# Why is work done by the system a negative quantity?

1. Jul 27, 2013

### swell9

Hello,

I'm reading a book about a gas volume inside a system. It says that when the volume expands due to the heated gas, the system is doing work. I understand that part. But it says that the value for work is negative because the system is doing work.

From all the physics I have been studying over the years, work is positive when the system does work and negative when the surroundings do work on the system. Isn't this right?

Thanks

2. Jul 27, 2013

### hilbert2

It's just a sign convention and does not have any consequences to the predictions of the theory, as long as you consistently use the same convention.

As far as I know, chemists tend to use the convention that the work done by a system is negative, while physicists use the opposite convention.

3. Jul 27, 2013

### swell9

Oh I think it is pretty irritating and kind of pointless to have two sign conventions. Thanks for help. Can anyone confirm this?

4. Jul 28, 2013

### BruceW

yeah, I remember the physicists and chemists use different sign convention for this. I never remember which way round though.

5. Jul 28, 2013

### Staff: Mentor

Yes, if the gas expands then it is doing positive work on its surroundings. The sign convention comes in when expressing the first law of thermodynamics. If you choose a convention where by work you mean work done by the system, then you'll need a minus sign to reflect the change in energy of the system. (If the work done by the system is positive, then the work done on the system is negative.)

6. Jul 28, 2013

### Staff: Mentor

When classical thermodynamics as we know it was being developed, a major practical problem in thermodynamics (probably the most important one!) was analyzing the operation of steam engines with the aim of improving them. It seems to me that it would have been natural to consider the heat into the system (the engine's "input") and the work done by the system (the engine's "output") to be both positive numbers. This leads to writing the First Law in the form ΔU = Q - W. I think engineers still tend to use this convention.

Physicists came to prefer to think of energy flow into the system as always being positive (because it increases the internal energy), which leads to the convention that work done on the system is a positive number, and ΔU = Q + W.

Some books, web sites, etc. do it one way, some do it the other way. You have to take note of which convention is being used, and "translate" from one to the other if necessary when you're using different sources.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook