## Expansion Work vs. Nonexpansion Work

$\Delta U=q+w$

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Ashley Garcia 2L
Posts: 33
Joined: Fri Sep 29, 2017 7:05 am

### Expansion Work vs. Nonexpansion Work

What is the difference between expansion work and nonexpansion work? Why does the equation for expansion work have a negative sign in front of the external pressure? What is the equation for nonexpansion work?

Equation for expansion work: w = -Pex ΔV

Nora Sharp 1C
Posts: 53
Joined: Sat Jul 22, 2017 3:00 am

### Re: Expansion Work vs. Nonexpansion Work

Part of your question has actually been already answered here: viewtopic.php?f=75&t=25593

The equation w = - (external pressure)(change in volume) actually only applies to one of the expansion work scenarios given by the book. This equation applies to what the book calls an irreversible process, because the system is being subjected to a measurably large constant external pressure that causes the volume to increase or decrease.

In this case, the sign is negative to account for the definition of work. Think of a gas in a container with volume that can change. When the gas expands, it expends energy by doing work on the container(work is negative because the system, the gas, loses energy). When the gas compresses, an outside force is using work to compress the gas( work is positive), which puts energy into the system.

So, deltaV = Vfinal- Vinitial. When the system loses volume(energy is put into the system), delta V is negative. When the system gains volume(energy is expended by the system and lost), deltaV is positive. However, when work is put into the system, work is positive, and when work is expended by the system, work is negative. If we didn't have that negative sign there, our equation w = P*deltaV would tell us that a system that loses energy would have a positive work sign, which doesn't fit with the definitions that were just established. The negative sign is there so that a decrease in volume means work is put into the system(w is positive), and an increase in volume means work is expended by the system ( w is negative).

Katie Blann 1E
Posts: 29
Joined: Tue Nov 15, 2016 3:00 am

### Re: Expansion Work vs. Nonexpansion Work

Would the equation for non expansive work just be w= force x distance then?

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