## Integral for work

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

Ellen Amico 2L
Posts: 101
Joined: Thu Sep 19, 2019 12:16 am

### Integral for work

Do we actually need to calculate the integral for the work equation when the system is at equilibrium or do we just calculate using -P∆V?

Rory Simpson 2F
Posts: 106
Joined: Fri Aug 09, 2019 12:17 am

### Re: Integral for work

When you have a reversible system, you would want to use the equation that you get from the integral because the changes in volume are infinitesimal. So, use w = -nRTln(V2/V1) for a reversible system, which you can derive from the integral.

Jasmine Fendi 1D
Posts: 108
Joined: Sat Aug 24, 2019 12:15 am

### Re: Integral for work

I don't think you need to directly calculate the work with the integral. Just memorize the equations that are derived from the integral and know when to use each one!

Brian J Cheng 1I
Posts: 115
Joined: Thu Jul 11, 2019 12:15 am

### Re: Integral for work

I would know why the equation exists. It exists in irreversible conditions (temperature constant, P and V changing at infinitesimally small intervals, so dw = -PdV. P becomes nRT/V, and if you take the integral of both sides you're left with w = -nRTln(V2/V1). It's just helpful to know in terms of linking concepts together.

Kristina Rizo 2K
Posts: 105
Joined: Wed Sep 18, 2019 12:19 am

### Re: Integral for work

Brian J Cheng 1I wrote:I would know why the equation exists. It exists in irreversible conditions (temperature constant, P and V changing at infinitesimally small intervals, so dw = -PdV. P becomes nRT/V, and if you take the integral of both sides you're left with w = -nRTln(V2/V1). It's just helpful to know in terms of linking concepts together.

This was extremely helpful thank you!!