## work integral

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

Ami_Pant_4G
Posts: 106
Joined: Sat Aug 24, 2019 12:17 am

### work integral

When exactly would we need to use the work integral rather than the simplified version of -p(delta)v? Thanks in advance.

JonathanS 1H
Posts: 101
Joined: Thu Jul 11, 2019 12:17 am

### Re: work integral

We can use -p(delta)v when we have constant pressure, because we can take of the p from the integral since it is a constant. In some way, we are always using the integral, but with constant pressure we can simplify it to make life easier. In the case of pressure not being constant, we must use the integral.

Angus Wu_4G
Posts: 102
Joined: Fri Aug 02, 2019 12:15 am

### Re: work integral

We use -p(delta)v when the pressure is constant, because it allows us to factor out the variable P from the integral to end up with just integrating the constant "1", which simplifies the integral into a simple -p(delta)v. If the pressure were not constant, then you cannot factor the P variable outside of the integral, and then you would need to use calculus and compute the value of the integral.

Noe BM 1J
Posts: 50
Joined: Sat Sep 07, 2019 12:17 am

### Re: work integral

Are there any homework problems where we have to use the integral instead of the simplified formula?

Angus Wu_4G wrote:We use -p(delta)v when the pressure is constant, because it allows us to factor out the variable P from the integral to end up with just integrating the constant "1", which simplifies the integral into a simple -p(delta)v. If the pressure were not constant, then you cannot factor the P variable outside of the integral, and then you would need to use calculus and compute the value of the integral.

Owen-Koetters-4I
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Joined: Fri Sep 28, 2018 12:16 am

### Re: work integral

integral calculus is used when we don't have constant pressure

Nick Lewis 4F
Posts: 111
Joined: Wed Sep 18, 2019 12:18 am

### Re: work integral

Does anyone know if we are going to have to deal with inconsistent pressure? Are we expected to know how to use calculus in this class?

Angus Wu_4G
Posts: 102
Joined: Fri Aug 02, 2019 12:15 am

### Re: work integral

Noe BM 1J wrote:Are there any homework problems where we have to use the integral instead of the simplified formula?

Angus Wu_4G wrote:We use -p(delta)v when the pressure is constant, because it allows us to factor out the variable P from the integral to end up with just integrating the constant "1", which simplifies the integral into a simple -p(delta)v. If the pressure were not constant, then you cannot factor the P variable outside of the integral, and then you would need to use calculus and compute the value of the integral.

I believe not, since we derived the integrated equation in class, which is w=nRTln(V2/V1), which is the work when the system is isothermal reversible. Whenever the pressure is not constant, simply use this equation. We only used the integral during lecture to help explain how this equation came about