## Work sign changes

$w=-P\Delta V$
and
$w=-\int_{V_{1}}^{V_{2}}PdV=-nRTln\frac{V_{2}}{V_{1}}$

rkang00
Posts: 69
Joined: Fri Sep 28, 2018 12:25 am

### Work sign changes

Typically if a system is compressed, is the sign for work + and - for expansion?
If so, what's the reason?

Hannah Yates 1K
Posts: 59
Joined: Fri Sep 28, 2018 12:27 am

### Re: Work sign changes

I think work is negative when the system is doing work, and positive when the system is getting work done to it. So when a system expands, work is negative, and when a system is compressed, work is positive.
I might be wrong though

Cole Doolittle 2K
Posts: 30
Joined: Fri Sep 28, 2018 12:20 am

### Re: Work sign changes

I believe this is because the formula is w = - P (delta V). If it is expansion, delta V will be positive and thus work negative. In compression delta V is negative and thus work is positive.

deepto_mizan1H
Posts: 65
Joined: Fri Sep 28, 2018 12:16 am

### Re: Work sign changes

When the system is expanding, the volume will be a positive value, ultimately making the work value negative.

When it's compressed, the volume will be a negative value, which makes the work in total a positive value.

So, when the system does work, it is negative. When work is done on the system, it'll be a positive value. Thinking of this in terms of the delta V and its sign will help to conceptualize why the work changes sign based on what is being done.