## Integral Calculations

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

Jeremy_Guiman2E
Posts: 82
Joined: Fri Sep 28, 2018 12:29 am

### Integral Calculations

I think we use the integral when we're trying to sum an infinite number of steps (in volume changes?), but can someone explain when to use it and how/why we need to?

peteryim
Posts: 54
Joined: Sat Sep 07, 2019 12:17 am

### Re: Integral Calculations

You're right, integrals are used to quickly find the sum of an infinite number of sums. I don't think Lavelle has given us any problems that require us to use it yet...

Ashley Fang 2G
Posts: 102
Joined: Fri Aug 30, 2019 12:17 am

### Re: Integral Calculations

You use the integral in a pressure vs volume graph to find the work of expansion
Since W=-PdeltaV, calculating the integral would give the area under the line (W)

For irreversible expansions, just calculating the rectangular area would be enough
But for reversible expansions, you have to use the integral to find the total area under the line

See Dr. Lavelle's attachments!
https://lavelle.chem.ucla.edu/wp-conten ... ansion.pdf
https://lavelle.chem.ucla.edu/wp-conten ... ansion.pdf

Brian Tangsombatvisit 1C
Posts: 119
Joined: Sat Aug 17, 2019 12:15 am

### Re: Integral Calculations

For reversible expansion, if we know the number of moles, temperature, and final/initial volume of the sample, we can just use the simplified version of the integral, which is w = -nRTln(V2/V1) instead of integrating. If we were to integrate, I believe we would need a function for pressure with volume as its input variable.