Submitted by Adam Johnson / Harvey Mudd College on Thu, 06/18/2020 - 16:06

A short play, by Adam, Nancy, Anne, and Barb.

Enter, four chemists, one scratching his beard in confusion, two trying desperately to help, not knowing their efforts are in vain, and one just waiting to make a self-serving gen chem dimensional analysis point...

Can someone quickly remind me why doubling a reaction doubles delta G but not E naught?

Nancy, 2:35 PM

Yes. E is a potential, G is a potential energy.

Anne, 2:36 PM

delta G equals negative nFE

Nancy, 2:36 PM

G is how much gasoline your trip will burn.

Anne, 2:36 PM

E is the height of the waterfall

oops, mixing metaphors.  I'm outta here.

Nancy, 2:36 PM

E is how much gasoline you burn per mile

(rofl)

Doubling your trip length doubles the gas consumption, not the mileage

Anne, 2:37 PM

n is the number of electrons going over your waterfall, and F is just a constant....  don't you have yours mixed up Nancy?

ok, I see your way of seeing it.

Still trying to think of what G would be in my case...exactly...

Nancy, 2:38 PM

Or, to use Anne’s analogy, E is the energy that a waterfall generates for each gallon of water

G is the energy generated by the total volume of water

So if you have a rainstorm, the energy generated doubles (or if you let the waterfall run for twice as long, it doubles...either way, double the water), but it doesn’t change energy per gallon.

I do like Anne’s “the E is the height” metaphor, because it captures the unit change.

F is a unit conversion fudge factor (like g in U = mgh)

n is like m, g is like F, and h is like E.

But we don’t talk about height as “gravitational potential”...we should...

Voltage is the “energy per electron” in weird units

The Anne and Nancy show confuses me more than I was before so I’m going to forget I looked.

Anne, 2:56 PM

But we do talk about height as gravitational potential, sometimes.  At least for this analogy, it works well.  Taller waterfalls lead to water hitting the ground with more energy.  (I have to admit, I'm not following the Anne and Nancy show 100%, either.)

Nancy, 2:57 PM

RIght.

The thing I don't like about height is that we don't internalize the idea that "height is just the measure of the energy per mass when you drop something". I mean, height is that, but we don't really internalize that this is what height "means".

We think about the impact of height on everything from whether we can reach something on a shelf to whether someone would make a good dance partner. So one might get the analogy and still miss the important bit: voltage is like height in that it is the energy per electron in the way that height is an energy per gram.

The thing that I think confuses people about E vs. G is that one is intensive and the other is extensive.

So while the traditional analogy is true (and, in fact, highly accurate), it may not alleviate the confusion.

This all would make sense if I wasn’t a founding member of the insomnia patrol.

Nancy, 3:08 PM

So, the waterfall analogy can work if you are sending students over a waterfall in barrels, all the students have the same weight, and you're using the impact energy of the students at the bottom to power a generator.

In this analogy, E is the height of the waterfall, G is the energy gained by sending your class over a waterfall in barrel, n is the number of students, and F is the (energy)/(student mass*meters) fudge factor.

Double the number of students, you double the energy gained, but you don't change the height of the waterfall.

Waterfalls aren't quantized, so you have to make the thing going over the waterfall into a quantum (a student in a barrel) like an electron.

I like quantizing energy in units of "students in a barrel." That’s 200 kJ/SiaB

Barbara, 3:19 PM

Sounds like a dimensional analysis problem in the making.

Nancy, 3:20 PM