Work onto Surroundings : Another Traditional Boondoggle 

It should be stated that there are those who realize that work as defined by W=PdV is work done onto the surroundings! But they all seem to fail to realize that this is Lost work i.e. W=(PdV)atm= PatmdVsys is irrreversible work! 

Examples of those that realize W=PdV is done onto the surroundings

      1)http://www.SFU.ca/~MBahrami/ENSC%20388/notes/first%20law%20of%20thermodynamics_closed%20Systems.PDF

 It is particularly interesting that books (1,2) on atmospheric physics tend to discuss how an expanding system and its surroundings are in mechanical equilibrium, and how work done is due to this mechanical equilibrium hence is defined by W=PdV . The most precise example being from the book "Encyclopedia of Atmosphere.." (3) where they write:

 "The type of work of primary importance in the atmosphere is expansion work which is defined as:

      dw=-pdv      (1)

 where dv is the differential volume change associated with the work done against the external pressure."

Again they all fail to realize that this is lost work and all that this means!

Of course the total work is the found by integrating eqn and for lost work which is an exact differential (path independent work we have Wlost= (PdV)atm=PatmdVsys

References:

1) Editors: Julio V. Iribarne and W.L. Godson  book "Atmospheric Physics" Springer Science  & Business Media 1981

2) Slaby, Murray L. "Physics of the Atmopshere and Climate" Cambridge University Press 2012  

3) Editors. North, Gerald R., Pyle, John A., Zhang Fuqing book" Encyclopedia of atmospheric Sciences Vol 1-6" Elsever Press  2014