Category Archives: Thermodynamics

Born in a barn

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108-0858_IMGIn my previous post [Traffic hold-ups, 13th March 2013] the application of Kirchhoff’s Law to the flow of electrons, water and traffic was discussed.  In this context, electrical current or electrons were conceived as flowing.  Instead, electrical current can be considered as electrical energy being transferred across a potential difference, or voltage.  When this terminology is used, then it is only a short step to extend the use of Kirchhoff’s law to consider the combined effect of multiple resistance to other forms of energy transfer, such as heat transfer.  Heat transfer occurs across a temperature difference, from hot to cold, and some materials offer more resistance than others, e.g. wood compared to glass.  Kirchhoff’s law can be used to calculate the total resistance to heat transfer of complex structure such as a house wall that some components in series, e.g. layers of brick, insulation and plasterboard, and some in parallel, e.g. doors and windows.  This information is important in designing a house to achieve minimum energy consumption and to specify the heating and cooling systems required.  Note that the inverse form of Kirchhoff’s Law means that the low resistance to heat transfer of a door or window dominates the heat transfer characteristics of a well-insulated structure.  Of course, the extreme case is when you leave the door open and on a cold day someone shouts at you: ‘Were you born in a barn?’.

Traffic hold-ups

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107-0722_IMGGustav Kirchhoff graduated from the University of Konigsberg in 1847 and married his professor’s daughter.  Many people are familiar with his name from studying electrical circuits at school.  His circuit law is an extension of the law of conservation of energy and governs how to combine the effect of multiple electrical resistors.  When resistors are connected in series, i.e. like barges towed by a tug one behind the other, then the value of the resistances can be added together to give a total resistance for the set of resistors.  So, three resistors of 2, 4 and 8 ohms connected in series provide a total resistance of 14 ohms.

However, when resistors are connected in parallel, i.e. like barges strapped alongside the tug, then the calculation of the combined resistance is a little more involved.  The inverse or reciprocal of each resistance must be added together and then the inverse taken of the sum.  So, three resistors of 2, 4 and 8 ohms connected in parallel provide a total resistance of 8/7 ohms [=1/(0.5+0.25+0.125)].

In a parallel circuit, the electrons have a choice about which resistance to flow through.  The same idea can be extend to the resistance to flow in water pipes and to traffic flow.  For traffic flow, the effect of road-works and other hold-ups on multiple routes can be modelled.

Two Cultures

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cpsnowThe term ‘Two Cultures’ was coined by Sir Charles Snow more than fifty years ago in his 1959 Rede Lecture to describe the gulf that existed then and persists today between scientists and non-scientists.  He equated not knowing the second law of thermodynamics to never having read anything by Shakespeare.  A number of my posts have referred to the Second Law of Thermodynamics because it explains why engines run and chemical reactions occur but to quote Peter Atkins, it is also ‘the foundation for understanding those most exquisite consequences of chemical reactions – acts of literary, artistic and musical creativity that enhance our culture‘.

Snow, C.P., The Two Cultures: and A Second Look, Cambridge University Press, Cambridge, 1964.

Atkins, P., The Laws of Thermodynamics –  A Very Short Introduction, Oxford University Press, Oxford, 2010.

Something for nothing?

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Let’s try a thought experiment, following on from my previous post (Beyond Zero on 20th February, 2013).  Imagine two equal amounts of matter, A and B at -350 Kelvin and 350 Kelvin respectively.  We would expect heat to flow from the hot one, that’s B to A, the cold one.  This would cause the internal energy of B to decrease with a corresponding rise in the internal energy of A so that B gets colder while A gets hotter, i.e. they both move closer to absolute zero with corresponding decreases in entropy.  The Second Law of Thermodynamics does not allow this to happen and in fact the reverse would occur, i.e. heat would flow from the cold one A to B, lowering the temperature of A and raising the temperature of B so that they both move away from absolute zero with corresponding increases in entropy.coldgraph2

IF we could actually make this happen then we would able to design engines with efficiencies higher that 100%.  One corollary of the Second Law of Thermodynamics is that heat cannot be converted into work without some of the heat being wasted or lost as entropy.  In a power station, heat is taken from a hot source (e.g. a nuclear reactor, solar concentrator or gas furnace) and some of it converted into shaft work, which turns a generator to produce electricity, while the remainder is dumped into a cold sink usually the environment via cooling towers.  However, if our cold sink was at a negative temperature on the Kelvin scale then we could take heat from the cold sink and the hot source at the same time!  Why aren’t we doing this?  Well, we don’t have any naturally occurring cold sinks at below zero Kelvin and to create one uses more energy than we would gain in our super-efficient power station – that’s the Second Law kicking in again.  So you can’t have something for nothing.