Work

[Victoria Liang 3L]

Question #3 in workbook

Consider a gas at an initial pressure of 5.0 atm and an initial volume of 1.0 L that undergoes a change to 2.0 atm and 4.0 L by two different pathways. The gas is at 298 K.

Pathway 1:
P1 = 5.0 atm P2 = 5.0 atm P3 = 2.0 atm
V1 = 1.0 L V2 = 4.0 L V3 = 4.0 L

Pathway 2:
P1 = 5.0 atm P2 = 2.0 atm P3 = 2.0 atm
V1 = 1.0 L V2 = 1.0 L V3 = 4.0 L

Calculate the work for these two pathways..


The solution says
work = -p (delta)V
Pathway 1: -5 atm (3L)
Pathway 2: -2 atm (3L)

I don't understand why they are different pressures...

[Kayla Denton 1A]

It's easy to visualize on the graph! If you plot the two pathways with pressure on the y axis and volume on the x axis, the work is simply the area under the graph.
If you're having trouble with that I'll try to explain it in words too. So w = -P x delta V. So you want to find a volume CHANGE and the constant pressure at which this change occurs.

Path 1 has the volume change at P = 5.0 atm so this is the pressure used for P x delta V.
Path 2 has the volume change at P = 2.0 atm so this is the pressure used for P x delta V.
Delta V is the same in both cases.

Hope this helps!

[Justin Le 2I]

Also, for this problem there needs to be two separate pathways because doing both at the same time is too difficult. It is easier if we split them up into two parts, one where the pressure changes and one where the volume changes. This is similar to when we have to separate irreversible changes into multiple reversible changes.