Thermodynamics - work in adiabatic, isothermal, isobaric

[eprparadox]

Homework Statement

21. A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal, or isobaric. Rank those three processes in order of the work required of an external agent, least to greatest.
A. adiabatic, isothermal, isobaric
B. adiabatic, isobaric, isothermal
C. isothermal, adiabatic, isobaric
D. isobaric, adiabatic, isothermal
E. isobaric, isothermal, adiabatic

Homework Equations

The Attempt at a Solution

If I graph these three curves on a P-V axes, it seems to me that the work by the external agent will be positive because the volume is getting smaller. Also, the work is like the area under the curve for any of these processes, and so I get it choice A as my answer.

The isobaric path encloses a rectangle, the isothermal a hyperbola and the adiabat, a path that encloses less area than the isothermal.

I'm only checking because the answer given is E. And I don't know where I'm going wrong.

Thanks a lot ahead of time.

 

[aim1732]

The problem lies in what you treat external work as. The most accepted convention-well at least in my part of the world-is that work energy coming in the system is negative hence the inequality you built would be reversed.Your logic seems good enough.