boundary.

The gas is actually getting the combined total work W=-Q.

Therefore, the heat to be removed from the gas is as triage's text says.

In a reciprocating piston-cylinder device, the work contribution from the surrounding air would cancel out.

 

[triage]

Thanks 25362, your explanation makes it clear
Triage