The economists John Kay and Mervyn King assert in their book ‘Radical Uncertainty – decision-making beyond numbers‘ that ‘economic forecasting is necessarily harder than weather forecasting’ because the world of economics is non-stationary whereas the weather is governed by unchanging laws of nature. Kay and King observe that both central banks and meteorological offices have ‘to convey inescapable uncertainty to people who crave unavailable certainty’. In other words, the necessary assumptions and idealisations combined with the inaccuracies of the input data of both economic and meteorological models produce inevitable uncertainty in the predictions. However, people seeking to make decisions based on the predictions want certainty because it is very difficult to make choices when faced with uncertainty – it raises our psychological entropy [see ‘Psychological entropy increased by ineffective leaders‘ on February 10th, 2021]. Engineers face similar difficulties providing systems with inescapable uncertainties to people desiring unavailable certainty in terms of the reliability. The second law of thermodynamics ensures that perfection is unattainable [see ‘Impossible perfection‘ on June 5th, 2013] and there will always be flaws of some description present in a system [see ‘Scattering electrons reveal dislocations in material structure‘ on November 11th, 2020]. Of course, we can expend more resources to eliminate flaws and increase the reliability of a system but the second law will always limit our success. Consequently, to finish where I started with a quote from Kay and King, ‘certainty is unattainable and the price of near-certainty unaffordable’ in both economics and engineering.
I am teaching thermodynamics to first year undergraduate students at the moment and in most previous years this experience has stimulated me to blog about thermodynamics [for example: ‘Isolated systems in nature?’ on February 12th, 2020]. However, this year I am more than half-way through the module and this is the first post on the topic. Perhaps that is an impact of teaching on-line via live broadcasts rather than the performance involved in lecturing to hundreds of students in a lecture theatre. Last week I introduced the second law of thermodynamics and explained its origins in efforts to improve the efficiency of steam engines by 19th century engineers and physicists, including Rudolf Clausius (1822 – 1888), William Thomson (1827 – 1907) and Ludwig Boltzmann (1844 – 1906). The second law of thermodynamics states that the entropy of the universe increases during all real processes, where entropy can be described as the degree of disorder. The traditional narrative is that thermodynamics was developed by the Victorians; however, I think that the ancient Greeks had a pretty good understanding of it without calling it thermodynamics. Heraclitus (c. 535 BCE – c. 475 BCE) understood that everything is in flux and nothing is at rest so that the world is one colossal process. This concept comes close to the modern interpretation of the second of law of thermodynamics in which the entropy in the universe is constantly increasing leading to continuous change. Heraclitus just did not state the direction of flux. Unfortunately, Plato (c. 429 BCE – c. 347 BCE) did not agree with Heraclitus, but thought that some divine intervention had imposed order on pre-existing chaos to create an ordered universe, which precludes a constant flux and probably set back Western thought for a couple of millennia. However, it seems likely that in the 17th century, Newton (1643 – 1727) and Leibniz (1646 – 1716), when they independently invented calculus, had more than an inkling about everything being in flux. In the 18th century, the pioneering geologist James Hutton (1726 – 1797), while examining the tilted layers of the cliff at Siccar Point in Berwickshire, realised that the Earth was not simply created but instead is in a state of constant flux. His ideas were spurned at the time and he was accused of atheism. Boltzmann also had to vigorously defend his ideas to such an extent that his mental health deteriorated and he committed suicide while on vacation with his wife and daughter. Today, it is widely accepted that the second law of thermodynamics governs all natural and synthetic processes, and many people have heard of entropy [see ‘Entropy on the brain’ on November 29th, 2017] but far fewer understand it [see ‘Two cultures’ on March 5th, 2013]. It is perhaps still controversial to talk about the theoretical long-term consequence of the second law, which is cosmic heat death corresponding to an equilibrium state of maximum entropy and uniform temperature across the universe such that nothing happens and life cannot exist [see ‘Will it all be over soon?’ on November 2nd, 2016]. This concept caused problems to 19th century thinkers, particular James Clerk Maxwell (1831 – 1979), and even perhaps to Plato who theorised two worlds in his theory of forms, one unchanging and the other in constant change, maybe in an effort to dodge the potential implications of degeneration of the universe into chaos.
Image: decaying ruins of Fountains Abbey beside the River Skell. Heraclitus is reported to have said ‘no man ever steps twice into the same river; for it’s not the same river and he’s not the same man’.
One of the implications of the second law of thermodynamics is that the thermal efficiency of power stations increases with their operating temperature. Thus, there is a drive to increase the operating temperature in the next generation of nuclear power stations, known as Generation IV reactors. In one type of Generation IV reactors, known as the Very High Temperature Reactor (VHTR), graphite is designed to be both the moderator for neutrons and a structural element of the reactor. Although the probability of damage in an accident is extremely low, it is important to consider the consequences of damage causing the core of the reactor to be exposed to air. In these circumstances, with the core temperature at about 1600°C, the graphite would be exposed to severe oxidation by the air that could change its material properties and ability to function as a moderator and structural element. Therefore, in recent research, my research group has been working with colleagues at the UK National Nuclear Laboratory (NNL) and at the National Tsing Hua University (NTHU) in Taiwan to conduct experiments on nuclear graphite over a range of temperatures. Our recently published article shows that all grades of nuclear graphite show increased rates of oxidation for temperatures above 1200°C. We found that large filler particles using a pitch-based graphite rather than a petroleum-based graphite gave higher oxidation resistance at these elevated temperatures. This data is likely to be important in the design and operations of the next generation of nuclear power stations.
The work described above was supported by the NTHU-University of Liverpool Dual PhD Programme [see ‘Citizens of the world‘ on November 27th, 2019] and NNL. This is the fifth, and for the moment last, in a series of posts on recent work published by my research group. The others are: ‘Salt increases nanoparticle diffusion‘ on April 22nd, 2020; ‘Spatio-temporal damage maps for composite materials‘ on May 6th, 2020; ‘Thinking out of the box leads to digital image correlation through space‘ on June 24th, 2020; and, ‘Potential dynamic buckling in hypersonic vehicle skin‘ on July 1st, 2020.
The image is figure 5: SEM micrographs of the surface of petroleum-based IG-110 graphite samples oxidized at various temperatures from Lo IH, Tzelepi A, Patterson EA, Yeh TK. A study of the relationship between microstructure and oxidation effects in nuclear graphite at very high temperatures. J. Nuclear Materials. 501:361-70, 2018.
Lo I-H, Yeh T-K, Patterson EA & Tzelepi A, Comparison of oxidation behaviour of nuclear graphite grades at very high temperatures, J. Nuclear Materials, 532:152054, 2020.
As engineers, we like to draw simple diagrams of the systems that we are attempting to analyse because most of us are pictorial problem-solvers and recording the key elements of a problem in a sketch helps us to identify the important issues and select an appropriate solution procedure [see ‘Meta-representational competence’ on May 13th, 2015]. Of course, these simple representations can be misleading if we omit parameters or features that dominate the behaviour of the system; so, there is considerable skill in idealising a system so that the analysis is tractable, i.e. can be solved. Students find it especially difficult to acquire these skills [see ‘Learning problem-solving skills‘ on October 24th, 2018] and many appear to avoid drawing a meaningful sketch even when examinations marks are allocated to it [see ‘Depressed by exams‘ on January 31st, 2018]. Of course, in thermodynamics it is complicated by the entropy of the system being reduced when we omit parameters in order to idealise the system; because with fewer parameters to describe the system there are fewer microstates in which the system can exist and, hence according to Boltzmann, the entropy will be lower [see ‘Entropy on the brain‘ on November 29th, 2017]. Perhaps this is the inverse of realising that we understand less as we know more. In other words, as our knowledge grows it reveals to us that there is more to know and understand than we can ever hope to comprehend [see ‘Expanding universe‘ on February 7th, 2018]. Is that the second law of thermodynamics at work again, creating more disorder to counter the small amount of order achieved in your brain?
Image: Sketch made during an example class