## Quasi-static (or quasi-equilibrium) processes

Here the idea of a quasi-equilibrium process is introduced. It’s important to understand that, even though the driving force (say a pressure difference) is infinitesimal, it is enough to move the state of a system very gradually in one direction. Inverting the infinitesimal difference will cause the process to reverse completely (albeit infinitely slowly).

## State property vs path dependent variable

It’s crucial to understand the difference between path-dependent and path-independent variables. In general Q and W are both dependent on the path taken between two end states. They are not properties of state.

## Zeroth law

Here, I’ve tried to put together the simplest possible version of the zeroth law. The main point is that it specifies when two systems have the same temperature, but says nothing about what happens if they have different temperatures…ie which direction heat transfer will occur when they are brought into contact with each other.

## Gibb’s phase rule

Another obscure rule is explained here. The idea of degrees-of-freedom is also used in the State Postulate but the SP and the GPR are independent of each other. This information is based on the work of Professor WR Salzman who has licensed it for non-commercial reuse (such as this post). I have tried to contact Salzman, to thank him for his beautiful explanations, but thus far to no avail.

(In the diagram above there is an image with some ‘billiard balls’ (red and black blobs) connected by springs. I realise that this needs some explanation. It is intended to represent the molecular behaviour of a cube of solid ice in liquid water. At 0 degC, the cube is in phase equilibrium with the liquid. Some molecules within the solid structure become liquid water molecules and an equal number of liquid molecules join the solid structure. At -5 degC, on the left, the liquid molecules have higher chemical potential energy in their bonds, than those in the solid phase and so there is a net tendency for them to move to a lower-potential state and become solid (freezing). The opposite is the case at +5 degC (where melting occurs). At equilibrium, the chemical potential of each phase is the same).

## State postulate

This post is intended to explain the rather magical fact that for certain simple systems, if you know two properties of state, you know them all.

## Why I think Thermodynamics is hard

I find many subjects hard to understand. That is partly because, as a visual thinker, I don’t take in lecture-based information at all effectively. It is also because I just can’t learn material which is inconsistent or vague. Beyond these personal difficulties (which are shared by many people with an Engineering mindset), Thermo is widely recognised as conceptually more demanding than many other university-level subjects. Some of the reasons for this are suggested below. I have tried hard to keep these in mind when considering which areas of this blog require special clarity. If, after reading some posts, you are still unclear about the subject matter, feel free to make contact with me. I will then attempt to a) sell you some additional material or tutoring and b)upgrade these notes accordingly.

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Concepts like ‘quasi-equilibrium’ are difficult, partly because they rely on infinitesimal differences which you can’t feel in your body. Removing sandgrains from a piston which restrains a sample of gently heated gas is a finely balanced process which can’t be easily sensed kinaesthetically. Even the idea of a heat reservoir can be hard to grasp if you have already studied heat transfer processes.

There is a fair bit of mathematics involved in Thermo (not usually an engineering student’s first enthusiasm). Does, for example, the difference between delta Q and dQ actually matter? (Answer: yes). This maths is often injected in between sections of physical reasoning that are themselves not straightforward…so sometimes the thread of an argument can get bogged down in the detail. Often, problems are set to give people a feel for the process of getting real, ie numerical, answers. These tend to involve an elaborate manipulation of high precision numbers in odd units….but this frenetic symbol manipulation mostly hides what underlies the calculation. This is a particular problem when using property data such as steam tables, whose origin is never explained.

Such steam tables are usually not well linked conceptually to the introductory thermodynamics of ideal gases. Suddenly, you can have solids appearing inside your piston/cylinder. This is offputting to anyone with an engineering background.

Engineers with a mathematical bent need to be told explicitly that certain important ideas are either the result of experimental observation (the Second Law) or adopted as axioms (eg the State Postulate). No proofs therefore exist. Dividing by differentials and unrestricted use of Jacobian determinants may seem cavalier. I’m personally less concerned about these niceties.

Conventions, intended to smooth calculations, can actually create confusion. Some authorities, eg certain MIT departments, regard work done by a system as having negative value.

Frequently, equations are derived based on some special set of conditions and then applied universally, without much in the way of justification. The idea that some state variables are ‘naturally’ dependent on a particular pair of other state variables is just wrongheaded.

It turns out that there can be many different statements of the same physics. The Second Law is the prime example in which seemingly unrelated phenomena are actually identical. This Law is known to have at least 30 different statements. Some ideas, like treating the entire Universe as an isolated system, are very ‘big picture.’ Engineers aren’t accustomed to working at such scales.

Which leads to Entropy. For example, WHY does adding heat to a system at low temperature allow the system more possible new states to explore than adding the same amount of heat at higher temperature? I was dissuaded from asking any ‘why’ questions as a student because these were considered ‘philosophical’ (a grave criticism in an Engineering department).

For those brave enough to dip a toe into the thermal bath of Statistical Mechanics, there are several possible sources of perplexity. It’s particularly important to explain that if some configuration of system components has a high probability of occurring, this is not the same as saying that it is “caused by probability”. It occurs because the system relentlessly explores its options and that its next move is hard to predict. (This happens even in systems composed entirely of Classical, deterministic, Newtonian billiard balls).

When it comes to applying the equations of Thermodynamics to different examples of real hardware, unless the underlying models are well grasped, the necessary simplifications will not be correctly made. The Otto cycle for a real internal combustion engine is rather different from the actual processes which take place in a vehicle.

It may be helpful to show elements of an analysis represented using several different techniques. This also has the potential to baffle students, though. I’m thinking particularly of the multiple diagrammatic views of a heat engine for example, which can be shown via several different graphs and cryptic block diagrams. (The diagram which is used to show two heat baths and a heat engine, almost never incorporates an arrow to indicate that some essential work is done on the engine).

Engineering Thermodynamics takes a particular pride in not using atoms to explain anything. This is a hangover from the historical origins of the subject, which began before the existence of subatomic particles had been demonstrated experimentally. The denial of particles is perverse and counter-intuitive, however, when someone is trying to understand for example the interaction between pressure and velocity in a flow field.

“R” (or is it R or R) can stand for several different things, depending on context. Unless you keep careful track, it’s quite possible to generate nonsense numerical results. What SI value does this have? kmol means Kg-mol ie the SI number you get when multiplying Kg and the number of moles of a substance. What exactly is a mole in a continuum world?

Most of my educational career has been spent in deep frustration at the fact that subject experts fail to express themselves nearly as clearly in (verbal) language as they do in mathematics. In general, experts are unaware of this problem -having either limited understanding of language and/or limited understanding that students have zero contextual clues -at least initially.

As well as vagueness of expression, there is a problem with different approaches and definitions -negentropy, free energy, exergy …etc are all related, but I find them deeply unintuitive. The terms “lost” work, “steam” tables and “one-way” work can also cause misunderstanding. The meaningless descriptor “saturated” comes from the 18th century, when heat was thought to be a fluid. It is of course possible to have an isentropic process in which entropy production is not zero. Even words like Ideal and Perfect gases should come with caveats.

Something as apparently simple as temperature requires a distinction between two versions of the Kelvin scale: one based on the performance of an ideal heat engine and one based on the behaviour of an ideal gas. The analyses undertaken in textbooks regarding heat engine efficiency usually do a double shuffle, whereby sign conventions for heat transfer are flouted and then magically reinstated. I try hard to avoid this.

Thermodynamics forms a coherent branch of science, but the order in which it was developed and the sequence in which it is taught are often at odds. Many fundamentals depend on each other and so determining an optimal learning path is never simple. Most teachers prefer to explain the laws in this sequence: 1st, 0th, 2nd. You should be aware that these notes do not attempt to comprise a unified course in Thermo. They are rather intended to help explain the sticky, difficult bits.

The material in this blog is certainly not a substitute for being taught Thermodynamics in a one-to-one supervision by an expert Engineering professor. Getting access to such experts is increasingly difficult, however, -certainly at undergraduate level.