## Finding W Equations

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

Sophia Diaz - Dis 1B
Posts: 73
Joined: Fri Apr 06, 2018 11:02 am
Been upvoted: 1 time

### Finding W Equations

I don't understand how the equation: w = -P$\Delta$V is found from the integral equation with the summation of steps (the one with the derivative). Can someone please explain where w = -P$\Delta$V comes from?

Follow up question: how does w = -P$\Delta$V relate to the the equation $\Delta$U = $\Delta$H - P$\Delta$V?

Melody P 2B
Posts: 35
Joined: Fri Sep 29, 2017 7:06 am

### Re: Finding W Equations

Hi! So the reason we ended up back with $w= -P\Delta V$ is because we were working with the DEFINITE integral which is basically VFINAL-VINITIAL which is just $\Delta V$
Keep in mind though that this is only when pressure is constant.
The derivative/integral was used for the reversible reaction example he discussed in class because the system was expanding VERY slowly and was doing MORE work.

$\Delta U=\Delta H-P\Delta V$ is $\Delta U=q+w$ but q and w are substituted for q=$\Delta H$ and $w= -P\Delta V$