# Why is Liter*atm equivalent to Joules?

1. Feb 17, 2015

### patrickbotros

Hey forum! My name's Patrick.
I've been staring at this FOREVER, but I cannot seem to come up with an answer on my own. I've taken 1.5 semesters of physics, but I cannot figure this out. The reason I posted this in Chemistry is because I realized that the R constant can be written as 8.314 J/(mol*K) or as .0821 L*atm/(mol*K). So why is the Joule just a constant multiplier away from L*atm. I think my dilemma is that I cannot think of a SINGLE thing that would have the units L*atm. In your answers, please don't just draw up a formula that you think I should know and then verify that the units work out. I want a CONCEPT that verifies this, not an EQUATION.
Thanks so much in advance! I feel like this is the smartest website on the internet! #IwillNotMissYahooAnswers

2. Feb 17, 2015

### Staff: Mentor

Hey Patrick. Welcome!

At the risk of being facetious, have you confirmed that the units are consistent? That, indeed, L*atm, when expressed in standard units, will be equivalent to Joules?

Then imagine a gas at some pressure (expressed in atm) expanding by some volume (in L). It seems reasonable to express the work done in units of L*atm. (Though I would stick with standard units.)

3. Feb 17, 2015

### patrickbotros

The conversion from L*atm to J is 101.32 J=1(l*atm). And I don't quite understand why that is reasonable, because I don't understand why I'm allowed to say that a gas is expanding. I think if you could sell me on this point then I would understand it: Why would the units of a gas expanding in some fixed volume be L*atm?

4. Feb 17, 2015

### Staff: Mentor

Do you agree that the work done by an expanding gas can be expressed as $P\Delta V$?

5. Feb 17, 2015

### Staff: Mentor

Gas doesn't expand in a fixed volume, gas expands changing volume. And it expands pushing things around apart.

6. Feb 18, 2015

### patrickbotros

Hmmm. I'm not sure if I know why that is. I see that the units would work out:
Work=Force*ΔPosition, so Work=(Force/(unit area))*(ΔVolume)=Pressure*ΔVolume, right? It still seems a bit iffy, though. I don't know what concept says that W=PΔV, so if you could tell me a little more of what you know about that formula, I'd REALLY appreciate it. I know that work is area under the force vs. time curve, but I can't figure out how to connect that fact to pressure and volume.
Thanks so much for all your help!

7. Feb 18, 2015

### Staff: Mentor

What is the most basic definition of work (hint: it involves force and displacement)?

What is the definition of the pressure?

Imagine a piston moving in a cylinder. Assume the piston has a head surface A and is in contact with a gas of pressure P.

What is the force acting on the cylinder?

Now imagine this piston moved by L, compressing the gas. What was the work done?

What is A×L?

8. Feb 18, 2015

### patrickbotros

Hey THANKS! It took me a few minutes, but I totally get it! Pressure=Force/A, So Work=Pressure*A*L, Work=Pressure*∆V!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!