A piano from a plane

What happens if you throw a piano from a plane? Would it be dangerous?

I think we should ban people throwing pianos out of planes!

Exactly, what would happen if you threw a piano out of a plane? Are you sure it would be dangerous?

Well, you say it’s obvious, but let me ask you some questions and then let’s see if you are so sure.

• How long will it take to fall? Will it be 10 seconds? One minute? Two minutes? Oh! you need to know how high the plane was flying before you can tell me how long it will take to fall? What what range of times will it take? What if the plane is only just above the ground – would that be dangerous?
• Will it break apart as it falls? Pianos are not known for their aerodynamic efficiency. So could the wind actually tear it apart? Well yes, it might. It could easily loose a lid, and some internal parts.
• How dangerous would a falling piano be? Very dangerous? Well doesn’t that depend on where it fell? And in how many pieces. And the range of speeds of those pieces. And of course, there are many types of piano.

So based on this we conclude that you want a blanket ban, but you don’t know exactly how long it would take to fall – that would need further research. And low altitude falls -from  say 1 metre would probably not be dangerous. You don’t know how many pieces it would break into – that too would need research. And you don’t know exactly how fast each part would be travelling when it hit the ground. And you would need to know where the piano exited the plane in order assess the likelihood of damage.

So without further research you can’t be sure that de-planing of pianos would definitely be dangerous. And yet you want a complete ban?

Is a blanket ban appropriate? Yes! Because despite the detailed uncertainty, we all know that one way or another the piano will hit the ground and damage whatever it happens to hit.

And it’s the same with putting 35 billion of tonnes of  carbon dioxide in the atmosphere every year. Lots of the details are uncertain, and much of the argument against actually doing something exploits this uncertainty. But the end result is simple to calculate.

As surely as a piano thrown from a plane will hit the Earth, carbon dioxide emissions will warm it.

BAD THING WILL HAPPEN, say scientists

Annual Global Temperature anomalies compared with 1950 to 1980 base line. The data are colour coded with red indicating an El nino event. We can characterise these events, but we can’t predict them. Graph from Wikipedia

I worry a lot. It’s deep rooted, and I can’t help it. But there you have it, I worry.

And reading about  the things that climate change “is going to cause” worries me a great deal. Not because I am worried about the things in the themselves. Bad as they are, we will face them when they happen – as we have done with events throughout history. What worries me is the consequences of them not happening.

For example today the Guardian reports that

MILLIONS FACE STARVATION AS EARTH WARMS, say scientists .

And last week I read that

CLIMATE CHANGE WILL LEAD TO BUMPIER FLIGHTS, say scientists. 

Please understand, I don’t want either of these things to happen – I am against mass starvation. But these stories worry me for another reason.

• Firstly, they fit the general formula which media of all kinds love. They are a chance to use the headline BAD THING WILL HAPPEN, say scientists. The ‘say scientists’ tag absolves the reporting organ from editorial responsibility. And from their perspective, the bigger and badder the ‘bad thing’ the better.
• Secondly, they are both based on models of Earth’s climate. And impressive as these models are, Climate Models cannot yet predict some very basic features of our climate – such as the timing of an El Nino event. An El Nino event is a periodic oscillation linking ocean and atmospheric circulation across the Pacific Ocean, and affecting climate world-wide – see the graph at the head of the page – El Nino years are globally hotter. To the best of my knowledge, we simply do not know if Climate Change will cause more of these events, or less, or none, or something else. But whether an El Nino event happens or doesn’t happen will affect the details of almost any climate prediction.
• Thirdly both of these predictions are about the future. Human beings are spectacularly bad at predicting the future. And when a particular prediction doesn’t come true then the credibility of all predictions is affected.

So together these three features worry me. I am worried that people will just grow weary of hearing about bad its going to be. And this will cause them to take the fundamental issue less seriously. And if specific prediction X doesn’t happen this will only be reinforced.

The actual message is so much simpler. Putting carbon dioxide into the atmosphere will inevitably warm the Earth’s surface for really simple reasons.  And as a result, ice will melt, sea levels will rise, some places will get wetter and some will get drier. There is no doubt about any of these predictions. And none of super Climate Models actually predict anything very different.

What the models do is attempt to say how quickly things will change, which places will get wetter, and by how much. And these details are – in honesty – still uncertain. Like a weather forecast they will often be right – but also commonly wrong. And like a weather forecast, climate models are useful – but never certain.

These are worrying times.

 

Why Measuring Stuff Matters

We live in a world in full of vast structures which change imperceptibly slowly, and tiny structures which change imperceptibly quickly. Measurement extends our senses into these realms.

One of the wonders of human psychology is how we deceive ourselves about the true nature of the world.

One of the triumphs of the human psyche is that – even while trapped within our own deception – we can break through and discover uncomfortable facts about the world. Facts that allow us to understand our limitations and learn how to overcome them. Experiments which allow us to experience our own blind spots are a classic example, but in fact we go much further than that.

We trust our measurements more than we trust ourselves. From basic measurements of length and time and mass, we have developed an infrastructure that allows us to make measurements – often simple in themselves – through which the nature of the Universe is revealed to us – despite our very human biases and blind spots. Sorry that sounds so pompous – but that’s how it is!

We make measurements and then we trust them more than our own eyes. If sensors tell us a light is flickering 100 times a second – we believe it – even though our eyes see nothing. If measurements indicate that continents are moving apart at 2 centimetres per year – we believe them – even though we experience nothing.

We have developed techniques of measurement that allow us to see ourselves and our world in richer detail than at any time in human history. Looking just through the open tabs on my browser I see have measurement ‘stories’ on all these themes:

• Body Mass Index by Country: A basic measurement but fascinating to see it plotted in this way
• The detection of the position of a football in a goal mouth – can that really work?.
• Scientists use air-dropped javelins to chart the motion of inaccessible Antarctic Glaciers and reveal the speed with which they are moving.
• The ISTI data bank with traceable measurements of the temperature of the air above the land surface of the Earth.
• The HadISDH database of humidity measurements above the land surface of the Earth, showing the moistening of the atmosphere
• Arctic Sea ice recorded daily showing the annual changes and revealing the recent excess melting.
• Measurements of the type and energy of particles in Cosmic rays may reveal details about nature of the Universe.
• Satellite measurements of the saltiness of seawater revealing fascinating patterns of circulation

In each case above, measuring things and comparing them with our expectations doesn’t simply provide a number – it allows us to view the world in new ways. And it allows us to extend our vision into the realms of the otherwise imperceptible, or the overwhelmingly vast. And that is why measurement matters!

Solar power gets real

Some of the long parabolic reflectors in the Shams 1 electric power plant in Abu Dhabi.I love to see this kind of machinery made real. Image from the Shams Image Gallery

I love seeing pictures of real solar electricity generating plant. In a sunny country where peak sun coincides with peak electricity demand – for air conditioning – this makes complete sense. I can’t speak for the finances, but in terms of EROEI, this looks a sensible energy investment.

The BBC recently showed footage of the SHAMS 1 plant in Abu Dhabi. The enterprise also has a web page and wikipedia entry.

There are loads of ways to generate electricity with solar energy. I don’t know that one technology can yet be said to make better sense than any other – but this plant looks relatively low tech and relatively expandable. This must be like in the early days of steam engines or powered flight where people struggled to find optimal engineering solutions.

This plant in fact appears to be a solar-assisted gas-fired steam turbine, where the solar heating is used to reduce the gas consumption, but where gas can be burned as back-up at night or on cloudy days.

There was a mention of the ability to store the solar heat for short periods and so spread the generating time, but it didn’t sound as though this had been implemented.

Why am I mentioning this? Because lots of places in the world are sunny – and many of these places have lots of space. This is unlikely to be a good technology for use in the UK, but for countries near the Equator such a plant must look attractive – exploiting a natural and inexhaustible resource and delivering valuable electricity.

It looks to me like a glimpse into the future. A sustainable future.

What should we do after we stop Global Warming?

The Keeling Curve using data up to 2150. Back in 2013 no one would have imagined that we could make it peak at only 512 ppm. I think this is one of humanity’s greatest collective achievements. Which problem should we tackle next?

Sometimes I like to imagine having different problems to solve. Somehow problems we face right now seem very hard, whereas non-urgent problems, or other people’s problems  seem to have obvious solutions.

While musing on this I considered the possibility that we had collectively solved the problem of Global Warming and Climate Change. Even just imagining this lifted my spirits. And so I was able to wonder: what problem should be next? If we can solve that one, surely there is nothing we can’t do?

“Hang on!” I hear you say, “Before you go solving humanity’s next eco-problem, could you just explain how we solved the Global Warming ‘thing’?”. Sure.

Well it took a few years of the usual equivocation. But then in 2019 several events conspired to focus the minds of governments. Firstly there was the 40% reduction in the US grain crop and a similarly bad year in Russia. This was the first summer in which the North Pole was ice-free for months – and this somehow shocked people and changed popular sentiment – even amongst ‘right-wing’ media.

The previous bitter winter in Northern Europe had been followed by a summer heat-wave with temperatures of 45 degrees in Scotland. These twin seasonal extremes had killed thousands of people and left crops and livestock devastated. So when governments met in the blistering heat of the 2020 International Brighton Conference – some how everything came together. Governments competed with each other to show how radical they could be.

Things moved quickly. During the following summer a vast international flotilla created millions of square kilometres of fog-mist in the Arctic Ocean, reflecting the summer heat and tying the circumpolar winds as far north as possible. After two years, the arctic sea ice began to thicken and its summer extent began to grow back. Even the permafrost began to cool again as a the snow-line moved south.

In the developed nations, radical measures were finally accepted. Enforced car-sharing, compulsory insulation of houses, night time switch-offs and widespread tele-working reduced  carbon emissions by 30% in just three years. The results could be seen on the Keeling curve. Then the 2043 eruption of Mount Biggo-Wunno dramatically affected global temperatures for the next decade, and despite the devastation, helped moderate the warming in both hemispheres.

Of course this just slowed the rate of increase – it took the rest of the century to turn around the rising CO2 levels, see them stabilise at the previously unthinkably low 512 ppm, and finally fall for the first time in 2092. There were plenty of problems along the way – and plenty of consequences of climate change to cope with.

During the first decades of the century, our understanding of climate, weather and computing all evolved exponentially. Our ability to make informed decisions was transformed with the 2029 implementation of the devolved computing paradigm (DCP). Immediately meteorologists were able to run realistic models that could predict real weather 3 weeks in advance. And climate modellers found that they could finally predict the effects of specific policy actions in way that convinced politicians.

But the modelling revealed what we had already known one hundred years previously. Without anthropogenic interference, the Earth would have been drifting towards a new ice age. Now, having changed our lifestyles and geo-engineered specific solutions, could we really let that happen just because it was a ‘natural’ trend?

New Nuclear?

Tony Blair (remember him?) with the Sellafield reprocessing plant in the background. Basically there has been no progress on the of building of new nuclear plants since 2004. (Image from The Guardian)

When I began Protons for Breakfast back in September 2004, one of the big questions we looked at was whether the UK would actually get around to commissioning new nuclear power stations. In that first presentation I quoted an article from the Daily Telegraph (11th July 2004)

“…even if the next administration decides in 2006 to build new nuclear stations, the planning and construction process means that new plants could not come on line until 2015 at the earliest.“

I also quoted the then prime minister, Tony Blair.

“If it were done when ’tis done, then ’twere well it were done quickly…”*

As we end the 17th presentation of the course in April 2013, we are still asking exactly the same question. If we had made a decision back in 2006, then we would now be just a year or two away from switching on perhaps 3 GW low-carbon electricity generation.

Back then it seemed as though the British Government would make the choice. Now it seems the choice lies with a company (EDF) owned by the French government, who will assess our offer of subsidy to see if it suits them. However did we get here?

The reason has to do with the uniquely capital-intensive nature of nuclear power and the essentially uninsurable nature of its risks.

We can build up wind farms, one rotor at a time with each rotor costing only a few million. Private capital can do this. We can build up solar power in the same way.

Conventional coal and gas power plants costing on the order of 1 billion pounds and with a well-understood lifetime cost can just about be built by private capital.

But putting up on the order of 10 billion pounds for which there will be no return on investment for a clear decade at best, requires a rock solid guarantee of a return on investment which only governments can provide. At the moment it looks like the subsidy for the first station might guarantee a price as high as £0.10p per kWh for the next 20 or 30 years.

EDF are perfectly reasonable in asking for this subsidy. Our weak position as a country is because of decades of under investment in the massive costs of generating and distributing electricity. There is no reason to think that ‘market forces’ will drive the level of investment required – only governments can do this.

Now you may think that we shouldn’t build any new nuclear power stations. This is a fair point, and we could discuss it at leisure. However, it really does feel like a matter of national shame that we can’t even make up our minds one way or the other and just get on with it.

* Actually Macbeth Act 1 Scene 7

Lessons from a cold spring

A helicopter delivering emergency supplies to farmers in Northern Ireland. Picture Credit Paul Faith/BBC

It’s been cold in the UK this spring 2013. Much colder than usual and even now at the start of April, the average temperature in London is only around 4 degrees Celsius.

In the North there is still snow on the ground, electricity supplies have been disrupted and livestock killed. The Daily Mail is shocked. The Guardian is concerned. And some even suggest this is a harbinger of changing climate resulting from last summer’s exceptional loss of Arctic Sea Ice.

Personally I don’t know if this weather does or does not result from the shocking Arctic Sea Ice decline. But I think there is one very important lesson we can learn.

This spring is only fractionally colder than most UK springs. And already we are losing livestock, crops yields are affected (so raising prices), heating bills are higher than expected, and it will cause significant road damage.

Now imagine if this happened every year. Or imagine if it happened for twice as long. Or for twice as long every year. In terms of climate change this would be the smallest of shifts. A small change in the position of atmospheric circulatory patterns. But life in the UK would be more unpleasant and more expensive.

At Protons for Breakfast people often ask – Is Climate Change a bad thing? Could there be a good sides to it? And of course Climate Change is not of itself good or bad. And there can be positive aspects to it.

What this spring brings home to me is how much our way of life is adapted to this particular climate, and how much even tiny changes leave us flumoxed. And that while we can adapt to changes – adaptation will cost money.

When climates have changed in pre-history populations have moved or adapted. But at no time in pre-history has the Earth supported 7 billion human beings. We now live highly optimised lives: crop yields that would have been an achievement 30 years ago would now be considered a disaster.

So even though climate change of itself is neither good nor bad. In almost every human situation, even a small amount of change – colder or warmer, wetter or drier – brings trouble, and extra costs.

World Population estimates from 1000 AD to 2011. Data fromWikipedia

Ahhh EROEI

The Ratio of the Energy Returned divided by the Energy Invested in producing electricity. The Green bars are global estimates and the purple bars apply to the US. There is considerable uncertainty in all the numbers.

How should we decide on the mix of technologies to use to generate electricity? There are pros and cons for all the choices.

• Coal is cheap but emits carbon dioxide.
• Gas is a bit more expensive but emits 50%  less carbon dioxide.
• Nuclear requires eye-watering up-front investment but is low carbon.
• Wind energy is intermittent but sustainable

So it is interesting to make quantitative comparisons between the differing technologies. We have many choices in comparing parameters. Initial costs; running costs;  immunity to world fuel prices; sustainability - the list goes on.

One interesting choice is EROEI: the Energy Return on Energy Invested. It is the answer to the sum:

EROEI = Useful energy produced ÷ Energy invested

So for example, if I use one unit of energy to dig coal from the ground, ship it around the world,  and then burn it to power a steam turbine and make electricity, how many units of electrical energy do I generate?

This is a simple question to ask, but a difficult one to answer. For example, one would obviously consider the energy used in shipping the coal. But what about the energy used in building the ship? Or some fraction of it? Using standardised rules one can produce estimates of EROEI and the results – in a chart at the top of the article are interesting.

Several things struck me about this chart

• First there is massive discrepancy between world-wide coal (18) and US coal (80). This is presumably because of the ease of extraction of US coal, and the short distance from mines to coal-powered  electricity-generating plant. The large numbers in each case help explain the popularity of coal in generating electricity both world-wide and in the US. The energy return of course takes no account for energy which might be needed to cope with the consequences of the massive carbon dioxide emissions, or the appalling environmental legacy of coal mines.
• Second is the number for wind (20 or 18) – which is more-or less the same as coal. At Protons for Breakfast many people ask whether in energy terms wind power is ‘worth it’. The answer from these studies is a definite ‘Yes’. However I suspect that the time to reap this return on investment may be longer which affects the financial return on investment.
• On reflection I was not surprised that hydroelectricity represents the best EROEI, but of course this does not cover the environmental costs of such schemes.
• The low value for gas (7 or 10) surprised me. I suppose this reflects the costs of discovery, transport, storage and delivery.
• And finally the numbers for solar energy more or less match the numbers for nuclear energy. These are not specific to the UK and so the same numbers are unlikely to hold here. However I was surprised at the low number for nuclear power and the relatively high value of Solar Photovoltaic generation.

EROEI is not a magic number – but it is a fundamental number. If this number is below unity, then in energy terms the activity makes no sense. And if the number is close to unity, then the activity is barely worthwhile unless there is some other benefit. Scientific American suggest that activities where the EROEI is below 5 represent a borderline below which electricity -generating technologies are no longer worthwhile. It is interesting that several current technologies – including nuclear power –  come close to that suggested border.

References

Mason Inman: Scientific American 2013: This contains lots of links to his sources – but many of these are behind pay walls

Wikipedia EROEI  This contains lots of links to sources – but many of these are behind pay walls as well

Watching pots boil

My previous article about kettles left me wondering: Can gas hobs really waste more than half of the calorific energy in the gas? I decided to try a few more experiments and finally I think I have an answer: ‘Yes’. Gas hobs really do fail to transfer a great deal of the calorific energy in the gas to the pan or kettle they are heating.

Experiment#1: Heating different amounts of water in the same pan

Experiment#1 Rather than measuring the total time to reach 100 °C, I measured the rate of temperature rise. Because the heat capacity of water is well known, this allowed me to estimate how much thermal power was entering the water. So I spent a happy hour or so heating up various amounts of water: first 200g, then 400 g, 600g and finally 800g and I measured the temperature every 20 seconds.

The temperature rise versus time of four different amounts of water on a 1.75 kW burner.

I knew the burner power was 1.75 kW, and after a little jiggery pokery with a spreadsheet I estimated the power entering the water as a function of temperature rise.

The estimated amount of thermal power entering the water for water on a 1.75 kW burner.

The data is a little noisy but it shows that initially only about 850 W of the burner power reaches the water. Since this is 1750 W (nominal) burner, this raises the question of where the remaining 900 W of power is going! It is also interesting that rate of heat input to the water decreases with temperature rise such that the rate of heat input at the boiling temperature (roughly 80 °C temperature rise) is barely more than half the initial rate of heat input. I have calculated the radiated heat from the upper surfaces of the kettle and it cannot account for this.

Experiment#2: Heating the same amount of water in the four different size pans.

Experiment #2 Now I fixed the amount of water (0.5 kg) but I used four different pans: a baby pan (0.487 kg: diameter 15 cm); a mother pan (0.601 kg: diameter 17 cm); a daddy pan (0.834 kg: diameter 19 cm) and a big daddy pan (1.8 kg: diameter 24.5 cm). I measured the water temperature at the start, heated for 60 seconds and measured the temperature again, and then heated for another 60 seconds. The results are shown in the chart below.

The temperature rise after 60 seconds and 120 seconds of 500 g water heated in four different size pans.

The main observation is that the water heats significantly faster in the largest pan. After 60 seconds the temperature of the water in the small pan had risen 20 °C whereas the water in the largest pan was 5 °C hotter – despite the extra 0.347 kg of steel that needed heating. This is consistent with the idea that a great deal of the heat energy is lost because the hot gas from the combustion does not remain in contact with the base long enough to transfer its heat. On small pans, hot gases escape around the edge of the pan.

Estimated efficiency of heat transfer to a pan versus the area of the base of the pan.

I estimated the heat capacity of the pans and then calculated the fraction of the energy of the gas that the [pan + water] combination had captured. The data show a linear dependence on area with the largest pan capturing a plausible 83% of the calorific energy of the fuel.

Two images of a kettle on a hob taken using infra red light. The image on the left shows the general situation of the kettle – notice the hot handle! The thermograph on the right shows details of the base with an estimated temperature of approximately 224 C.

Experiment #3 It occurred to me that the underside of the kettle (or pans) might become extremely hot and radiate a significant amount of energy. However borrowing a thermal camera from work, the hottest features I could see were only just over 200 °C. Even accounting for the considerable uncertainties in this estimate, the radiated energy from the base of the kettle is only a few tens of watts at most, and can’t account for the energy losses of hundreds of watts that I have observed. A picture of the kettle on the hob shows the strong heating of the base of the cooker and the handle – which was indeed too hot to hold.

Summary

So now a general picture emerges: although cooking with gas uses a primary fuel, typically half of that energy is lost on the hob. Using a large pan on a small flame, I managed to capture as much as 83% of the primary energy, but for a kettle, 50% is probably more typical. Using a large flame on a small kettle will easily waste more than 50% of the energy.

And I can now answer my initial question: Should I use an electric kettle (in which 60% of the primary energy is discarded at the power station, but which is essentially 100% efficient in my kitchen) or a gas kettle (in which nearly all the energy of the primary fuel is delivered but which is only rough 50% efficient in my kitchen)? My answer is that it makes very little difference. It is best to use whichever device allows you to easily boil the correct amount of water – and not to boil water which is then unused.

Which kettle to choose: Gas or Electric?

Which kettle is more energy efficient?

Boiling water is an essential pre-requisite for the preparation of tea – and as such it is an activity central to the cultural life in England. For example, six cups of tea were drunk while preparing this article. Boiling water is also an energy intensive activity and so for all the usual reasons, it’s a good idea to boil water in an efficient manner. But should one use an electric kettle or a gas kettle? This was the subject of my first ever blog posting back on 1st January 2008 – and because that blog is no longer available, I thought it worthwhile to re-post and re-visit the problem now.

Initially, I was confident that using a gas kettle would save energy compared with an electric kettle. This is because electricity is generated at power stations which have an overall efficiency which is often less than 40%. That’s a guideline figure for any thermally-generated electricity (coal, gas or nuclear). It means that roughly 60% of the energy content of the fuel is lost before the electricity leaves the power station. Some gas generation using CCGT technology is more efficient: up to 60% in the best cases but relatively little electricity is generated this way. Additionally, typically 10% of the energy which leaves the power station is lost in transmission to my home. So only perhaps 36% of the original energy content of the fuel is fed into my kettle element.

Since raw methane is distributed directly to my kitchen, all a gas kettle has to do is capture a bit more than one third of the chemical energy and I would be better off than using electricity. So I was confident that by using a gas kettle I would be making an environmentally friendly decision.

Was I right? I compared the time boil 1 litre of water with the time expected if the device used the energy supplied to it in the kitchen with 100% efficiency. I then applied a ‘Network Efficiency’ factor.

The Electric Kettle (2 kW) took 210 seconds to boil 1 litre compared with an expected time of 188 seconds, so the ‘in-kitchen’ efficiency was 90%.

The Gas kettle had three burners:

• The 1 kW Burner took 680 seconds to boil 1 litre compared with an expected time of 380 seconds, so the ‘in-kitchen’ efficiency was 56%.
• The 1.75 kW Burner took 450 seconds to boil 1 litre compared with an expected time of 210 seconds, so the ‘in-kitchen’ efficiency was 48%.
• The 3 kW Burner took 380 seconds to boil 1 litre compared with an expected time of 127 seconds, so the ‘in-kitchen’ efficiency was 33%.

The Microwave Oven (800 W) took 720 seconds to boil 1 litre compared with an expected time of 300 seconds, so the ‘in-kitchen’ efficiency was 66%.

And the results? 

Result #1 Heating water using a gas kettle is a more efficient use of fuel, but only at low gas settings. And even at low settings, a gas kettle wastes 50% of the energy supplied to it. Using higher gas settings wastes an even larger fraction, up to 67%!

Result #2 Heating water using an electric kettle is the fastest way to heat water, being roughly twice as fast as the high-power gas burner – and with very similar efficiency.

Result #3 Using a microwave to heat water was definitely the least efficient of any of the methods – but this result may change when heating small quantities of water.

Overall the data indicate that gas kettles are amazingly wasteful. In subsequent articles I will be looking to see if they really are as bad as they seem.

The efficiency of different ways of heating water. The blue dots show the efficiency with which fuel supplied to the kitchen is converted to heat energy in the water. The red dots show the efficiency when taking account of the conversion of chemical energy from the primary fuels. The shocking news is that even when boiling water slowly with gas, around half of the energy is wasted! If one is boiling the water quickly then there is no difference in overall efficiency between using gas or electricity – they both waste two thirds of the energy!

Experimental Details

• I began by measuring the initial temperature of water from the tap which turned out to be close to 10 Celsius.
• I then weighed the vessel (electric kettle, gas kettle or glass jug ) before and after filling with water.
• I estimated the energy required to raise water from 10 °C to 100 °C using the measured water mass and the heat capacity of water (roughly 4200 J per °C per kg and rather constant in this temperature range).
• For the electric kettle I used its power rating of 2000 W (which I had previously measured and found to be a good estimate.)
• For the gas I used data for the gas burners which indicated they had a rated power of 1 kW, 1.75 kW and 3 kW.
• For the microwave (rated power 800 W) I used a power meter to record the actual consumed power (1240 W)
• I then recorded the time taken for the water to reach 100 °C and compared with the expected time if the device were 100% efficient.

I then factored in the efficiency of the network, assuming that

• For electrical heating: 36% or the original calorific energy of the fuel was delivered to the house.
• For gas: 90% of the original calorific energy of the fuel was delivered to the house, with the remainder being used to power the pumps on the gas pipeline.

Finally on rewriting this in December 2012 I decided to re-check my numbers. I boiled the same kettle on the 1.75 kW burner and got an ‘in-kitchen’ efficiency of 41% compared with 43% that I estimated previously. So I estimate that these numbers have an uncertainty of around 1% or so.