Category Archives: Engineering

Impossible perfection

Carnot’s equation for ideal efficiency of a cyclic device converting heat to work and operating between two temperatures specified on the Kelvin scale

In my last post [National efficiency on 29th May, 2013] I calculated the efficiency of the nationwide process of electricity generation in the UK [35.8%] and made no comment on the relatively low value. It will be similarly in all industrialised countries as a consequence of the second law of thermodynamics and the requirement for all real processes to increase entropy. A French engineer / scientist, Sadi Carnot [1796-1832] demonstrated from the second law, that the maximum efficiency achievable in ideal conditions by a process operating in a cycle to convert heat into work is a ratio of the temperatures of the heat source and cold sink to which excess heat is dumped. In a power station the heat source might be a fossil-fuelled furnace, a nuclear reactor or a solar concentrator. The cold sink is usually the environment, perhaps in the form of river or sea water. So both source and sink temperatures are limited. The sink by the local climate and the source by the temperatures that modern materials can withstand.

The very best efficiency based on Carnot’s expression for a maximum material temperature of 350 degrees Centigrade [=623 Kelvin] and environment temperature of 5 degrees Centigrade [278 Kelvin] is 55%. Of course a real power station will never operate at this level because ideal conditions are not achievable – perfection is impossible.

The ideal efficiency improves as the operating temperatures of the heat source and sink are moved further apart and this quest to raise this temperature difference drives a substantial proportion of materials research. However, even operating with a heat source at 800 degrees Centigrade, using expensive, high temperature alloys, such as Hastelloy N [a nickel-chromium alloy], on a winter day in the Canadian capital, Ottawa where the average January daytime temperature is -7 degrees Centigrade, the Carnot efficiency of a power station would be only 75% [=1-(266/1073)].

Energy diversity

Noise transfer

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This is not the author’s house!

We are privileged to have magnificent views of the river and mountains beyond from our city centre house. However, the house was built before the motor car was invented when the loudest event outside might have been rowdy party-goers heading for home. We still have some party-goers walking home under our bedroom window at night but most of them travel by noisy taxis. I look forward to when the price of fossil fuels, or legislation will force taxis to become electric-powered. In the meantime, we have been designing secondary glazing that will offer a high resistance to noise transmission and be in keeping with the early 19th century windows. Noise is a form of energy transfer by vibrations, acoustic energy would be an alternative term for it, and so the combined resistance of the outside wall of my bedroom can be calculated using Kirchhoff’s law, as discussed for heat transfer in my last post [Born in a barn, 20th March, 2013]. In this case, the thin and badly-fitting but antique glass is the dominant component of both the heat and noise resistance. We were happy to deal with the poor resistance to heat transfer by using plenty of bedclothes, i.e. adding a large resistance in series, but the same approach does not work with noise because earplugs are uncomfortable, fall out in your sleep and have a low resistance at the frequency of taxi-generated noise. So, the solution is secondary glazing and the best performance is achieved using an acoustic laminate consisting of a polymer sandwiched between two sheets of glass which should be different thickness to avoid resonant effects. Of course this will also improve the resistance to heat transfer which will be advantageous in winter, but perhaps not in summer…

Born in a barn

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In 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?’.

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