### Sign for compression vs expansion

Posted:

**Sat Mar 17, 2018 1:46 am**When using the equation for w=-P is it true that for compression the answer will be positive and for expansion it will be negative?

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=75&t=30115

Page **1** of **1**

Posted: **Sat Mar 17, 2018 1:46 am**

When using the equation for w=-P is it true that for compression the answer will be positive and for expansion it will be negative?

Posted: **Sat Mar 17, 2018 1:49 am**

Yes, compression is a negative delta V, which multiplied by negative P, gives you a positive value for work.

Same methodology for expansion, positive delta V.

Same methodology for expansion, positive delta V.

Posted: **Sat Mar 17, 2018 1:52 am**

To determine the sign, think about if the work is done to the system or by the system. W is positive if work is done by the system, and negative if work is done on the system

Posted: **Sat Mar 17, 2018 2:00 am**

Yes, that is correct. You can assume pressure is 1 atm and then plug in values for delta V to check. If you compress something, Vf-Vi will be negative, so the two negative signs will combine to make a positive value. Delta V is positive for expansion, so the value will end up being negative.

Posted: **Sat Mar 17, 2018 11:19 am**

W=-P∆V. ∆V = V_f - V_i.