# Energy density of coal

One kilogram of coal contains between fourteen and thirty-three megajoules of chemical potential energy, depending on the type of coal (lignite, bitumous or anthracite).

Coal also contains trace amounts of uranium, ranging from one to ten parts per million; in a worst-case scenario one kilogram of coal could therefore be expected to contain one thousandth of one gram of uranium. As uranium has an energy density of 79.5 trillion joules per kilogram that means that one kilogram of coal contains 79.5 megajoules of energy as nuclear potential energy.

Or in graph format (and remember, this is the best-case scenario for coal and the worst-case scenario for uranium):

So there you have it: you can get more energy out of coal by grinding it up and extracting the uranium than you can from actually burning it in a coal-fired power station.*

(It’s also worth noting that coal contains about two-and-a-half times as much thorium as it does uranium, and that thorium is also a nuclear fuel.)

* You could of course burn the coal first, and then extract the uranium from the ash produced, but unlike nuclear power, burning coal is bad for the environment.

# The Drinking Bird

Is the Drinking Bird a perpetual motion machine?

Depending on what type of perpetual motion machine is being described, all perpetual motion machines violate either the First or Second Law of Thermodynamics, so the answer is no, the Drinking Bird is not a perpetual motion machine.

So what powers the Drinking Bird? If it is moving it must have kinetic energy and the Principle of the Conservation of Energy says that this kinetic energy must have come from somewhere. It does not come from the water as, despite what you might have read about “water powered cars”*, water is not a fuel and does not store or transfer energy.

The correct answer is that the Drinking Bird is powered by the ambient heat of the room it is placed in. The process that occurs is as follows:

1. The head of the bird is placed in the water and the cloth material of its head soaks up some of this water.
2. The water evaporates from the cloth head, lowering the temperature of the vapour trapped inside it. The movement of the head through the air as the bird oscillates back and forth helps speed up this evaporation. (The red fluid is dyed dichloromethane and the bird is evacuated during construction so that only dichloromethane and dichloromethane vapour is present in the central column.)
3. As the temperature of the vapour decreases it turns back into a liquid, lowering the pressure inside the central column.
4. This lowered pressure draws dichloromethane from the reservoir at the base of the bird up the central column.
5. The fluid being drawn up the central column of the bird raises its centre of gravity and causes it to tip over.
6. As the bird tips over, the central column becomes open to the reservoir at the base of the bird, causing pressures to equalise and the fluid to drain back out into the reservoir. At the same time the head is resubmerged into the water and the process repeats.

The Drinking Bird is a heat engine that uses the difference in temperature between the head and the base of bird to perform work, transferring thermal energy to kinetic energy. This temperature difference is created by evaporation that is powered by a room’s ambient heat. If you were able to perfectly insulate a room so that no thermal energy could enter or leave then you could cool the room down by leaving a drinking bird running.†

* “Water powered cars” are actually being powered by hydrogen fuel cells. The hydrogen comes from the water and is extracted using electricity, making “water powered cars” actually powered (indirectly) by electricity.

† Friction between the air and the bird, and between the bird and its bearings would transfer some of the bird’s kinetic energy into thermal energy, heating the room back up.

# Why is Quincy, Washington so popular with tech companies?

Quincy, WA is a small town (population 6750) in the north-west of the US. So why have technology giants Microsoft, Yahoo!, Dell, Vantage Data Centers, Sabey and Intuit all chosen to build huge data centres there? Quincy is now home to nearly 190 000 square metres (more than two million square feet) of data centre.

The answer is very simple: electrical power.

The town of Quincy is close to the Columbia river, the fourth largest (by volume) river in the US. There are fourteen hydroelectric dams on the Columbia river, two of which, the Priest Rapids Dam and Wanapum Dam, provide electricity to Quincy.

The Priest Rapids Dam

The Wanapum Dam

Hydroelectric power is cheap,* but more importantly from the point of view of data centre operators, it is very reliable. The reliability of the electricity supply to Quincy is better than 99.99% which is very important for “mission-critical” always-on services like cloud computing. Using renewable non-polluting hydroelectric power also helps service providers demonstrate their green credentials. Server farms consume a huge amount of electricity – more for cooling than for processing – and using hydroelectric power helps to reduce their associated carbon footprints.

* The local utility company, Grant County Public Utility District, offered electricity at a discount rate to attract users to the area.

# Why kettles boil slowly in the US

I saw a tweet recently that intrigued me:

The voltage of mains electricity varies from country to country: the majority of countries use between 200 and 240 volts, but a small minority (most notably the US, Canada and Japan) use between 100 and 127 volts.

Countries using 100-127 volts are shown in red; countries using 200-240 volts are shown in blue. Countries with a mixture of the two systems are shown in purple.

The voltage* of an electrical supply is what pushes electrons around in a circuit. The higher the voltage, the faster the electrons move and thus the higher the current (one amp is equivalent to about six billion billion electrons flowing past a point per second). With a low voltage the rate of transfer of electrical energy is therefore much slower. In the UK, with a mains voltage of 230 V and a limit of 13 A per socket the maximum possible power to one appliance is 2990 watts (2990 joules per second). In the USA, with a mains voltage of 120 V and a limit of 15 A per outlet the maximum possible power is reduced to only 1800 watts, which is why in the US many large appliances (e.g. washing machines, tumble dryers) have to be connected to a separate high-voltage circuit.

To raise the temperature of one litre of water from 15°C to boiling at 100°C requires a little bit over 355 kilojoules of energy. An “average” kettle in the UK runs at about 2800 W and in the US at about 1500 W; if we assume that both kettles are 100% efficient† than a UK kettle supplying 2800 joules per second will take 127 seconds to boil and a US kettle supplying 1500 J/s will take 237 seconds, more than a minute and a half longer. This is such a problem that many households in the US still use an old-fashioned stove-top kettle.

* As a physicist I would normally use the term “potential difference” in place of “voltage” but voltage is better understood by the general public. Looks like the engineers (who prefer “voltage”) won that battle.

† As electric kettles actually use the joule heating effect that is responsible for most of the energy wasted in other electrical devices this isn’t a terribly unfair assumption.

# UK electricity import and export

The UK doesn’t have enough electricity.

The amount of electricity that the UK produces (from various sources) is not enough to meet demand, and the UK relies heavily* on imports from France and the Netherlands in order to meet its needs. This energy gap is due to the closure of coal-fired power stations that cannot meet emission standards and the shutdown of aging nuclear power stations.

The import and export of electricty uses submarine high voltage direct current (HVDC) cables. HVDC cables waste less electricity than AC cables (about 3% per 1000km) and are simpler to construct and operate. A 73 km cable connects Bonningues-lès-Calais in France to Sellindge in Kent; a 55 km cable connects Auchencrosh in Scotland and Ballycronan More in Ireland; and a 260 km cable connects Maasvlakte in the Netherlands to Grain in Kent.

The graph below shows electricity import and export (in GWh) for the eight months since February†, when the Britned Interconnector began operating. When the value is positive (when the line is above the origin) the UK is importing electricity and when it is negative electricity is being exported.

One of the most interesting features of the graph is the change in the import/export to Ireland via the Moyle Interconnector. On 26th June at 0417 one of the 250 megawatt cables failed, halving the cable’s capacity, and at 1409 on 24th August the cable failed entirely and has not transferred any electricity since.

The cause of the failure is unknown and the MV North Sea Giant, the world’s longest offshore construction vessel, is currently moored in the Irish Sea investigating the fault. The cable has been dug out of the seabed 200m below the surface, cut in half, and both ends raised to the surface so the cause of the fault can be investigated. The fault is expected to take up to six months to fix and were a similar fate to befall the Cross-Channel or Britned interconnector the UK would have a very serious energy problem.

If it is to close the growing energy gap the UK must accelerate the pace of construction of energy infrastructure, in particular the construction of safe, zero-carbon nuclear power stations.

* The UK is the world’s sixth largest importer of electricity despite being eleventh in terms of electricity production and twenty-second in terms of population.

† The graph shows a seven day moving average of import/export values. For half-hourly data you can download the full dataset as an Excel spreadsheet.