Work done is given by $W = -P_{ext}dV $ according to convention.

Which should mean that in cases of expansion, work done on the system would be negative. If work done is negative, isn't it wrong to say that work done in isothermal reversible process is maximum? Because in irreversible expansions, area covered is smaller but then, if the value is negative, then wouldn't it be that minimum work is done in case of reversible isothermal expansion and maximum for irreversible case?

enter image description here

Image for clarification. This image is for expansion. The dark gray area is for irreversible process and the light gray + dark gray is the work done by reversible process. Clearly reversible process has higher area and hence higher negative value.

  • $\begingroup$ What is the maximum of -5 and -8? $\endgroup$ May 16 '20 at 19:18
  • 1
    $\begingroup$ The work done by the system is maximum. $\endgroup$
    – Buck Thorn
    May 16 '20 at 19:59
  • $\begingroup$ -5 is bigger than -8. Magnitude wise, 8 is bigger than 5. $\endgroup$ May 16 '20 at 20:00
  • $\begingroup$ @BuckThorn Ahh, is that what they actually mean? $\endgroup$ May 16 '20 at 20:00
  • $\begingroup$ Well, in the opposite direction (compression) you would say that the work done by the surroundings is least for a reversible process. $\endgroup$
    – Buck Thorn
    May 16 '20 at 20:04

When we talk about the work done in the above equation,

$W=-P_{ext}dV$ ,

the negative sign only tells us about whether the work is done by the system or work is done on the system. So during expansion the work comes out to be negative indicating the work is done by the system. It is just a physical notion and has nothing to do with the actual magnitude, as we have for acceleration or velocity where negative indicates the opposite direction, just like that.


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