## Negative sign on work equation

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

Moderators: Chem_Mod, Chem_Admin

romina_4C
Posts: 100
Joined: Thu Jul 11, 2019 12:17 am

### Negative sign on work equation

Why is there a negative on the w = - P times delta V? Is there any situation where this would not be the case?

Tai Metzger 3K
Posts: 103
Joined: Sat Aug 24, 2019 12:17 am

### Re: Negative sign on work equation

W will be negative if the system is doing work (expansion) and will be positive when work is being done on the system (compression). I hope this helps!

Veronica_Lubera_2A
Posts: 106
Joined: Sat Sep 14, 2019 12:16 am
Been upvoted: 1 time

### Re: Negative sign on work equation

Yes, in expansion there will be a negative sign because the system is losing energy.

DanielTalebzadehShoushtari2A
Posts: 53
Joined: Fri Aug 02, 2019 12:16 am

### Re: Negative sign on work equation

I agree with the above explanations in that the whole term for w is positive/negative depending on whether or not the system is expanding or being compressed. You can think of the negative sign in the formula in a different way: w stands for work being done on the system. In this way, expansion would make delta V positive, and work done on the system is negative (because work is being done by system instead). It works similarly for compression.
In this way, w can be put into the context of U = q + w and make sense because work being done on the system is part of the total energy that the system has.

Return to “Calculating Work of Expansion”

### Who is online

Users browsing this forum: No registered users and 1 guest