William Thomson’s Struggle with Heat and Work
In 1847, when William Thomson (later Lord Kelvin) (1824–1907) learned of Joule’s experiments (on the mechanical equivalent of heat) demonstrating that work could be converted to heat, he immediately recognized the impact of this discovery. Moreover, it was clear, although not explicitly demonstrated by Joule’s experiments (but nonetheless claimed by Joule), that this equivalence meant that one would expect the conversion of heat into work to be possible as well. This caused problems for Thomson, since at that time, he was still a proponent of caloric theory, which stood in direct opposition to Joule’s conclusion.
Nonetheless, Thomson resolved this struggle to full satisfaction when he published On the Dynamical Theory of Heat. But Thomson still struggled with another issue: what happens to the work Joule described when heat simply flows, or is conducted through an object, as it moves from a region that is hot to one that is cold?
Indeed, one can use a heat engine to generate work from heat. But if instead we take this same quantity of heat and allow it to simply flow – bypass the heat engine altogether – it appears the amount of work that would have been otherwise obtained has actually been lost; this troubled Thomson. To be sure, in the case of Carnot’s reversible heat engine one gets the maximum amount of work possible from a given amount of heat while, on the other hand, with Fourier’s free conduction theory of heat, we are left with the minimum amount of work possible – no work at all, in fact, being produce. In the latter case, it is as if the available work has simply disappeared, and Thomson wanted to know exactly where it had vanished. He writes:
“The difficulty which weighed principally with me in not accepting the theory so ably supported by Mr Joule was that the mechanical effect stated in Carnot’s theory to be absolutely lost by conduction, is not accounted for in the dynamical theory [of Joule] otherwise than by asserting that it is not lost …”
Energy’s True Nature
In 1852, Thomson published the short article On a Universal Tendency in Nature to the Dissipation of Mechanical Energy. In this article, Thomson states that not all energy is created equally. Some energy can be used to do work and some energy, unfortunately can’t. Consider the energy available in a river compared to that in the ocean. Clearly, the ocean has much more energy than a river. You need only look out upon the ocean and watch the crashing of the waves upon the shore to be convinced. But how do you actually extract this energy out and do work with it?
There are numerous challenges to this, and all of them have to do with the random (disordered) nature of the motion of the waves. Fluctuations in size, strength, direction, and duration of the ocean’s waves all make it challenging to squeeze out the enormous amount of energy, that is indeed available, to produce work. Whereas, the mostly constant, steady, uniform (ordered) flow of a river makes it a much better candidate for energy extraction. This is why we build hydroelectric plants on rivers and not oceans.
Thomson concludes that nature favors this random or dissipated type of energy, thus once it has been dissipated (as in the case of the ocean) it becomes essentially impossible to extract for useful work. In fact, if it is possible, and you do want to get this energy out, it will actually take work to do it. Indeed, this requisite work signifies the (primarily one-way and irreversible) dissipation of energy as the direction favored by nature.
Prelude to the Second Law
Thomson’s Law of Dissipation alluded to a behavior of energy not accounted for in the first law. Consider Carnot’s heat engine where we are able to use only some of the inputted heat to create work and the rest is simply inevitably tossed to the surroundings. So even in the most perfect of scenarios where the most efficient of all possible heat engines is used, the universe still demands the waste or dissipation of some heat. There’s simply no way around it since, as Thomson puts it: this is the “universal tendency”. And if we make no attempt whatsoever to harness the flow of heat for work, with any sort of heat engine, then all of it will be dissipated as described by Fourier’s theory.
So, in either case an amount of heat will be dissipated but not lost. This dissipated heat goes into the random motions making up the matter it flows into – like the random motion of the ocean’s waves. So, not all energy is equal, nature tends towards wasting (dissipating) energy as heat, and this wasted energy is neither lost nor destroyed, rather it’s simply passed to the atoms comprising the matter, thus becoming unavailable for work.
From these concepts comes the idea that “ordered” energy represents a higher quality than “disordered” energy since it can be used for work. Once again, consider our example of the ocean with its disordered energy manifested in the chaotic motion of the waves versus the higher quality ordered energy of the uniformly flowing river that can provide us with work. Thus dissipation of energy is a process of degradation of energy to that of a lower quality from its previous higher quality state; a degradation from order to disorder.
The first law tells us that energy is neither created nor destroy but merely transformed from one form to another, and therefore it’s conserved. However, Thomson’s Law of Dissipation made it clear that so much more is going on with energy than the first law describes. Energy is not only conserved, but it has a tendency to dissipate. Moreover, this dissipation results in its degradation from a higher quality (ordered) to lower quality (disordered). Thus, energy has a “preferred direction” to its dissipation, and reversing this direction requires an amount of work. Indeed, Thomson’s Law of Dissipation may have been his biggest contribution to the area of thermodynamics. In fact, Thomson’s Law of Dissipation provides a conceptual statement of the second law of thermodynamics.