Category Archives: Thermodynamics

Delaying cataclysmic events might hasten their advent

detail tl from abstract painting by Zahrah RIn thermodynamics, students are taught to draw a boundary around the system they want to analyse and to decide whether the boundary is open or closed to transfers of mass and energy based on the scenario they want to model.  The next step is to balance the energy flows across the boundary with the change in the energy content of the system.  This is an application of the first law of thermodynamics which is that energy can neither be created nor destroyed.  Rudolf Clausius is credited with discovering entropy when he realised that when energy flowed as heat across a system boundary it became entropy or disordered energy. For instance, when a steam engine does work and discharges heat to the environment. The second law of thermodynamics states that entropy of the universe increases in all real processes.  Thermodynamicists are not the only people who draw boundaries and decide whether they are open or closed.  Politicians and generals draw national boundaries occasionally and more frequently decide whether they are open or closed to people, goods and capital.  After the first world war economists, such as Friedrich Hayek and Ludwig von Mises, proposed that conflict would be less likely if people, goods and capital could flow freely across national boundaries.  These ideas became the principles on which the IMF and World Bank were formed at Bretton Woods in July 1944 in the closing stages of the second world war.  Presidents of the USA, since Ronald Reagan, have taken these ideas a step further by unleashing capitalism through deregulation of markets in the belief that markets know best.  However, ever-growing capital generates an ever-increasing rate of creation of entropy and disorder in the world [see ‘Existential connection between capitalism and entropy‘ on May 4th 2022] and perhaps attempting to reduce conflict by unfettering capital actually accelerates the descent into chaos and disorder because entropy increases in every transaction.


Rana Foroohar, When the market fails us, FT Weekend, 23 April/24 April 2022.

Gary Gerstle, The Rise and Fall of the Neoliberal Order: America and the World in Free Market Era, Oxford: OUP, 2022.

The cataclysmic events referred to in the title are those identified by Thomas Piketty as being the only means by which economic inequality is reduced, i.e., wars and revolutions [see ‘Existential connection between capitalism and entropy‘ on May 4th 2022].  The title was inspired by correspondence from Bob Handscombe with whom I wrote a book entitled ‘The Entropy Vector: Connecting Science and Business‘.

Existential connection between capitalism and entropy

global average temperature with timeAccording to Raj Patel and Jason W Moore, in his treatise ‘Das Kapital’ Karl Marx defined capitalism as combining labour power, machines and raw materials to produce commodities that are sold for profit which is re-invested in yet more labour power, machines and raw materials.  In other words, capitalism involves processes that produce profit from an economic perspective, and from a thermodynamic perspective produce entropy because the second law of thermodynamics demands that all real processes produce entropy.  Thermodynamically, entropy usually takes the form of heat dissipated into the environment which raises the temperature of the environment; however, it can also be interpreted as an increase in the disorder of a system [see ‘Will it all be over soon?’ on November 2nd, 2016].  The ever-expanding cycle of profit being turned into capital implies that the processes of producing commodities must also become ever larger.  The ever-expanding processes of production implies that the rate of generation of entropy also increases with time.  If no profit were reinvested in economic processes then the processes would still increase the entropy in the universe but when profit is re-invested and expands the economic processes then the rate of entropy production increases and the entropy in the universe increases exponentially – that’s why the graphs of atmospheric temperature curve upwards at an increasing rate since the industrial revolution.  As if that is not bad enough, the French social economist, Thomas Piketty has proposed that the rate of return on capital, “r” is always greater than the rate of growth of the economy, “g” in his famous formula “r>g”.  Hence, even with zero economic growth, the rate of return will be above zero and the level of entropy will rise exponentially.  Piketty identified inequality as a principal effect of his formula and suggested that only cataclysmic events, such as world wars or revolutions, can reduce inequality.  The pessimistic thermodynamicist in me would conclude that an existential cataclysmic event might be the only way that this story ends.


Raj Patel & Jason W. Moore, A history of the world in seven cheap things, London: Verso, 2018.

Thomas Piketty, A brief history of equality, translated by Steven Rendall, Harvard: Belknap, 2022.

Diane Coyle, Piketty the positive, FT Weekend, 16 April/17 April 2022.

Image: Global average near surface temperature since the pre-industrial period from

From nozzles and diffusers to stars and stripes

Schematic diagram of explanation in textAt the end of a lecture on energy flows in my first year undergraduate course on thermodynamics, I talk about nozzles and diffusers as examples of practical applications of the rest of the material in the lecture.  It is hazardous to sit in the front row of the lecture theatre because I take in a water bottle with a trigger spray to demonstrate how the nozzle increases the velocity of the fluid at the expense of pressure while gently sprinkling water on the front row.  I am always intrigued by the symmetry of nozzles and diffusers.  Diffusers increase pressure of a fluid at the expense of its velocity, i.e., a mirror image of the action of a nozzle.  The cross-sections are also mirror images because a nozzle has a cross-section that decreases in the flow direction while a diffuser has a cross-section that increases in the flow direction.  At least for sub-sonic flows, because the shapes are reversed for super-sonic flow; so a sub-sonic nozzle looks like a super-sonic diffuser and a sub-sonic diffuser looks like a super-sonic nozzle.  If that all sounds like fluid mechanics then the thermodynamic message is that, in nozzles and diffusers, the rates of heat and work transfer are approximately zero while the change in the kinetic energy of the fluid is very large.  I finish the lecture with a video clip of a school quartet of trombones playing ‘Stars and Stripes Forever’ which wakes up the students who have slept through the lecture and allows me to point out the diffusers (bell of the trombone) transmitting acoustic pressure.

You can watch the video clip on YouTube at

Energy transformations

I mentioned a couple of weeks ago that I am teaching thermodynamics at the moment [see ‘Conversations about engineering over dinner and a haircut‘ on February 16th, 2022].  I am using a blended approach [see ‘ Blended learning environments‘ on November 14th, 2018] to deliver the module to more than 300 first year undergraduate students with one hour in the lecture theatre each week while the students follow the components of the MOOC I developed some years ago [see ‘Free: Energy! Thermodynamics in Everyday Life‘ on November 11th, 2015, and ‘Engaging learners online‘ on May 25th, 2016].  I have found that first year undergraduates are reluctant to participate in the online discussions that are part of the MOOC and so last year I asked them to discuss each topic in small groups with their academic tutor.  I got some very positive feedback from tutors who had interesting and stimulating discussions with their students.  We are repeating the process again this year.  The first discussion is about energy transformations: noting that energy is always conserved but constantly transformed into different forms, each student is asked to start from an energy state of their choice and to trace the transformations backwards until they can go no further.  In the lecture preceding the discussion with their tutor I provide some examples for starting states, including breakfast cereal, a pole vaulter in mid-jump and a bullet train.  I also describe the series of transformations from the Big Bang to tectonic plate movement: after the initial expansion caused by the Big Bang, the universe cooled sufficiently to allow the formation of sub-atomic particles followed by atoms of hydrogen and some helium and lithium that gravity caused to coalesce into clouds which became the early stars, or solar nebula.  A crust formed on the solar nebula which broke away to form planets.  Our planet has a molten core with temperatures varying from 4,400 to 6000 degrees Celsius, compared to around 5,500 degrees on the surface of the sun.  The temperature variation in the Earth’s core cause thermal currents which drive the movement of tectonic plates and so on [see ‘The hills are shadows, and they flow from form to form, and nothing stands‘, on February 9th, 2022].  Most chains of energy transformation lead backwards to the sun and forwards to dissipation of energy into some unusable form which we might call ‘entropy’ [see ‘Life-time battle‘ on January 30th, 2013].