# 1st law of thermodynamics, confusing

Discussion in 'MCAT Discussions' started by tiger85, Mar 25, 2007.

1. ### tiger85

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I am preparing for MCAT from TPR and Kaplan and they both different eqation for the 1st law of Thermodynamics.

In TPR

Change in Internal E = Q - W

and IN kaplan it says

Change in Internal E = Q + W

I also noticed that they both different signs for the work done by the system on its surroundings

In TPR W is Negative and in Kaplan W is positive.

This is pretty confusing I think TPR is right because I think work done by the system that means the energy is lost so it has to be negative (just like enthalpy is negative)

Any suggestion on my opinion.

3. ### soccerpunk60 Junior Member

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I don't know what you're reading, but I'm using kaplan and it gives the equation for internal energy as :

U = Q - W

U as the internal energy of the system

4. ### RPedigo Physician FacultyModerator Emeritus

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No, the change in internal energy is

&#916;U = q + w

And can be written as &#916;U = q - P&#916;V

q = heat
q = work = -P&#916;V for PV-related work-- the MCAT would not ask you about non-PV-related work. If they do, they would first explain it in the passage.

&#916;E and &#916;U, for the purposes of the MCAT, can be used interchangeably. &#916;U can be really used in lieu of &#916;E when you're talking about a system at rest, with no external fields.

5. ### RPedigo Physician FacultyModerator Emeritus

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I will also add, if it really says this, that is a pretty egregious error on their part, and I hope it's been rectified since.

6. ### killinsound Physician

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why would it be egregious? it's all relative.

just know it intuitively...

if you are compressing something, you are putting energy into the system so you need to add the "work", if you are expanding you're taking energy out of the system you are subtracting it.

7. ### RPedigo Physician FacultyModerator Emeritus

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Because no matter how you put it, w = -P&#916;V

If you plug that into their above and incorrect equation, you'll get that:

&#916;U = q + P&#916;V, which gives the incorrect answer.

8. ### killinsound Physician

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i guess... if you want to memorize everything.

9. ### DiverDoc KCUMB 2012

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You just need to be careful and know how to correctly designate whether work is being done BY the system as in U=q-w or on the system for sign values and you will still get the correct answer.

10. ### RPedigo Physician FacultyModerator Emeritus

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I agree with both of you in that intuition is the better approach, but it doesn't change the fact that it is a very significant error on their part, because it's the formula that much of thermodynamics is based off of. I personally didn't consciously memorize the equation, but my research is in the realm of physical chemistry, so I happen to know it.

11. ### killinsound Physician

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agreed.

i think kaplan defines work as P delta V which is "incorrect", but nonetheless serves their purpose and works fine for the mcat...

kinda makes you wonder if that's the reason they left out the enthalpy equation.

12. ### MSTPbound student Moderator Emeritus

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for the first law. Everyone means the same thing, but depending on the field they express it differently, e.g. from the perspective of the system vs. perspective of the environment.

If you check your Chemistry textbook against your Physics text, you may or may not see the same expression for the 1st law... and if you do, grab an engineering text, and I'm CERTAIN you won't see identical expressions, even if they are equivalent.

I came across a nice blurb on Wiki about this, so I'll just link it up here... for those interested in REALLY understanding vs. "plugging and chugging," you might enjoy this explanation:

http://en.wikipedia.org/wiki/First_law_of_thermodynamics#Sign_convention

13. ### RPedigo Physician FacultyModerator Emeritus

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Ah, I did not realize that they also defined work as +PdV. Seems a bit counter-intuitive as a definition, but whatever works for them.

14. ### paranoid_eyes

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E = q - w? That's funny, in my gen chem text it said E = q + w?? Anyways, I always remembered the first law as, "the change internal energy (E) of an isolated system is zero." therefore, in an isolated system, q = -w.

15. ### arsenewenger

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Both eqns are right. It all depends on what is going on in the system.
Expansion... system does work on the surrounding and system therefore loses energy resulting in E = Q-W(i.e. when PV work is done by the system)

Compression...surrounding does work on the system and system therefore gains enegy resulting in E= Q+ W(i.e. PV work is done on the system)

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