W= - P external x Delta V

[Trang Tran 1H]

Hi. I was wondering whether the formula W=-P. delta V, the negative sign shows it goes against the external pressure. So if the problem doesn't say it goes against the external pressure, do I still include the negative sign in the front? Thank you

[Jennifer Huynh 3I]

I think the equation makes sense with the negative sign both when the volume of the system increases or decreases.
W = -P(deltaV)
When the system does work on the surroundings and the piston moves up, the volume of the system increases (deltaV = Vf - Vi = +), and work is a negative value because the system loses energy as work is done.
When the surrounding does work on the system and the piston compresses, the volume of the system decreases (deltaV = Vf- Vi = -), and work done is a positive value (negative P times negative change in volume = positive work) because the energy from the surroundings is put into the system.