Can Someone Explain the Calculation of Work Done by Gas Expansion?

[lipwe]

I have little confusion about understanding a lecture note for calculation of work done by a expansion of gas.

According to text, Work done against a force w= - Fx

So work done on the system by surrounding when piston moving w = - P(external)(power exert by outside force on the piston) . X

but I did not get this one.

Work done by the system on surrounding. According to text

W' = -Fx
I did not get this point (minus in front of F) as what ever force exert by system on should be in the direction of movement and in this case exact opposite of - P(external) Am I right? ) but equation gives the right answer i.e w'= - (- P(external))x= P(external )X . In-contrast my one is incorrect

Can somebody help me out to clear this . Thanks for your time in advanced
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[Doc Al]

A bit of semantics here. If F is the force you are pushing against, then the force you must exert is -F, thus the work you do on the system is -Fx.

On the other hand, if F is the force you exert, then the work you do is simply Fx.