Tag Archives: entropy

More on white dwarfs and existentialism

Image by Sarah

Image by Sarah

When I was writing about cosmic heat death a couple of weeks ago [see ‘Will it all be over soon?’ posted on November 2nd, 2016], I implied that our sun would expire on a shorter timescale of about 4 to 5 billion years but without mentioning what we expect to happen.  The gravitational field associated with every piece of matter is proportional to the mass of the piece of matter and inversely proportional to distance from its centre.  The size of the sun implies it should collapse under its own gravitational forces, except that the fusion of hydrogen in its core causes an outwards heat transfer, which prevents this from happening. The sun remains a sphere of hot gases with diameter of about 864,000 miles by ‘burning’ hydrogen.  When the hydrogen runs out, the gravitational field will take over and the sun is expected to collapse to a 30,000 mile diameter ball of atoms and free electrons, or a white dwarf.

These are all spontaneous processes and so the total entropy must increase although there are some local reductions.  The heat dissipated following the fusion of two hydrogen nuclei generates more entropy in the surroundings than the local reduction caused by the fusion.  The collapse to white dwarf would appear to represent a substantial reduction of entropy of the sun because the atomic particles are crushed together. However, this is countered by the release of photons to the surroundings which ensures that the entropy of the surroundings increases sufficiently to satisfy the second law of thermodynamics.

Source:

Isaac Asimov, The roving mind: a panoramic view of fringe science, technology, and the society of the future, London: Oxford University Press, 1987.

An extract is available in John Carey (editor), The Faber Book of Science, London: Faber & Faber, 2005.

Will it all be over soon?

milkywayNASAAs you may have gathered from last week’s post [Man, the Rubbish-Maker on October 26th, 2016], I have been reading Italo Calvino’s Complete Cosmicomics.  In one story, ‘World Memory’ the director of a project to document the entire world memory in the ‘expectation of the imminent disappearance of life on Earth’ is explaining to his successor that ‘we have all been aware for some time that the Sun is halfway through its lifespan: however well things went, in four or five billion years everything would be over’.  The latter is one of the scientific conclusions around which Calvino weaves these short stories and this one put into perspective the concerns expressed by some of my students on both my undergraduate course and MOOC in thermodynamics the prospect of a cosmic heat death resulting from the inevitable consequences of the second law of thermodynamics [see my post ‘Cosmic Heat Death‘ on February 18th, 2015].  The second law requires ‘entropy of the universe to increase in all spontaneous processes’.   Entropy was defined by Rudolf Clausius about 160 years ago as the heat dissipated in a process divided by the temperature of the process.  The dissipated heat flows into random motion of molecules from which it is never recovered.  So, as William Thomson observed, this must eventually create a universe of uniform temperature – an equilibrium state corresponding to maximum entropy where nothing happens and life cannot exist.   Entropy has been increasing since the Big Bang about 13.5 billion years ago.  And as Calvino writes, the sun is about halfway through its life – it is expected to collapse into a white dwarf in 4 to 5 billion years when its supply of hydrogen runs out.  These are enormous timescales: the first human cultures appeared about 70,000 years ago [see my post ‘And then we discovered thermodynamics‘ on February 3rd, 2016]  and history would suggest that our civilization will disappear long before the sun expires or cosmic heat death occurs.  A more immediate existential threat is that our local production of entropy on Earth destroys the delicate balance of conditions that allows us to thrive on Earth.  See my post on Free Riders on April 6th, 2016 for thoughts on avoiding this threat.

Sources:

Italo Calvino, The Complete Cosmicomics, London: Penguin Books, 2002.

 

Man, the Rubbish Maker

167-6734_IMGBruce Sterling wrote that our current civilisation would be best described as ‘Man, the Rubbish Maker’ if we were to be judged by our efforts that will best survive the passage of time.  Paleontologists have found flint-knapping workshops more than two million years old that have out-lasted any record of the speech, culture or beliefs of the craftsmen that laboured in them.  Pollution and waste is not consumed and hence tends to persist while useful things wear out.  In a short story called ‘Daughters of the Moon’ published in 1968 as part of his third collection of Cosmicomics, Italo Calvino describes a world in which cars wear out more quickly than the soles of your shoes.  He goes on to describe a region where the road petered out in a hilly area created by ‘the layers of things that had been thrown away: everything that the consumerist city expelled once it had quickly used it up so it could immediately enjoy the pleasure of handling new things’.  Calvino was imagining a future world but we are rapidly approaching his vision, or perhaps we are already there.  Our junk, rubbish, and trash, is a form of entropy – an increase in the level of disorder created by the processes that provide our man-made lifestyle and required as a consequence of the second law of thermodynamics [see my post ‘Unavoidable junk‘ published on January 14th, 2013].  And ‘entropy requires no maintenance’, to quote Sterling, so much of our rubbish will still be here long after we have disappeared.

If we want to avoid Calvino’s vision of cities surrounded by layers of discarded things, then we have to learn to love old but serviceable belongings.  They are good enough and will suffice.  If they break then we should have them repaired, preferably locally in order to stimulate our economy and reduce our ecological footprint rather than replacing them with something made abroad.  This will require engineers to think more about repairs when designing artefacts and consumers to learn to appreciate the patina of age and usage as a virtue, something of beauty.

Sources:

Bruce Sterling, Shaping Things, Boston: MIT Press, 2005.

Italo Calvino, The Complete Cosmicomics, London: Penguin Books, 2002.

Edwin Heathcote, Make and Mend, Financial Times, 30/31 March, 2013.

Subtle balance of sustainable orderliness

129-2910_IMGI wrote this short essay a couple of weeks for another purpose and then changed my mind about using it.  So I thought I would share it on this blog.

Whenever we do something, some of our useful resource gets converted into productive activity but some is always lost in useless waste.  In other words, 100% efficiency is impossible – we can’t convert all of our resource into productive activity.  Engineers call this the second law of thermodynamics.  Thermodynamics is about energy transitions, for instance converting chemical energy in fossil fuels into electrical energy in a power station, and in these circumstances, the useless waste is called entropy.  At the time of the industrial revolution, Rudolf Clausius recognised that entropy can be related to the heat losses which occur whenever we do something useful, such as generating electricity in a power station, cleaning the house with an electric vacuum cleaner or running to catch the bus.

Clausius’s definition of entropy was really useful for designers of 19th century steam engines but it is difficult to use in other walks of life.  Fortunately Ludwig Boltzmann gave us a more valuable description.  He equated entropy to the number of states in which something could be arranged, or its lack of orderliness.  In other words, the more ways you can arrange something, the less ordered it is likely to be and the higher its entropy.  So a box of children’s building blocks has a low entropy when the blocks are packed in their box because there is a relatively small number of ways of arranging them to fit in the box.  When the box is emptied onto your living room floor, there are very many more possible arrangements and so the blocks have a high entropy.  The chance of knowing the whereabouts of a particular block is small. Whoops!  Now we’ve wondered into information theory.

Let’s get back to the second law, which using Boltzmann’s description of entropy, we can express as the level of orderliness should always decrease.  Stephen Hawking describes this as the arrow of time.  Because, if someone shows you a video clip in which steam gathers itself together and returns into a cup of coffee, or that box of children’s blocks repacks itself, then we know the video is being run backwards because these processes involve decreasing entropy and this can only happen spontaneously if we reverse the direction of time.  If this is true then why do we exist as highly ordered structures?

Erwin Schrödinger in his book, ‘What is Life’ says that organisms suck orderliness out of the environment in order to exist, so that the orderliness of the universe, that’s the organism and its environment, decreases.  Humans digest highly-ordered food to sustain life and food, in the form of plants, is brought into existence by metabolising energy from the sun and releasing entropy in the form of heat.  When we die these processes cease and the orderliness is sucked out of us to sustain insects, maggots and bacteria.

We are organisms, known as Sapiens, that organise ourselves into cultures and societies.  Organisation implies an increase in the level of orderliness in apparent contradiction of the second law.  So, we would expect to find a corresponding increase in disorder somewhere to counterbalance the order in society.  The more regimented society becomes the greater the requirement for counterbalancing disorder to occur somewhere in order to satisfy the second law, which might happen unexpectedly and explosively if the level of constraint or regulation is too great.  This is not an argument for anarchy or total deregulation, the financial sector has already demonstrated the risks associated with this path, but for an optimum and sustainable level of orderliness.  This requires subtle judgment just like in elegant engineering design and living a healthy life, both physically and psychologically.