Thermo Sign Convention, Help!

[Nateftw]

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Hello everyone,

I am having some issues with sign conventions. I have always been taught that if a system does work on its surroundings, work is negative; W=- PdV and dE=Q+W. However, the opposite is true according to Kaplan. dE=Q-W and W=+PdV. If a system does work on its surroundings, work is positive.

Now, in theory everything would be fine and dandy, and I would get the same answers no matter what convention I use...EXCEPT that the sign would be complete opposite.

So now, i'm worried about which convention to use. I do not want to get an answer wrong due to a sign error. Here is an example of what I am talking about.

Straight from Kaplan..

One mole of a monoatomic ideal gas undergoes an isobaric expansion, gaining 1 cubic meter of volume. If the pressure of the gas is 1000 Pa, what is the work done by the gas?

A)-1500J
B)-1000J <----what I put
C)+1000J <---"real answer"
D)+3000J

My logic..: W= - PdV where dV is positive because the final volume> initial volume. Therefore work is negative.

Is the DAT going to test on this? Help appreciated, thank you

 

[lippy104]

Hello everyone,

I am having some issues with sign conventions. I have always been taught that if a system does work on its surroundings, work is negative; W=- PdV and dE=Q+W. However, the opposite is true according to Kaplan. dE=Q-W and W=+PdV. If a system does work on its surroundings, work is positive.

Now, in theory everything would be fine and dandy, and I would get the same answers no matter what convention I use...EXCEPT that the sign would be complete opposite.

So now, i'm worried about which convention to use. I do not want to get an answer wrong due to a sign error. Here is an example of what I am talking about.

Straight from Kaplan..

One mole of a monoatomic ideal gas undergoes an isobaric expansion, gaining 1 cubic meter of volume. If the pressure of the gas is 1000 Pa, what is the work done by the gas?

A)-1500J
B)-1000J <----what I put
C)+1000J <---"real answer"
D)+3000J

My logic..: W= - PdV where dV is positive because the final volume> initial volume. Therefore work is negative.

Is the DAT going to test on this? Help appreciated, thank you

Well it says the work done by the gas. Think of your system as the gas and it has a pressure exerted on it. Intuitively you would think this gas would have to do some work to expand against the opposing pressure, so the sign would have to be positive. The sign on the equation you posted depends on the convention your using, so it can be positive or negative really. Theres nothing too complicated on the DAT regarding thermo, so you should be fine just using intuition.

 

[Nateftw]

Well it says the work done by the gas. Think of your system as the gas and it has a pressure exerted on it. Intuitively you would think this gas would have to do some work to expand against the opposing pressure, so the sign would have to be positive. The sign on the equation you posted depends on the convention your using, so it can be positive or negative really. Theres nothing too complicated on the DAT regarding thermo, so you should be fine just using intuition.

ok thanks for the response. To be safe, I think i'm going to just switch my convention anyway to the one you are using. System doing work on the surroundings= +w (it is more intuitively friendly). It's just the opposite that I was taught in gen chem...physics...biochem..and pchem... haha oh well. Thanks again

 

[Baylor2011]

Hmm..chad uses the - convention too...he also says that when the system does work w = -. When work is done on the system, w is positive. That's weird...

via wiki:

Chemical thermodynamics studies PV work, which occurs when the volume of a fluid changes. PV work is represented by the following differential equation:[8]

where:

• W = work done on the system
• P = external pressure
• V = volume

So W is work done ON the system...and if you think about it...that sounds right because the gas is EXPANDING, therefore work is negative on the system. Now if you look at it from the gas point of view...it has to put a lot of energy in to expand therefore it's work should be positive. If you look at it like a piston in a cylinder. If the gas expands, it's going to push the piston up...therefore its work expenditure is "negative" since it's not doing work, it's actually getting pushed back. From the gas POV, its having to use a lot of energy to push the piston and expand, therefore a positive energy expenditure "work"

So to sum it up..if it asks work done by the gas, or done on the system...have to be careful what it's asking. By the gas would be positive, but by the system would be negative

 

[Nateftw]

Hmm..chad uses the - convention too...he also says that when the system does work w = -. When work is done on the system, w is positive. That's weird...

via wiki:
So W is work done ON the system...and if you think about it...that sounds right because the gas is EXPANDING, therefore work is negative on the system. Now if you look at it from the gas point of view...it has to put a lot of energy in to expand therefore it's work should be positive. If you look at it like a piston in a cylinder. If the gas expands, it's going to push the piston up...therefore its work expenditure is "negative" since it's not doing work, it's actually getting pushed back. From the gas POV, its having to use a lot of energy to push the piston and expand, therefore a positive energy expenditure "work"

So to sum it up..if it asks work done by the gas, or done on the system...have to be careful what it's asking. By the gas would be positive, but by the system would be negative

It depends on what you define the system to be. I thought that the gas was the system?

Kind of confused on what you said. "by the gas would be positive, but by the system would be negative." Isn't the gas the system?

If a gas is in a cylinder, and pushing the piston up, one convention will say that work is positive, and one will say work is negative. Which one are you sticking with?

 

[lippy104]

It depends on what you define the system to be. I thought that the gas was the system?

Kind of confused on what you said. "by the gas would be positive, but by the system would be negative." Isn't the gas the system?

If a gas is in a cylinder, and pushing the piston up, one convention will say that work is positive, and one will say work is negative. Which one are you sticking with?

Don't overthink it theres not going to be an extremally hard thermo question on the test. Just think that if you have to push against a force or something, the work would be positive. And if you basically let something happen the work will be negative. So you would say the work done by the gas is positive and the work done by the surroundings would be negative, but they would both have the same sign.