## Calculus in Chem

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

katherinemurk 2B
Posts: 68
Joined: Wed Nov 15, 2017 3:02 am

### Calculus in Chem

Hi! I never took calculus in high school let alone AP calculus. Can someone explain to me why we need integrals? I know Professor Lavelle answered this question in class but I didn't get the answer. Thank you!

David Effio 1H
Posts: 38
Joined: Wed Feb 14, 2018 3:01 am

### Re: Calculus in Chem

An integral is a very complicated thing to explain (especially in writing), but here is a basic breakdown of why it is useful:

In calculus, an integral allows us to determine the area under a graph using two reference points (the number at the bottom of the S shape, and the number at the top). This is very useful for finding a lot of other things, such as finding an object's change in position from its velocity vs time graph in physics.

In the case of the integral Lavelle showed us in class, it really was just a fancy way of saying:

w = -P * v2 - (-P * v1) = -P * (v2-v1)

Which really just means w = -P * deltaV. This refers to pressure being constant.

I hope that helps!