The integral equation

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

Hector Acosta Discussion 1H
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Joined: Fri Sep 29, 2017 7:04 am

The integral equation

Why do we need an integral to calculate work?

Xin He 2L
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Joined: Fri Sep 29, 2017 7:05 am

Re: The integral equation

You don't need to use calculus, you just need the use the equation given in the book for isothermal reversible expansion. I believe the equation is w=nRT log(Vfinal/Vinitial )

Kevin Tabibian 1A
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Re: The integral equation

The integral is an equation that gave origin to several others we derived in class. It was meant to help our comprehension, yet we do not need it in our calculations.

Yea Eun Lee 1H
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Joined: Fri Sep 29, 2017 7:06 am

Re: The integral equation

The integral is used for deriving the equation for finding work in a reversible gas expansion. The integral is used to find the area of the curve in a volume vs. pressure graph (you can find that on p 266 of the textbook). The graph is curve because in a reversible gas expansion, the external pressure is reduced infinitesimally, and the area underneath the curve is the work since PV= w (and it's a volume vs pressure graph). Hope that made sense!

Abigail Yap 2K
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Re: The integral equation

We used integrals to derive the work equations because when systems are at equilibrium, changes within them occur infinitesimally. The integral allows us to sum together all of these small steps to calculate the total work. As mentioned above, the integrals were only used for the formula derivations and are not needed for actual work calculations.

Tasnia Haider 1E
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Re: The integral equation

Will we need to know how to derive the integral for the test/ midterm coming up?

Niyanta Joshi 1F
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Joined: Thu Jul 13, 2017 3:00 am

Re: The integral equation

I believe we are expected to understand how the equations come into place, however I doubt that we would actually need to do calculations to derive the equation on the test.

Christina Bedrosian 1B
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Joined: Fri Sep 29, 2017 7:05 am

Re: The integral equation

I also don't believe we will actually have to derive anything on the tests because it isn't the point of the equation. We only derived it to help us understand where it came from.

Marina Georgies 1C
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Joined: Sat Jul 22, 2017 3:00 am

Re: The integral equation

The equation is similar when dealing with pressure right? Except it's Pinital/Pfinal because of the inversely proportional relationship between P and V?