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I do not understand sentences like "Work done on the system is negative". Total work done on a system is a quantity defined as the line integral of the dot product of the net force vector and the displacement vector, over the path of the system. The sign of the value of work done will depend on the force and displacement vectors. Then how does the original sentence make any sense? And I have heard that this sign is opposite in chemistry to what it is in physics. Can someone clear up this mess?

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  • $\begingroup$ The sign of the value of work done will depend on the force and displacement vectors. Right, so why are you confused that work can be negative? $\endgroup$
    – Ghoster
    Commented Oct 19, 2022 at 17:12
  • $\begingroup$ I am not confused about work done, what I am confused about is why do people then say "work done on the system is negative in physics, and positive in chemistry" The question I am asking is not only referring to the opposite signs in physics and chemistry, but also the meaning of assigning such a sign. $\endgroup$ Commented Oct 19, 2022 at 17:13
  • $\begingroup$ Ask the chemists. You’ve correctly stated how physicists define work. How do chemists define work? $\endgroup$
    – Ghoster
    Commented Oct 19, 2022 at 17:14
  • $\begingroup$ Alright, I will ask them too. $\endgroup$ Commented Oct 19, 2022 at 17:15
  • $\begingroup$ Your statement about chemistry was an afterthought introduced by “And…”. It was not the core of your question as written. $\endgroup$
    – Ghoster
    Commented Oct 19, 2022 at 17:16

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This just boils down to the two ways the 1st law of thermodynamics is written:

$$\Delta U=Q-W \ ; \ \Delta U=Q+W$$

The difference simply lies in how you define $W$. In the first equation, $W$ is the work done by the system on its surroundings. Therefore, $W$ is positive when the system expands and negative when it contracts. In the second equation, $W$ is the work done on the system by the surroundings. It's positive if the system contracts (because the surroundings "push" on the sytem) and negative if the system expands.

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