treeses t1_j9sq9vg wrote on February 24, 2023 at 7:47 AM

As far as I'm aware, the sign conventions for work are the same. If the surroundings do work on the system, that would be negative work for the surroundings and positive work for the system. Can you give an example of what you mean?

Coomb t1_j9u6gq4 wrote on February 24, 2023 at 4:16 PM

Plenty of engineering and physics texts define dE for a system (or dU depending on terminology and assumptions) = dQ - dW, that is, they treat work done by a system on its surroundings as positive.

Here's one example.

https://web.mit.edu/16.unified/www/FALL/thermodynamics/thermo_4.htm

As far as the reason why, the answer is that when you're working from the perspective of a machine using a working fluid, it's natural to conceive of the working fluid as gaining energy when heat is added and losing energy when it's doing work. We usually talk about engines as being rated for output in terms of Watts or horsepower and not negative Watts or horsepower. In your convention, the engine's work is negative.

treeses t1_j9ud74o wrote on February 24, 2023 at 4:59 PM

Thanks, that makes a lot of sense. Now that I've looked deeper, I actually do have both physical chemistry and physics book that have the dE = dQ - dW convention, and ones with the opposite. So it doesn't seem to be a strict physics vs chemistry vs engineering thing.

Something I noted though, when the convention is dE = dQ - dW, PV work at constant pressure is +PdV, while when it is dE = dQ + dW, work is -PdV. You end up with the same dE = dQ - PdV expression, and I'd guess that all the other thermodynamic quantities end up not being different as well. Does the sign convention really not manifest in any meaningful way? I guess it makes sense that this is such a small detail that I didn't even notice it.

Coomb t1_j9v6ofp wrote on February 24, 2023 at 8:07 PM

What I will call the mechanical engineering convention (i.e. work done by a system is positive) since it's certainly the convention that was either exclusively or overwhelmingly used in mechanical engineering when I was taking my classes 10 years ago or so, has an (arguable) pedagogical advantage when introducing enthalpy, which is an extremely commonly used parameter in mechanical engineering and probably in most other forms of engineering.

By definition, H = U + PV. If we assume that the internal energy is the only parameter of the working fluid that is changing, and not other things like its gravitational potential energy or its bulk kinetic energy, the engineering convention equation for the change in energy associated with heat addition and work performed is dU = dQ - dW.

The differential form of the enthalpy is dH = dU + d(PV) = dU + PdV + VdP.

Substitute and you have dH - PdV + VdP = dQ - dW. Make the further assumption of constant pressure and then

dH - PdV = dQ - dW

The pressure work done by the fluid as its enthalpy is increased, and the work done by the system on its surroundings, have the same sign. It makes it more obvious that the PdV component is the amount of enthalpy "lost" by allowing the fluid to expand against external pressure.

The toy problem that is usually used to introduce this is gas in a well insulated cylinder with a piston head held down by weights on the head. What happens when you add heat to the gas? Some of the energy goes into increasing the temperature (and therefore internal energy) - obviously the gas heats up. But just measuring the internal energy of the gas before and after you've added heat to it doesn't accurately tell you how much heat you added. This is of course because some of the heat also goes into raising the weight on the piston against gravity. For people who are mechanically inclined, this is a relatively intuitive physical scenario, and it helps illustrate why enthalpy is a more useful parameter for many engineering problems than internal energy alone.

treeses t1_j9veqsm wrote on February 24, 2023 at 8:58 PM

That does seem like a nice pedagogical step. You still get the same sign for enthalpy though, regardless of which convention you use. My observation was really just that, it isn't a meaningful convention in terms of the results you get. (Unlike, say, using a convention that current is the flow of negative charge carriers, which would change all sorts of signs all over the place. That would be crazy...)

Coomb t1_j9wg3jb wrote on February 25, 2023 at 1:21 AM

You're right. The positive or negative sign in that expression is just a bookkeeping convention and doesn't really have any further consequences. In some sense, it's a one-dimensional problem (the "heat dimension"). An EM analog might be nodal current analysis. For the purposes of analyzing nodal currents, it doesn't actually matter if you say that the sum of all the currents is zero, or if you say that the sum of currents flowing in, minus the sum of currents flowing out, is zero (and call all of the currents positive). In either case, you're preserving the information about whether something is going in or going out, just with a different system of bookkeeping -- are the negative signs attached to each current individually, or a group of currents that you identify and sum?

Once you start involving multiple spatial dimensions, as is common in EM problems, of course your choice of sign convention has more implications downstream.