# Internal energy question

#### medscholhopeful

##### New Member
10+ Year Member
okay i always alway get turned around on this equation U= Q - W. This is my question from my topical

3 moles of a diatomic gas undergoes an adiabatic expansion. If the internal energy of the gas decreases by 200J what is the work done by the gas.
The ans choices
-200
66.7
-66.7

i chose A= -200 joules because i figured sine it is adiabatic no heat is lost so the equation above is U= -W and therefore the workdone by the gas is negative. Unfortunately this is not so according to the answer can someone pls explain..thank you!

#### crazybob

btw U = q + w
in an adiabatic expansion, q = 0, w = - PV and U = -w = - PV
U = -200 = -w, so w = +200

#### Hemichordate

##### Peds
10+ Year Member
I thought U = Q-W

#### thebillsfan

##### Unseasoned Veteran
10+ Year Member
5+ Year Member
I thought U = Q-W
this is a sticky situation. it depends on how you define W. can someone enlighten us as to how the MCAT defines W? all the books say you can define it however you want, but in a question like this, you cannot define it how you want

#### RogueUnicorn

##### rawr.
7+ Year Member
btw U = q + w
in an adiabatic expansion, q = 0, w = - PV and U = -w = - PV
U = -200 = -w, so w = +200
work is not equal to PV in an adiabatic expansion.

#### RogueUnicorn

##### rawr.
7+ Year Member
this is a sticky situation. it depends on how you define W. can someone enlighten us as to how the MCAT defines W? all the books say you can define it however you want, but in a question like this, you cannot define it how you want
if the gas DOES the work, then it's positive. if the gas RECEIVES the work, then it's negative.

#### rocuronium

10+ Year Member
this is a sticky situation. it depends on how you define W. can someone enlighten us as to how the MCAT defines W? all the books say you can define it however you want, but in a question like this, you cannot define it how you want
It is unlikely that this question is from an AAMC test. I highly doubt that a question on the MCAT would make you distinguish between two answers based on a controversial sign convention.

Know the concept behind the law and then the sign conventions won't be an issue.

#### RogueUnicorn

##### rawr.
7+ Year Member
It is unlikely that this question is from an AAMC test. I highly doubt that a question on the MCAT would make you distinguish between two answers based on a controversial sign convention.

Know the concept behind the law and then the sign conventions won't be an issue.
disagree, this is VERY MCAT like where they won't let you take the easy way out by getting just the number alone. the sign convention is not controversial and is entirely conceptual.

#### rocuronium

10+ Year Member
disagree, this is VERY MCAT like where they won't let you take the easy way out by getting just the number alone. the sign convention is not controversial and is entirely conceptual.
We disagree then. As was stated earlier, it depends on how you define work (W).

#### Compass

##### Squishy
Moderator Emeritus
10+ Year Member
Sign conventions have been on every MCAT I've taken, across all subjects, be it motion, velocity, electrical charge, pH, etc.

---

U= Q - W

U = -200
Q = 0
-200 = 0 - W
-200 = - W
200 = W

No sign issues here <.<

#### rocuronium

10+ Year Member
I didn't say that sign conventions wouldn't be on the MCAT. There's more to it than just a positive or negative sign, however. If the positive and negative signs mean different things for different people then there can be some confusion.

#### RogueUnicorn

##### rawr.
7+ Year Member
I didn't say that sign conventions wouldn't be on the MCAT. There's more to it than just a positive or negative sign, however. If the positive and negative signs mean different things for different people then there can be some confusion.
if you stay consistent it should be no problem. i still do not understand where you are getting this supposed controversy from

#### medscholhopeful

##### New Member
10+ Year Member
btw U = q + w
in an adiabatic expansion, q = 0, w = - PV and U = -w = - PV
U = -200 = -w, so w = +200
yeah i get the math part of it.. what i had a question on was the convention + vs - but i think i may have figured it out.. thks

#### rocuronium

10+ Year Member
if you stay consistent it should be no problem. i still do not understand where you are getting this supposed controversy from
I completely agree.

My point is that different sign conventions exist, and that I can understand how people can be confused, especially when people are adamant that their convention is correct. That's what I mean about controversial.

As I said from the beginning: Know the concept behind the law and then the sign conventions won't be an issue.

#### medscholhopeful

##### New Member
10+ Year Member
this is a sticky situation. it depends on how you define W. can someone enlighten us as to how the MCAT defines W? all the books say you can define it however you want, but in a question like this, you cannot define it how you want
I agree with you cos this is where i get thrown off, i have been consistently missing these type of questions based on this convention crap but i think i may have found a way to make it make sense.

U= Q -W
I look at it from the perspective of the surroundings instead of the system.. for instance i say when the work done by a gas is positive, it could mean that the gas is increasing the energy of the surrounding..hence value for W is positive(because energy of surroundings in increasing). When the gas is being worked on, then the surrounding is losing heat to the system.. therefore it is negative.

So using this new found logic of mine the ans above become +200 because the process is adiabatic so no heat is being exchanged, so Q= 0 which gives the equation U= -W - this expression means the work is being done by the gas which translates to surroundings gaining energy in the form of wok thus W is +200J

This might be a lil weird but when i used this method of thinking i got the right answers to 4 other questions i missed so......hope it helped.

#### RogueUnicorn

##### rawr.
7+ Year Member
I completely agree.

My point is that different sign conventions exist, and that I can understand how people can be confused, especially when people are adamant that their convention is correct. That's what I mean about controversial.

As I said from the beginning: Know the concept behind the law and then the sign conventions won't be an issue.
gotcha

#### inaccensa

10+ Year Member
I agree with you cos this is where i get thrown off, i have been consistently missing these type of questions based on this convention crap but i think i may have found a way to make it make sense.

U= Q -W
I look at it from the perspective of the surroundings instead of the system.. for instance i say when the work done by a gas is positive, it could mean that the gas is increasing the energy of the surrounding..hence value for W is positive(because energy of surroundings in increasing). When the gas is being worked on, then the surrounding is losing heat to the system.. therefore it is negative.

So using this new found logic of mine the ans above become +200 because the process is adiabatic so no heat is being exchanged, so Q= 0 which gives the equation U= -W - this expression means the work is being done by the gas which translates to surroundings gaining energy in the form of wok thus W is +200J

This might be a lil weird but when i used this method of thinking i got the right answers to 4 other questions i missed so......hope it helped.
I look at this a little differently. When the work is done by the gas, W =P delta V, we are looking at the change in volume. So, when gas done the work in moving the piston, the volume of the gas is expanding and thus the final volume is greater than the intial volume and thus the change in volume is positive and the work done by the gas is positive. Here the internal energy is decreasing.

Now when the piston is forced down, the volume of the gas decreases and thus the final volume is less than the initial volume and therefore the work done is negative. Here the internal energy is increasing.
Is this correct, i never think of this interms of internal energy

10+ Year Member
7+ Year Member