## Integral

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

Diana_Diep2I
Posts: 130
Joined: Sat Aug 17, 2019 12:17 am

### Integral

Will we be using the integral equation? When will we use w=-P∆V and when will we use the integral? What is the difference between them? Is it because in the integral, external pressure may not be constant?

Izzie Capra 2E
Posts: 103
Joined: Sat Sep 07, 2019 12:19 am

### Re: Integral

I believe Lavelle will simplify the integral equation next lecture. In the textbook, there is an equation that is much easier to work with--I believe he will be discussing that. This one was used when discussing reversible, isothermal expansion reactions: the ones done in small steps (hence the integral). P is constant but volume is changing. Expansion of gas held at constant pressure is represented by the equation w=p times delta v.

Leonardo Le Merle 1D
Posts: 56
Joined: Wed Feb 27, 2019 12:16 am

### Re: Integral

I also had confusion with this part of the lecture as I'm currently in Math 3B and we haven't covered integrals yet; if someone could clarify what exactly v1{v2 means that'd be great.

Bryce Barbee
Posts: 103
Joined: Wed Sep 18, 2019 12:20 am

### Re: Integral

I dont think that we will use the integral equation. I think it is more to show that the Wby is equation to the area under a graph of pressure vs volume.

Anisha Chandra 1K
Posts: 118
Joined: Thu Jul 11, 2019 12:17 am

### Re: Integral

I think you should just know that an integral is used to sum a series of steps, and in this case infinitesimal changes. It's basically the area under a curve, so the reason we use it to sum up infinitesimal changes is so we can sum the change in a pressure/volume curve.