Tag Archives: heat transfer

Isolated systems in nature?

Is a coconut an isolated thermodynamic system?  This is a question that I have been thinking about this week.  A coconut appears to be impermeable to matter since its milk does not leak out and it might be insulated against heat transfer because its husk is used for insulation in some building products.  If you are wondering why I am pondering such matters, then it is because, once again, I am teaching thermodynamics to our first year students (see ‘Pluralistic Ignorance‘ on May 1st, 2019).  It is a class of more than 200 students and I am using a blended learning environment (post on 14th November 2018) that combines lectures with the units of the massive open online course (MOOC) that I developed some years ago (see ‘Engaging learners on-line‘ on May 25th, 2016).  However, before devotees of MOOCs get excited, I should add that the online course is neither massive nor open because we have restricted it to our university students.  In my first lecture, I talked about the concept of defining the system of interest for thermodynamic analysis by drawing boundaries (see ‘Drawing boundaries‘ on December 19th, 2012).  The choice of the system boundary has a strong influence on the answers we will obtain and the simplicity of the analysis we will need to perform.  For instance, drawing the system boundary around an electric car makes it appear carbon neutral and very efficient but including the fossil fuel power station that provides the electricity reveals substantial carbon emissions and significant reductions in efficiency.  I also talked about different types of system, for example: open systems across whose boundaries both matter and energy can move; closed systems that do not allow matter to flow across their boundaries but allow energy transfers; and, isolated systems that do not permit energy or matter to transfer across their boundaries.  It is difficult to identify closed systems in nature (see ‘Revisiting closed systems in nature‘ on October 5th, 2016); and so, once again I asked the students to suggest candidates but then I started to think about examples of isolated systems.  I suspect that completely isolated systems do not exist; however, some systems can be approximated to the concept and considering them to be so, simplifies their analysis.  However, I am happy to be corrected if anyone can think of one!

Image: https://www.flickr.com/photos/yimhafiz/4031507140 CC BY 2.0

Entropy on the brain

It was the worst of times, it was the worst of times.  Again.  That’s the things about things.  They fall apart, always have, always will, it’s in their nature.’  They are the opening three lines of Ali Smith’s novel ‘Autumn’.  Ali Smith doesn’t mention entropy but that’s what she is describing.

My first-year lecture course has progressed from the first law of thermodynamics to the second law; and so, I have been stretching the students’ brains by talking about entropy.  It’s a favourite topic of mine but many people find it difficult.  Entropy can be described as the level of disorder present in a system or the environment.  Ludwig Boltzmann derived his famous equation, S=k ln W, which can be found on his gravestone – he died in 1906.  S is entropy, k is a constant of proportionality named after Boltzmann, and W is the number of arrangements in which a system can be arranged without changing its energy content (ln means natural logarithm).  So, the more arrangements that are possible then the larger is the entropy.

By now the neurons in your brain should be firing away nicely with a good level of synchronicity (see my post entitled ‘Digital hive mind‘ on November 30th, 2016 and ‘Is the world comprehensible?‘ on March 15th, 2017).  In other words, groups of neurons should be showing electrical activity that is in phase with other groups to form large networks.  Some scientists believe that the size of the network was indicative of the level of your consciousness.  However, scientists in Toronto led by Jose Luis Perez-Velazquez, have suggested that it is not the size of the network that is linked to consciousness but the number of ways that a particular degree of connectivity can be achieved.  This begins to sound like the entropy of your neurons.

In 1948 Claude Shannon, an American electrical engineer, stated that ‘information must be considered as a negative term in the entropy of the system; in short, information is negentropy‘. We can extend this idea to the concept that the entropy associated with information becomes lower as it is arranged, or ordered, into knowledge frameworks, e.g. laws and principles, that allow us to explain phenomena or behaviour.

Perhaps these ideas about entropy of information and neurons are connected; because when you have mastered a knowledge framework for a topic, such as the laws of thermodynamics, you need to deploy a small number of neurons to understand new information associated with that topic.  However, when you are presented with unfamiliar situations then you need to fire multiple networks of neurons and try out millions of ways of connecting them, in order to understand the unfamiliar data being supplied by your senses.

For diverse posts on entropy see: ‘Entropy in poetry‘ on June 1st, 2016; ‘Entropy management for bees and flights‘ on November 5th, 2014; and ‘More on white dwarfs and existentialism‘ on November 16th, 2016.


Ali Smith, Autumn, Penguin Books, 2017

Consciousness is tied to ‘entropy’, say researchers, Physics World, October 16th, 2016.

Handscombe RD & Patterson EA, The Entropy Vector: Connecting Science and Business, Singapore: World Scientific Publishing, 2004.

Georgian interior design and efficient radiators

My lecture last week, to first year students studying thermodynamics, was about energy flows and, in particular, heat transfer.  I mentioned that, despite being called radiators, radiation from a typical central heating radiator represents less than a quarter of its heat output with rest arising from convection [see post entitled ‘On the beach‘ on July 24th, 2013 for an explanation of types of heat transfer].  This led one student to ask whether black radiators, with an emissivity of close to one, would be more efficient.  The question arises because the rate of radiative heat transfer is proportionate to the difference in the fourth power of the temperature of the radiator and its surroundings, and to the surface emissivity of the surface of the radiator.  This implies that heat will transfer more quickly from a hot radiator but also more slowly from a white radiator that has an emissivity of 0.05 compared to 1 for black surface.

Thus, a black radiator will radiator heat more quickly than a white one; but does that mean it’s more efficient?  The first law of thermodynamics demands that the nett energy input to a radiator is the same as the energy input required to raise the temperature of the space in which it is located.  Hence, the usual thermodynamic definition of efficiency, i.e. what we want divided by what we must supply, does not apply.  Instead, we usually mean the rate at which a radiator warms up a room or the size of the radiator required to heat the room.  In other words, a radiator that warms a room quickly is considered more efficient and a small radiator that achieves the same as large one is also considered efficient.  So, on this basis a black radiator will be more efficient.

Recent research by a team, at my alma mater, has shown that a rough black wall behind the radiator also increases its efficiency, especially when the radiator is located slightly away from the wall.  Perhaps, it is time for interior designers to develop a retro-Georgian look with dark walls, perhaps with sand mixed into the paint to increase surface roughness.


Beck SMB, Grinsted SC, Blakey SG & Worden K, A novel design for panel radiators, Applied Thermal Engineering, 24:1291-1300, 2004.

Shati AKA, Blakey SG & Beck SBM, The effect of surface roughness and emissivity on radiator output, Energy and Buildings, 43:400-406, 2011.

Image details:

Verplank 2 002<br />
Working Title/Artist: Woodwork of a Room from the Colden HouseDepartment: Am. Decorative ArtsCulture/Period/Location: HB/TOA Date Code: Working Date: 1767<br />
Digital Photo File Name: DP210660.tif<br />
Online Publications Edited By Steven Paneccasio for TOAH 1/3/14


Ample sufficiency of solar energy?

Global energy budget from Trenberth et al 2009

I have written several times about whether or not the Earth is a closed system [see for example: ‘Is Earth a closed system? Does it matter‘ on December 10th, 2014] & ‘Revisiting closed systems in Nature‘ on October 5th, 2016).  The Earth is not a closed thermodynamic system because there is energy transfer between the Earth and its surroundings as illustrated by the schematic diagram. Although, the total incoming solar radiation (341 Watts/sq. metre (W/m²)) is balanced by the sum of the reflected solar radiation (102 W/m²) and the outgoing longwave radiation (239 W/m²); so, there appears to be no net inflow or outflow of energy.  To put these values into perspective, the world energy use per capita in 2014 was 1919 kilograms oil equivalent, or 2550 Watts (according to World Bank data); hence, in crude terms we each require 16 m² of the Earth’s surface to generate our energy needs from the solar energy reaching the ground (161 W/m²), assuming that we have 100% efficient solar cells available. That’s a big assumption because the best efficiencies achieved in research labs are around 48% and for production solar cells it’s about 26%.

There are 7.6 billion of us, so at 16 m² each, we need  120,000 square kilometres of 100% efficient solar cells – that’s about the land area of Greece, or about 500,000 square kilometres with current solar cells, which is equivalent to the land area of Spain.  I picked these countries because, compared to Liverpool, the sun always shines there; but of course it doesn’t, and we would need more than this half million square kilometres of solar cells distributed around the world to allow the hours of darkness and cloudy days.

At the moment, China has the most generating capacity from photovoltaic (PV) cells at 78.07 GigaWatts or about 25% of global PV capacity and Germany is leading in terms of per capita generating capacity at 511 Watts per capita, or 7% of their electricity demand.  Photovoltaic cells have their own ecological footprint in terms of the energy and material required for their production but this is considerably lower than most of our current sources of energy [see, for example Emissions from photovoltaic life cycles by Fthenakis et al, 2008].


Trenberth KE, Fasullo JT & Kiehl J, Earth’s global energy budget, Bulletin of  the American Meteorological Society, March 2009, 311-324, https://doi.org/10.1175/2008BAMS2634.1.

World Bank Databank: https://data.worldbank.org/indicator/EG.USE.PCAP.KG.OE

Nield D, Scientists have broken the efficiency record for mass-produced solar panels, Science Alert, 24th March 2017.

2016 Snapshot of Global Photovoltaic Markets, International Energy Agency Report IEA PVPS T1-31:2017.

Fthenakis VM, Kim HC & Alsema E, Emissions from photovoltaic life cycles, Environmental Science Technology, 42:2168-2174, 2008.