Positive work done on a gas, and the new Pretty Good Physics - Secure site

"Pretty Good Physics - Secure" is essentially a wiki for physics teachers.  It includes all sorts of files - old tests, lab activity sheets, quizzes, homework problems, whatever people have shared.  It also includes most publicly released AP materials.  The College Board is okay with that, because we are sharing teacher-to-teacher.  Gardner Friedlander and Paul Lulai do tremendous work managing the wiki, being sure that yes indeed everyone who accesses it is an actual physics teacher.

You can access the site here, and follow the directions to join.  (If you're a physics student, you must ask your teacher to join.  Gardner brings out the nuclear arsenal upon non teachers who request access.  And he does know some nuclear physics.  :-)  )

One of the new features of the wiki, since it migrated to google this summer, is that it's easy to subscribe to an email list for all members.  People can ask physics teaching questions of the community, and generally a response comes back within hours.  Don't worry, you don't have to subscribe to this list to access the wiki.  I like it, though, because it has provided a venue for some excellent discussions, it's helped a lot of relatively new teachers, and it has a positive vibe (unlike some other notorious teacher message boards).  One commenter mentioned that it's "just like the old days", presumably harkening back to USENET or stone tablets or something. 

Just yesterday, a participant asked for clarification about a problem in the 5 Steps to a 5: AP Physics 2 book.  Before I answer, a disclaimer - while I wrote the Physics 1 and Physics C versions of the 5 Steps series, I didn't write the Physics 2 book.  This is not my question.  I very much LIKE this question.

A teacher said he was "boggled" - great, great word choice there - with the sign convention for positive and negative work.  And in particular, what is up with the signs in the solution?  Why are there so many negative signs?  Aarrgh!  Boggled, indeed.

Much as I like this question, I would have written the answer very differently.  It's making this teacher and his students think about irrelevant mathematical details rather than concepts.

I prefer the simple and conceptual approach - work done ON a gas is considered positive, because work done ON the gas generally contributes to an increase in the gas's internal energy.  Compression is work done ON the gas.  In every case in the problem, the volume is compressed - therefore, each process represents positive W.

Then, the amount of work done is the area under the PV graph.  By inspection, the area under the D graph is greater than under E or F.  So more positive work done in the D process.  THAT'S IT!