Carnot efficiency

Twist 1.5, Major's Hill Park, Ottawa

For a bit of light entertainment, I have been reading Tom Rogers’ book Insultingly Stupid Movie Physics, which basically covers the same terrain as his entertaining website, though at greater length and with more detail. Of course, one can never entirely escape climate change related information, and the book includes a discussion of Carnot efficiency: the maximum theoretical efficiency with which heat engines can convert thermal energy into useful power.

The efficiency depends on two factors: the high temperature produced using combustion, solar energy, geothermal energy, etc, and the cold temperature where the heat is expended into the surrounding environment:

Efficiency = ( 1 – Cold temperature / Hot temperature ) * 100

This has implications for technologies like the co-generation of heat and power. If the heat source for a power plant is 375°C (648°K) and it is dumping waste heat into 10°C (283°K) outdoor weather, the Carnot efficiency is about 56.3% (the actual efficiency is lower, for various reasons). If, instead, it is dumping the heat into buildings at 25°C (198°K), the Carnot efficiency falls to 54.0%. In a case where the heat source is just 200°C (473°K), the difference between a 10°C cold area and a 25°C cold area cuts the Carnot efficiency from 40.2% to 37.0%. In many cases, cogeneration is still worthwhile, despite the loss of useful electrical or kinetic energy, but it should be appreciated that the redirection is not without cost.

Carnot efficiency also helps explain why waste heat is not always worth capturing. If the temperature difference between the source and an available destination for the thermal energy is not large, there isn’t much useful power that can be produced.

[Update: 4:47pm] Remember to express the temperatures in Degrees Kelvin, by adding 273.15 to the figure in Degrees Celsius.

Embassy artwork

Ugly statue outside the American Embassy, Ottawa

The city of Ottawa is quite well provisioned with public art. Some pieces, like the wooden spiral in the park near the mint, are quite charming. The piece above, located in the US embassy compound, is probably the worst of the lot.

As you can see, the sculpture looks a bit like a balloon animal where the balloons have been replaced by black steel beams and the angles have been randomly altered by twenty or thirty degrees. Sitting within a perimeter fence that never contains a visible human, the statue also symbolizes how faceless and harsh the whole compound is.

While concerns about security are obviously of enormous importance for an American diplomatic facility, nothing about them seems fundamentally at odds with good taste. A less ghastly bit of art, and an embassy that somehow demonstrates that the United States is a nation full of people basically just like Canadians rather than an imposing neo-military facade, might be a start along that road.

P.S. In the spirit of fairness, it should be noted that the British High Commission is equally externally unpopulated and far more lacking in architectural virtue.

P.P.S Two other statues notably for their oddness and lack of aesthetic appeal are the strange rocket ship / polar bear statue at the building formerly intended to become city hall and the giant evil spider outside the National Gallery.

Comprehensible art

Perhaps my favourite thing about Vladimir Nabokov is how he never sacrifices clarity for the impression of brilliance. So many great modern authors seem to take delight in baffling their readers, whether with torturous sentences, incomprehensible plots, or surrealism. James Joyce is especially guilty, but hardly alone, in his use of such approaches. While such writing can push the boundaries of language, it is likely to try one’s patience as well. As such, it is especially pleasant to see genius expressed in a straightforward form: excellence in a fairly traditional format.

It’s rather like the different kinds of modern art. There may be some profound idea in the mind of the artist who has splattered a crumpled canvas with Burger King condiments, but I have a lot more respect for the one who made the elegant sculpture in wood or marble or bronze.


Luminox in Oxfordshire

The Luminox festival is really quite something. Essentially a celebration of combustion, it runs all along Broad Street from 7:00pm to 10:00pm for the next two days. The event involves a combination of fire-based artistic displays and live music. The whole thing seems to be paraffin powered, and it includes both static displays and manned installations that are made to flare up with the removal of chokes. Spaced along the road are braziers of coal and wax-burning metal chimneys that glow orange hot. Hanging from a crane beside Balliol College is a massive chandelier of flame.

Having such an immediate experience with fire would be impossible in lawsuit-happy North America, but it is quite engaging and beautiful. I actually took about fifty pictures, so expect to see them crop up on future days when I am too busy to find something new.

PS. Today, I also saw the inside of the Green College tower tonight, and got a photo of Mansfield for my growing collection of Oxford college images.

PPS. Did you know that you can set Google Calendar to automatically notify you of upcoming appointments by SMS? During the breaks, I have trouble keeping track of exactly which generally unstructured day I have an event in. With this free service, I have a very helpful aide memoire.

Early birthday gift

Klein Bottle in WadhamAs soon as I saw the box from Meghan in the porter’s lodge, I knew that there was a closed, non-orientable, boundary-free manifold in Wadham. Despite my birthday not being for another four days, not opening it at that point would have been pointless and superfluous. After all, it is better to have a Klein Bottle on display than a Klein bottle which you know to be in a box. I trust that Meghan will understand.

As you are like to find in the office of a particularly cool mathematician, it is a genuine Klein Bottle: such as you would get if you could glue the edges of two Mobius strips together. While that is not actually possible in three dimensional space, the Klein Bottle is a three-dimensional cross section of that higher dimensional object. Imagine, for a moment, a hair elastic twisted into a figure-eight shape. In three dimensions, you can do that without having it intersect itself. If you were to draw that figure-eight hair elastic, however, or take a photo, it would look as though it intersects itself. The same is true of a Klein Bottle embedded in three dimensional space. Note that even if our universe really does have ten spacial dimensions, or more, as postulated by string theory, there are still only three of them unfurled enough to put parts of a glass Klein Bottle in.

Invented by Felix Klein – a German professor of mathematics – in 1882, a Klein Bottle has only one side (no inside and outside like a balloon), yet also no rim or lip (like a bowl or an open wine bottle). It’s the only gift I’ve ever received that I printed off an encyclopedia article about, for use in explaining to guests. You can also tell people it’s a work of modern art.

Many thanks Meghan, for furnishing me with what may be the geekiest thing I have ever owned. Like surviving through a battle in which your friends died, getting a Klein Bottle creates a commitment to live the rest of your life in a certain spirit. It’s also dramatically quieter than my rock tumbler used to be.