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

Reply to comment by treeses in why is sign convention for work different on chemistry and physics? by Melodic-Recipe2618

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.