## Sign of Work

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

Junghyuk_Park_1I
Posts: 34
Joined: Wed Sep 21, 2016 2:56 pm

### Sign of Work

When is work positive or negative in terms of thermodynamics? When the system is doing work (what sign)? When work is done on the system (what sign)?

Zoe Robertson 2H
Posts: 28
Joined: Fri Jun 17, 2016 11:28 am

### Re: Sign of Work

When the system is doing work, it's negative.
When work is done on the system, it's positive.

If it helps, you can think of it like a person doing work... if they do it, they're exerting energy and will become tired (negative), and if someone does work on them, they're gaining energy so it would be positive (not so sure what a real life analogy would be lol) but yeah that's just something I use!

Amy Ko 3C
Posts: 24
Joined: Sat Jul 09, 2016 3:00 am

### Re: Sign of Work

Hi there!
To figure out the sign of work, we should refer to...
If we define work as W= -PΔV, we can figure out the sign of W to plug intp ΔU = Q + W
If the piston moves out, then there is an increase in volume. Thus, W = -PΔV and ΔV is positive. W is negative. The energy of the system has decreased by an amount of W. The work is done by the system.
If the piston is compressed, there is a decrease in volume. Thus, W = -PΔV and ΔV is negative. W is positive. The energy of the system has increased by an amount of W. The work is done on onto the system.

Hope this helps! :)

angelicapayne
Posts: 10
Joined: Wed Sep 21, 2016 2:58 pm
Been upvoted: 1 time

### Re: Sign of Work

when a system does work on its surroundings, the system is exerting work so work is negative. if the surroundings are doing work on the system, work is positive because the system is absorbing the work!

samuelkharpatin2b
Posts: 55
Joined: Wed Sep 21, 2016 2:57 pm

### Re: Sign of Work

When the system itself is doing work, the sign is negative because it's losing work. When something is doing work on the system, the sign is positive because the system is absorbing the work.