Old Mission Point, Michigan, USA
Season’s Greetings
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Stimulating students with caffeine
Food and drink seems to have been a recurring theme in my undergraduate lectures recently which as we are approaching a festive season is perhaps not inappropriate. At the moment, I am teaching thermodynamics to three hundred first year undergraduate students. Zeroth and first laws of thermodynamics before the Christmas break and then the second and third laws in the New Year. Toast, pizza, barbecued steaks, hot coffee, bottled water, and cold milk shakes have all featured as Everyday Engineering Examples of thermodynamic systems in recent lectures. We can define a thermodynamic system as a quantity of matter capable of exchanging energy with its environment. And, most food preparation processes involve heating, chilling and, or doing work on the food by stirring, beating etc. which are all forms of energy exchange, so the opportunities for Everyday Engineering Examples are many and varied.
In one recent lecture, I asked the class to consider the quickest way to cool your coffee with milk. It was a multiple choice question to which students could respond in real-time using their phones and a website called polleverywhere.com. There was more than one correct answer depending on the assumptions you made about the quantity and temperature of the milk as well as the temperature of the coffee and environment. The core issue is that the rate of cooling is proportional to the temperature difference. While discussing the possible answers, I made a throw-away remark about stirring the coffee involving doing work on the coffee and thus increasing its internal energy and temperature, which would be a step in the wrong direction. I was delighted when one of my students picked me up on this and sent me this link about stirring tea.
It is great to know that at least one student is listening and sufficiently engaged to do a little research. Only 299 left to inspire!
Footnote:
The hot coffee will transfer heat to its cooler surroundings by natural convection and radiation at its free surface and by conduction through the ‘walls’ of the cup. Similarly, the cup will transfer heat to its surroundings by natural convection and radiation from its outer surfaces. This process will establish a temperature gradient in the coffee that will induce a very slow convection flow that would be accelerated by stirring, i.e. introducing forced convection. This is likely to increase heat transfer slightly by carrying hotter coffee to the surfaces. The additional heat transfer (loss) might be more or less than the work done to stir the coffee. Who would have thought something as simply as stirring coffee or tea could be so complicated!
Previous posts on Zeroth Law: ‘All Things Being Equal ‘ on December 4th, 2014, ‘Arbitrary Zero‘ on February 13th, 2013 and ‘Lincoln on Equality‘ on February 6th, 2013.
Previous posts on First Law: ‘Thunderous Applause‘ on July 16th, 2014, ‘Sizzling Sausages‘ on July 3rd, 2013, ‘Closed system on BBQ‘ on June 19th, 2013 and ‘Renewable energy‘ on January 7th, 2013
Sources:
‘The Thermodynamics of Pizza‘ by Harold J. Morowitz, Rutger University Press, 1992.
Is Earth a closed system? Does it matter?
Earth’s annual global mean energy budget, from Kiehl and Trenberth 1997
The dictionary definition of a system is ‘a set of things working together as parts of a mechanism or an interconnecting network; a complex whole’. So it is easy to see why ‘systems engineering’ has become ubiquitous: because it is difficult to design anything in engineering that is not some kind of system. Perhaps the earliest concept of a system in post-industrial revolution engineering is the thermodynamic system, which is a well-defined quantity of matter that can exchange energy with its environment.
Engineers define thermodynamic systems by drawing arbitrary boundaries around ‘quantities of matter’ that are of interest, for instance the contents of a refrigerator or the inside of the cylinder of a diesel engine [see my post entitled ‘Drawing Boundaries‘ on December 19th, 2012]. These boundaries can be permeable to matter in which case the system is described as an ‘open system’, as in the case of an diesel engine cylinder into which fuel is injected and exhaust gases ejected. Conversely, the boundary of a ‘closed system’ is impermeable to matter, i.e. the refrigerator with the door closed. The analysis of a closed system is usually much simpler than for an open one. In his Gaia theory, James Lovelock proposed that the Earth was a self-regulated complex system. Is it also a closed thermodynamic system? It is clear that energy exchange occurs between the Earth and its surroundings as a consequence of solar radiation incident on the Earth (about 342 Watts/square meter) and radiation from the Earth as a consequence of reflection of solar radiation (about 107 Watts/square meter) and its temperature (235 Watts/square meter). This implies that we can consider the Earth as a thermodynamic system. The Earth’s gravitation field ensures that nothing much leaves; at the same time the vast of emptiness of space means that collisions with matter happen only very occasionally, so the inward flow of matter to Earth is negligible. So, perhaps we could approximate Earth as a closed thermodynamic system.
Does it matter? Yes, I believe so, because it influences how we think about our complex life support system, or spaceship Earth that sustains and protects us, as Max Tegmark describes it in his book ‘Our Mathematical Universe’. In a closed system there is finite amount of matter that cannot be replenished, which implies that the Earth’s resources are finite. However, our current western lifestyle is focused on consumption which is incompatible with a sustainable society in a closed system. Even the Earth’s energy balance appears to be in equilibrium based on the data in the figure and so we should be careful about massive schemes for renewable energy that might disturb the Gaia.
Sources:
Tegmark, M., Our Mathematical Universe, Penguin Books Ltd, 2014.
All things being equal
Some of the greatest insights and inventions are obvious once they have been pointed out to you and you wonder how you could not have spotted them yourself. Is it luck or genius that allows someone to be the first to have a great idea? The quest for more efficient engines to power the industrial revolution led the likes of Sadi Carnot, Rudolf Clausius, William Rankine, William Thomson and James Watt to experiment and think deeply about thermodynamics or what might be called energy science or energy engineering. They established the First Law of thermodynamics (energy is always conserved) and Second Law of thermodynamics (entropy increases in all processes) of thermodynamics but initially missed the more fundamental, and arguably simpler, Zeroth Law (two systems in thermal equilibrium with a third must also be in thermal equilibrium each other). Rankine, working around 1850, is often attributed with identifying the Zeroth Law but probably the credit should go to Euclid (380-260 BC) who appears to have got there first in the fifth of his series of six books, ‘Elements’ [see my post entitled ‘Lincoln on equality‘ on February 6th, 2013).
The first English translation of ‘Elements’ is believed to have been by Sir Henry Billingsley in 1570. A later version by Oliver Byrne was published in 1847 and you can read it on-line. Go to page 173 to find a version of the Zeroth Law which can be paraphrased as ‘Things that are equal to the same things are equal to each other’.
Oliver Byrne, was Surveyor of Her Majesty’s Settlements in the Falkland Islands which presumably left him plenty of time to be the ‘author of numerous mathematical works’ as the title page to his book states. The title page also tells us that ‘coloured diagrams and symbols are used instead of letters for the greater ease of learners’. The bold primary colours and straight lines remind me of the paintings in the recent Mondrian exhibition at the Tate Liverpool. Maybe Piet Mondrian (1872 – 1944) was inspired by Oliver Byrne’s beautiful book, which was an early example of innovative graphic design and as well as an attempt to make mathematical concepts more accessible – something many writers of modern textbooks make little serious effort to do!
Realize Engineering 