Sign conventions for work done by/on a system

[cookiemnstr510510]

Homework Statement

Consider the reaction between zinc and hydrochloric acid as it takes place in a nearly evacuated, insulated container attached to a piston-cylinder assembly. When this reaction happens the piston moves up slightly due to the chemical reaction. Is the work positive or negative? Take the Zinc and hydrochloric acid as the system.

Relevant Equations

conventions?

I am a bit confused on the definition/convention of work. In some books I see statements that say :

"If work is done on the system, its sign is positive. If work is done by the system, its sign is negative."

And in other books I see things like:
"By convention, work is regarded as positive when the displacement is in the same direction as the applied force and negative when they are in opposite directions."

Since the system is the zinc and HCl and the piston moves then work is being done BY the system so work would be negative (according to the first quoted statement).

But if I look at the second quoted statement above I get a bit confused, is the "Applied Force" coming from the chemical reaction? If so then the force and displacement are in the same direction and work should be negative.

Or is the point that some books use one convention and other books use the other?

I would like to make sure that in this example the "Applied Force" is coming from the chemical reaction. I guess another possibility is the "Applied Force" is coming from the surroundings holding the piston in place with whatever atmospheric pressure it is applying to the system.

Thanks!

 

[anuttarasammyak]

Say we have a system and its environment and energy flows from the system to the environment,
work done is negative for the system and positive for the environment.
Similarly say energy flows from the environment to the system, work done is negative for the environment and positive for the system. I think it is the way to investigate the sign.

 

[Chestermiller]

I don't like either of your definitions. Here is a 2-step recipe for always getting it right:

STEP 1: Specifically identify what work you are talking about, in terms of saying in words what entity is doing work on what entity. For example, say "I am talking about the work being done BY A ON B." In your example, you would say "I am talking about the work being done BY the reaction mixture (my system) ON the piston (the surroundings)"

STEP 2: Once STEP 1 is completed, look at the force exerted by entity A on entity B. If it is in the same direction as the displacement of the interface between entities A and B, then the work is positive, and, if it is in the opposite direction of the displacement of the interface between entities A and B, then the work is negative. In your example, the force exerted by the reaction mixture is in the same direction as the displacement of the interface with the piston, so the work you have identified in STEP 1 is positive.

That's all there is to it.

 

[rude man]

Also, there is confusion in stating the 1st law of thermodynamics.
Physicists usually write dS = dQ - dW
where work W is done BY the system (gas etc.)
wheras chemists for some reason prefer dS = dQ + dW
where W is work done ON the system.

 

[Chestermiller]

Also, there is confusion in stating the 1st law of thermodynamics.
Physicists usually write dS = dQ - dW
where work W is done BY the system (gas etc.)
wheras chemists for some reason prefer dS = dQ + dW
where W is work done ON the system.

I think you meant dU, not dS.

 

[rude man]

I think you meant dU, not dS.

Hi Chet,
I think I did too.

 

[cookiemnstr510510]

I don't like either of your definitions. Here is a 2-step recipe for always getting it right:

STEP 1: Specifically identify what work you are talking about, in terms of saying in words what entity is doing work on what entity. For example, say "I am talking about the work being done BY A ON B." In your example, you would say "I am talking about the work being done BY the reaction mixture (my system) ON the piston (the surroundings)"

STEP 2: Once STEP 1 is completed, look at the force exerted by entity A on entity B. If it is in the same direction as the displacement of the interface between entities A and B, then the work is positive, and, if it is in the opposite direction of the displacement of the interface between entities A and B, then the work is negative. In your example, the force exerted by the reaction mixture is in the same direction as the displacement of the interface with the piston, so the work you have identified in STEP 1 is positive.

That's all there is to it.

Hello @Chestermiller
I really like your explanation and I can follow this formula each time.

Will your method always work? Or does it depend on different books conventions?

Thanks a bunch!
Have a great day

 

[jbriggs444]

Hello @Chestermiller
I really like your explanation and I can follow this formula each time.

Will your method always work? Or does it depend on different books conventions?

The short answer is that it always works. It won't tell you whether a particular quantity that the book uses is work done "by the system" or work done "on the system". But it will always tell you whether the work done "by the system" at a particular interface is positive or negative.

But...

One place where things can get tricky is when you have an interface where the material at the interface is moving one way and the interface itself is moving a different way. That will not happen with a piston. The interface at the piston moves with the piston. But it can happen in other situations.

It is the movement of the target material acted on by the force that matters. Not the movement of the point where the force is applied.Consider, for instance, a car driving at 60 kph down the highway as you watch from a car driving at 30 kph and being passed. You ask yourself: "Is the work being done by the tire on the highway positive or negative?"

From your point of view, the interface between tire and highway is moving forward past you at 30 kph. The force by the tire on the highway is rearward. The movement of the interface is forward. You could apply the rule and conclude that the work being done on the highway is negative. This conclusion would be incorrect.

You should be looking at the movement of the highway surface at the point of contact. The highway surface is moving rearward. That is the same direction as the force on that highway material. The work being done on the highway is positive from your point of view. As you should expect -- it tends to make the rearward-moving highway move even faster rearward.

 

[Chestermiller]

The short answer is that it always works. It won't tell you whether a particular quantity that the book uses is work done "by the system" or work done "on the system". But it will always tell you whether the work done "by the system" at a particular interface is positive or negative.

But...

One place where things can get tricky is when you have an interface where the material at the interface is moving one way and the interface itself is moving a different way. That will not happen with a piston. The interface at the piston moves with the piston. But it can happen in other situations.

It is the movement of the target material acted on by the force that matters. Not the movement of the point where the force is applied.Consider, for instance, a car driving at 60 kph down the highway as you watch from a car driving at 30 kph and being passed. You ask yourself: "Is the work being done by the tire on the highway positive or negative?"

From your point of view, the interface between tire and highway is moving forward past you at 30 kph. The force by the tire on the highway is rearward. The movement of the interface is forward. You could apply the rule and conclude that the work being done on the highway is negative. This conclusion would be incorrect.

You should be looking at the movement of the highway surface at the point of contact. The highway surface is moving rearward. That is the same direction as the force on that highway material. The work being done on the highway is positive from your point of view. As you should expect -- it tends to make the rearward-moving highway move even faster rearward.

Just a thought for your consideration: Sometimes, as in the case of a neophyte like the OP, less is better..

 

[George Jones]

Also, there is confusion in stating the 1st law of thermodynamics.
Physicists usually write dU = dQ - dW
where work W is done BY the system (gas etc.)
wheras chemists for some reason prefer dU = dQ + dW
where W is work done ON the system.

These days, the $\Delta U = Q + W$ convention is used quite often in physics texts. For example, the text "Thermal Physics" by Schroeder is used very widely in North America, and it uses this convention. This convention also is used in the two first-year physics texts by Serway, and the two texts by Knight. I have used all of these as texts for physics courses that I have taught.

The first-year book by Halliday, Resniick, and Walker, however, uses the other convention. So, both conventions are used extensively in physics, and students (and others) should be careful.

At my university, students see thermal/statistical physics in first-year in Serway (+W), in second-year in Schroeder (+W), and in fourth-year in Baierlein (-W).

Another place where one has to take care is the term "adiabatic". Different texts ascribe different meanings to this term.