A Mini-Fridge Investigation

May 24, 2023

Friends, on 7th June I will be giving a talk at the Cheltenham Science Festival with the illustrious Andrea Sella on the topic of Heat Pumps. And I am growing increasingly anxious.

Click on the image for a larger version. Sadly the publicity for our talk at Cheltenham has used the wrong title! But which title have Andrea and I chosen?

I’ve been working on the talk with Andrea for weeks, but there are still parts that we haven’t finalised, including exactly which demonstrations to include. In my search for demonstrations, I thought I would take a look at a mini-fridge that would be easy to position on a table-top. Forty pounds later, a mini-fridge arrived.

Click on Image for a larger version

I managed to get some nice thermal images, and while I was playing around, I thought I would see if I could work out the actual cooling power of such a tiny refrigerator.

Click on image for a larger version


My idea was to measure the rate at which a glass of water cooled inside the fridge. From the definition of the heat capacity of water, I knew that to cool one gramme of water by 1 °C required the removal of 4.18 joules of energy. If I measured the time taken to cool a glass of water, I could work out the rate at which heat energy was being removed in joules per second i.e. watts.

So I poured 300.7 grams of water into a glass weighing 371.9. grams. I then placed the glass inside the refrigerator. I deployed four thermocouples to monitor the progress of the cooling.

  • I put one thermocouple in the water.
  • I put one thermocouple on the cold plate at the back of the inside of the fridge.
  • I put one thermocouple on the hot plate at the back of the outside of the fridge
  • I used one thermocouple to monitor the temperature of the ambient air.

I then used a datalogger to record the temperatures every 30 seconds. The results from the first 8 hours are shown below.

Click on image for a larger version. Graph showing the temperature versus time of the four thermocouples positioned around the fridge. See text for details of their location.

The data looked pretty much as I expected, with a couple of anomalies. I do not know the cause of the ‘spike’ at 5.2 hours, but the change in cooling rate just before six elapsed hours was caused by leaving open the door of the kitchen laboratory.

The graph below is the same as the previous graph, but has arrows to show the heat flows.

Click on image for a larger version. Heat flows naturally from the water to the cold sink. The heat pump then moves that heat from the cold sink to the hot sink at the rear of the refrigerator. Heat then flows naturally from the hot sink to the air in the room.

Cooling Power

To work out the cooling power, I started with the data of temperature versus time for the water.

Click on image for a larger version. Graph showing the temperature (°C) of the water versus time.

I then worked out the slope of graph above. The cooling rate is only a few thousandths of a degree per second, so in order to measure this with thermocouples with a resolution of only 0.1 °C, I averaged the cooling data over ±10 minutes.

Click on image for a larger version. Graph showing the cooling rate (°C/s) of the water versus time.

Just after the fridge is switched on, the cooling rate peaks at around 1.5 thousandths of a degree per second, or 5.4 °C/hour. The oscillations in the cooling rate are probably due to convection of the water in the glass.

To convert this cooling rate into an estimate of cooling power, one needs to multiply the data above by the heat capacity of the water and the glass, in this case, 1575 J/°C.

Click on image for a larger version. Graph showing the cooling power (W) of the refrigerator.

The data suggests that the cooling power peaks at around 2.5 watts and then falls to just a fraction of a watt. The electrical power drawn was 40 W so overall the efficiency was around 6%.

Lowest Temperature

The cold plate in the back of the fridge gets impressively cold, cooling to below -5 °C. So why doesn’t the water cool to this temperature?

To investigate this, I plotted the rate of heat flow out of the water (in watts) not versus time, but versus the temperature difference between the water and the cold plate.

Click on image for a larger version. Graph showing the cooling power (W) of the refrigerator as measured by the cooling rate of a glass of water, versus the difference in temperature (Delta T) between the water and the cold back plate.

The data show that the cooling rate is roughly proportional to the temperature difference between the water and the back plate. But the cooling rate falls to zero when there is around 9 °C of temperature difference. Why doesn’t the water keep on cooling?

The reason is that heat is flowing into the water through the walls of the refrigerator. The cooling power of the heat pump probably remains at around 2 or 3 W, but as the internal temperature of the fridge falls, heat ‘leaks’ through the insulating the walls.

Click on image for a larger version. A more elaborate version of the graph above. showing additionally heat flowing into the cold sink from the hot sink, and the room. The fridge uses insulation to try to minimise these flows, but they are not zero.

An analogy would be using a water pump to bail out a leaking vessel. When the rate of bailing is equal to rate at which water is leaking in, then the water level doesn’t change. Similarly, the colder the inside of the refrigerator becomes, the more significant heat leaks become. The lowest temperature occurs when the rate at which the heat pump removes heat is equal to the rate at which heat leaks from the environment.


Friends, the mini fridge was a little more powerful than I expected, and I was pleased that I managed to remember how to operate the data logger. But none of this is relevant to the talk I am trying to finish with Andrea – somehow these simple measurement exercises seem very attractive when there is proper work to be done.

Hydrogen in the UK

May 23, 2023

Isambard Kingdom Brunel

Friends, on Monday I visited a Brunel University Hydrogen Event. This meant getting up(!) and travelling far beyond the borders of Teddington on TWO buses – so when I arrived in Uxbridge at  11:00 a.m. it had already been an exciting day for a retiree like me.

It was the kind of event I might have attended when I worked at NPL, but when I worked for NPL I would have gone along to promote something, or to give a talk. So it was liberating to be there with no agenda: I went with the simple goal of educating myself. And I did learn a thing or two. So I thought I would jot down a few of the things I learned.

Thing#1: Electrolysers

I learned that ITM Power is one of the world’s leading manufacturers of electrolysers, with a capacity to manufacturer around 1 GW of electrolysers per year – in the UK! Remember that only hydrogen manufactured using electrolysis powered by renewable electricity has the capability to create green hydrogen with practically zero CO2 emissions.

Thing#2: Fuel Cell Vehicles

I learned that many people are still very keen on fuel-cell powered vehicles. Talking with a fellow delegate I pointed out the relative inefficiency of using fuel cell vehicles (FCVs) compared to battery electric vehicles (BEVs) – you can read my previous article on this here. However the delegate was dismissive of efficiency as a metric, whereas I consider it to be overwhelmingly important.

Remember that if we begin with 100 kWh of renewable electricity, after creating hydrogen we will have only 80% of the energy available, and only half of that makes it to the wheels of the vehicle – so only 40% of the initial energy is useful. However if we use that renewable electricity to charge a battery and discharge it, around 85% of the energy is useful.

What this means is that to run a fleet of vehicles using hydrogen fuel cells requires more than twice the renewable electricity resource. In the future we may have an excess of renewable electricity, but this will not be the case for many years.

The delegate explained that efficiency was only relevant if a BEVs had the capacity of a FCV, by which I think they were referring to power and range. So the delegate thought that fuel-cell drive trains would ‘win’ in this area. And it may be that for large vehicles or trains, there may be a niche for fuel cells, but I remain sceptical.

Things#3: Hydrogen Combustion Engines 

To my surprise some people are still pursuing hydrogen combustion for motive applications.

Some people are working on retrofit apparatus for existing diesel engines and some are working on radical new concepts which would operate at very high temperatures and have a thermodynamic efficiency approaching 70% compared with about 25% for a conventional  Internal Combustion Engine (ICE) car i.e. ICE cars throw away 75% of the energy of combustion as heat.

A 3-D printed model of a hydrogen internal combustion engine.

I would have dismissed this completely, but Japanese manufacturers are still clinging to the idea (News Story 18 May 2023) and one of the world’s leading manufacturer’s of construction equipment – JCB – is planning on using such engines in their vehicles.


Click on Image for a larger version. The discussion panel consisting of (from Left to Right): Ben Madden, Rita Wadey, Ben Todd and the keynote speaker, Graham Cooley.

The keynote presentation was given by Dr. Graham Cooley, CEO of ITM-Power, and I found it quite inspiring. I won’t try to précis the talk but instead just note one point.

He noted that technological cultures are built on both molecules and electrons. Historically we have started with hydrocarbon molecules (coal, oil and gas), and burned these molecules to make electricity. But in the current energy transformation, this pattern is being reversed. For a green technological culture, we start with renewable electricity and use that to make molecules – specifically hydrogen – which then seeds the synthesis of larger molecules. I guess this seems obvious to a man who runs an electrolyser firm!

The discussion panel was fascinating, consisting of an investor, an entrepreneur and a policy specialist. Collectively their comments painted a picture of an ever-changing forest of complex incentives, indecision in government, and continuing lack of support. In short, nothing new.

When I asked the panel’s views about heating, one panel member pointed out the astonishing extent and complexity of the gas distribution network, and commented that “...if they can’t find something to put in their pipes, they’re toast!“. I think this explains the desperate efforts of the gas companies to promote hydrogen for home heating – something which would be a disaster for the UK.


Friends, I went along to this event to learn, and I learned that there is a lot of experience in a range of hydrogen technologies in the UK and that Brunel University is full of smart, business-focussed engineers.

But overall I was surprised at the continued focus of research on hydrogen for transport. I wish all the companies involved well, but I didn’t understand their enthusiasm.

I didn’t see any work on hydrogen for aviation, and as I see it, hydrogen for terrestrial transport will only be a niche market – heavy equipment and large lorries. And this niche market is a market that will inevitably contract as battery technology improves, providing vehicles with ever improving specifications in terms of range, load and cost.

But what do I know? Time will tell.



A Short Talk about my Low-Carbon Home

May 20, 2023

Friends, today I abandoned my usual Saturday morning ritual of doing a quiz and a crossword with my wife at our local café.

Instead I travelled far beyond the borders of Teddington to give a  “A Short Talk about my Low-Carbon Home” at the Kingston Efficient Homes Show. There were many celebrities there include Ed Davey, the leader of the Liberal Democrats, and the Green Man, whom Wikipedia informs me is not in fact a pagan mythological figure.

The Green Man visited the Kingston Efficient Homes Show.

I was a little discombobulated at the start of the talk because nobody turned up to introduce me, and the clock in the lecture room was slow. And so while I was just waiting to start, I should already have started. And at the end I was being told to wind up, when in fact I still had many minutes left. Hey Ho.

I promised the audience I would put the Powerpoint slides from the show here, and below is a belated re-recording of the 20 minute talk for those who missed it. Somehow, it is 30 minutes long :-(.


I found the event very moving: it was full of people trying to make the world a better place.

  • There were slightly bewildered members of the public prepared to spend money on heat pumps and insulation and solar PV and batteries.
  • There were installers – the shock troops on the front line of combating climate change.
  • There were architects – including the designers of the fantastic Bale House in Hastings.
  • There were members of the local Council and politicians.

But one thing annoyed me: the endless request for estimates of ‘payback time’ or ‘return on investment’.

As Bill Nye, the mild-mannered American science communicator so eloquently put it, “The planet is on fire“. And people still want to find out whether it’s worth their while to put out the fire? He was actually rather more pithy than that.

If you found that video amusing, here’s another more upbeat version.

Breville HotCup: Thermodynamic Reflections

May 18, 2023

Friends, you may recall my long-standing fascination with boiling water efficiently: see for example:

So ‘boiling water’ was a topic on which I thought I had written my last word. But visiting some sophisticated neighbours, I saw that they had a Breville HotCup – a kettle that held a reservoir of water, but which then dispensed just a single cup of boiled water at the push of a button. Wow!

Remember that in a conventional kettle one almost always boils too much water, thus wasting energy. And in a Quooker one keeps several litres of water at 100 °C so it is ready when you require hot water. Could the HotCup be the clever device that boils exactly the right amount of water just when you need it, without wasting energy on ‘standby’?

Well, after reflecting on the future rubbish I was creating, I bought one and tested it. It is a perfectly pleasant item, and does indeed dispense individual cups of water quickly – and since this is how I generally consume tea – I must confess to being pleased.

But after assessing its performance from an energy efficiency standpoint, I found myself disappointed. At best, it is ~ 80% efficient, but at its worst it is only 25% efficient! It took me some time to work out how it could be so bad, but I did eventually figure it out. Allow me to explain.

What is a Breville HotCup?

There a number of HotCup models, but the key idea behind them all is that it is a kettle which holds a reservoir of water, and then boils and dispenses just a single ‘cup-full’ – variable between 150 ml and 320 ml – at a time.

The video below shows the HotCup in operation along with the equipment I used to make measurements.


I couldn’t see immediately how the device worked, but I set out to measure its performance using the standard techniques of ‘kitchen calorimetry’.

  • I weighed the HotCup when empty and then filled it with about 1.5 lites of water. I then weighed the amount of water dispensed (g).
  • I measured the temperature of the water reservoir, and the maximum temperature of the dispensed water (°C).
  • I recorded the electricity used on a plug-in electricity meter (in kWh).
  • I timed the boiling process using the timer on my phone (s).

From the mass of water dispensed and its rise in temperature, I could work out how much heat energy had been given to the water. I could then compare this with the measured amount of electrical energy consumed. Comparing these two figures I could work out the efficiency with which the consumed energy had been converted into hot water.

Remembering the Golden Rule of Experimental Physics, I repeated the experiment multiple times to assess more or less what was going on. Then when I had practiced a couple times, I made one set of readings with the HotCup set to dispense small cups of water (~150 ml) and one with it set to dispense large cups of water (~330 ml). For each setting I repeated the measurements until the reservoir appeared to be empty. The results are shown below.

Click on image for a larger version. Results for successive SMALL cups of water dispensed. Top Left: The temperature of the reservoir was observed to rise as cups of water were dispensed reaching nearly 80 °C. Top Right: The time taken to dispense a cup of water decreased from about 50 s to about 20 s. Bottom Left: The maximum temperature recorded in the cup into which the water was dispensed. Bottom Right: The estimated efficiency of water heating. The average efficiency is only 25%.

Click on image for a larger version. Results for successive LARGE cups of water dispensed. Top Left: The temperature of the reservoir was observed to rise as cups of water were dispensed. Top Right: The time taken to dispense a cup of water was about 40 s. Bottom Left: The maximum temperature recorded in the cup into which the water was dispensed. Bottom Right: The estimated efficiency of water heating. The average efficiency is about 80%.


Having observed the device in operation and measured its performance, I think I can now see how it works.

I think that the HotCup always boils the same amount of water in a boiling chamber – a mini kettle-within-the-kettle. The device uses the pressure built up within the chamber to push out the boiled fluid, and then discharges the unused hot liquid back into the reservoir.

By analysing the inefficiency of the device as a function of the amount of water dispensed, I estimated the volume of the boiling chamber to be approximately 400 ml.

Click on image for a larger version. Plotting the inefficiency as a function of dispensed volume, I estimate that the ‘boiling chamber’ within the HotCup has a volume of approximately 400 ml.

The TOP LEFT graphs in the two panels above show that the reservoir temperature rises after each cupful has been dispensed. It is clear that this rise is larger for the small cup (150 ml) dispensation in which most of the hot water (400 ml – 150 ml = 250 ml) is put into the reservoir. I made a model of this – shown as a dotted red line – and this seems to roughly describe the data.

Thermodynamic Reflections

Friends, I have had this device in my house now for a couple of months, and since my wife and I generally boil the kettle for individual cups of tea, it is quite convenient.

But as a calorimetric thermodynamicist, I must confess that after making these measurements I was at first disappointed. But on reflection, the performance is actually not so bad.

The inefficiency is the exactly the same as if one used 400 ml of water in a kettle to prepare a single beverage. This volume is close to or below the minimum fill level for many kettles. And so although these results look bad, they are probably no worse than using a kettle.

However, if my wife and I both wanted to drink tea at the same time, or if I wanted to boil larger volumes of water for cooking, a conventional kettle would be more efficient.

2 Gs

May 14, 2023

Friends, sometime today, 15 May 2023, I will have been alive for about 2 billion seconds. Or as we metrologistas say, two gigaseconds (Gs).

Long periods

We traditionally celebrate our ages in years – orbits around our Sun. And at my age, these milestones pass with tedious regularity. And we take special note of decades, of which we might hope to live for a couple of handfuls. We mark these special birthdays with fear or wild celebration. But these super-long periods are interesting.

Astrologers discuss the significance of the ‘Saturn Return‘ which occurs typically every 29 years and this has something in common with a gigasecond, which is 31.7 years.

I am fortunate to have made it past my first gigasecond – which could be considered to encompass my youth. And  I feel especially fortunate to be alive to experience my second complete gigasecond – which I guess has encompassed what we generally refer to as middle age. But realistically, I am unlikely to be alive to celebrate my third gigasecond, which will pass just after my 95th birthday. This is not a maudlin reflection, this is just statistics. And even considering the oldest people who have ever lived, no one has ever reached four gigaseconds.

And so while it is unusual to measure the length of a human life in seconds – very roughly heartbeats – the gigasecond is a useful unit because our lives can be considered on such a very simple scale: 1, 2, 3…

Friends, whatever your age, I urge you, if you can, to pause to enjoy the day on which I embark on my third gigasecond.

Best wishes


Food and Climate Change Without The Hot Air: A Review

May 11, 2023

Friends, as you may recall I have reduced emissions from my home from about 3.7 tonnes per year to around 0.7 tonnes per year, and this should come down in future years as the electricity supply incorporates a greater fraction of renewable generation.

But my house is only one of the ways in which I emit carbon dioxide. And in the last year I have been working on reducing carbon dioxide emissions associated with my consumption of food. This is a much cheaper endeavour financially, but one which forces me to address habits I have ingrained over the my life. And that makes it hard emotionally.

My minor triumph in this area was giving up milk in tea and coffee (link). Throughout my life I have drunk prodigious quantities of tea and coffee with milk, and so this was initially a real sacrifice. But one year later, I have incorporated this into my lifestyle. And I have been working on reducing the residual meat and dairy in my diet, though rather less successfully.

In order to improve my understanding, last year I bought “Food and Climate Change without the hot air” (FACCWTHA) by Sarah Bridle and read it avidly. I had meant to write a review last year, but somehow despite the slow pace of my life in Teddington, I somehow could not find the time! But a couple of months ago I heard Professor Bridle speak and felt re-inspired.

Admirably (in my opinion), Professor Bridle began her career researching the physics of extra-galactic astronomy, but switched fields to help address climate change. Her research now focuses on using data to help transform food systems.


Friends, working out the carbon dioxide emissions associated with food is a colossally difficult problem. It has all the hallmarks of carbon accounting – which I hate!

Let me give you an example: when one goes to the supermarket to buy – say – a tomato, there is no fixed answer to the question: how much carbon dioxide emission is associated with each tomato. It depends on the time of year, the country of origin, how it was grown, how it was transported to the UK, how we will take it back home from the shop, and how it will be cooked. And the same is true for almost everything we eat.

And so FACCWTHA is not a database in which one can just look up a food stuff. Rather it is a narrative description of the factors which affect the emissions associated with our food choices. Consider it a book written to raise your own consciousness.

In the introduction Professor Bridle writes:

When I first learned about the impact of food on climate change I went vegan for a while. I put my jacket potato into the oven for two hours and waited around smugly with my can of beans, unpacking my suitcase after a transatlantic flight. I drove to the shop 3 km (1.86 miles) down the road just to buy some plant milk, and also probably picked up a pack of green beans flown in from another continent.

Following up on this paragraph, Professor Bridle then compares the emissions associated with her flight, ‘popping’ to the shops by car, and using an oven for two hours.

  • Flight: about 9 kg/day averaged over 1 year
  • Car: about 0.5 kg
  • Oven: about 2.5 kg

The emissions associated with the potato itself (about 0.3 kg) are almost negligible.

In the introduction Professor Bridle explains emissions associated with food amount to about a quarter of global emissions – equivalent to about 10 billion tonnes per year. If we divide that by the world population (around 8 billion), and by 365 we arrive at around 3 kg/day/person. But in wealthy countries, we often have associated emissions much higher than this. So Professor Bridle suggests we use around 3 kg/day as a target.

It might seem that there is no hope: that everything we eat is part of a web of actions and connections that can never be disentangled. And indeed, it is practically impossible to place a definitive amount of emissions on a specific purchase of a specific type of food. But there is hope!

In FACCWTHA Professor Bridle takes us on a tour through typical breakfasts, lunches and dinners and very quickly patterns emerge, and one begins to the learn the things which tend to have low associated emissions and things which tend to have high emissions.

For example, when she returns to analyse baked potatoes in Chapter 11 we are already familiar with the elements of a high emission meal. A single baked potato cooked in an oven and accompanied by ‘lashings’ of cheese could lead to more than 3 kg of emissions (a day’s worth or emissions) whereas the same baked potato cooked in a microwave with low-impact toppings might lead to only 0.3 kg of emissions.

(Cooking tip! Personally when I prepare baked potatoes I microwave them (typically four at a  time) for 15 minutes first before transferring them to a small oven to crisp up).

Click image for a larger version: Graphic illustrating the different emissions associated with a baked potato cooked in different ways and accompanied by different toppings.

As we go through the classic meals of the day, the themes emerge:

  • Food which has been flown to the UK has high associated emissions, but food which has been shipped to the UK can have surprisingly low emissions.
  • Plants of all kinds generally have low associated emissions arising mainly from cooking, transport and the use fertiliser.
  • Dairy products have higher emissions than vegetables and products such as cheese – that require large volumes of milk – can have very high associated emissions.
  • And meat products have high emissions, most especially beef and mutton because of the methane emissions associated with the animals processing of grass.

And although the book is not a database, it does handily summarise the carbon dioxide emissions associated with 1 gram of a variety of foods: I’ve compiled a list at the end of this article.

Most foods give rise to – very roughly – their own mass in  emissions. And since people typically eat between 1 kg and 2 kg of food per day, then it should be no problem to keep below 3 kgCO2 emissions per day.

However there are a few foodstuffs that have such high associated emissions, that in order to keep below 3 kgCO2/day, one would needs to restrict their consumption to being only – on average – a few grams per day.

In practical terms this corresponds to restricting consumption of these foodstuffs, making them rare ‘treats’ rather than regular staples. And these foodstuffs are, unsurprisingly, meat, cheese, greenhouse-grown vegetables, and farmed fish.

For example to restrict emissions to below 1 kgCO2/day on average one would need to eat less than 150 g of beef per week.

Click image for a larger version: Graphic illustrating the different emissions associated with three different evening dinner options.


Friends, FACCWTHA addresses an urgent issue. How do we reduce carbon dioxide emissions associated with what we eat? The book is engagingly written, well-researched with extensive references, and after reading it I found my consciousness had indeed raised, and it was now just up to me.

After reading the book I was reminded of Michael Pollen’s assertion that to eat well we should:

“Eat food. Not too much. Mostly plants”

And I understood that far from being mysterious, reducing carbon dioxide emissions from the food I eat is simple: but it requires that I re-balance my diet. This is hard because I am an old man and my habits are well set. But even at my advanced age, I can happily recommend this book, and suggest that you browse You Tube for inspiration for recipes. Personally, I have enjoyed the easy-vegan style of Will Yeung.

Carbon Intensity of foodstuffs

The table below is compiled from FACCWTHA and shows roughly the emissions associated with eating 1 gram of each of the foodstuffs listed.  The columns also show how much of that food can be eaten each day (and each week) to reduce that food item’s impact to 1 kg CO2/day on average.

Category 1 gram of … produces


kg to keep below 1 kgCO2/day kg to keep below 1 kgCO2/week
meat steak 46 0.02 0.152
meat lamb 43 0.02 0.163
drink instant coffee powder 17 0.06 0.412
dairy cheese 16 0.06 0.438
salad tomatoes, heated greenhouse 13 0.08 0.538
meat ham 11 0.09 0.636
sweets milk powder 9 0.11 0.778
meat chicken 9 0.11 0.778
dairy butter 8 0.13 0.875
transport anything 5000 km by air 8 0.13 0.875
fish salmon 8 0.13 0.875
packaging aluminium 6 0.17 1.17
egg egg 5 0.20 1.40
dairy cream 5 0.20 1.40
fish cod 5 0.20 1.40
snacks peanut butter 4 0.25 1.75
drink teabag 3 0.33 2.33
drink sugar 3 0.33 2.33
spread jam 3 0.33 2.33
grain cereal 3 0.33 2.33
spread relish 3 0.33 2.33
vegan Quorn slices 3 0.33 2.33
vegetables frozen oven chips 3 0.33 2.33
sweets cocoa 3 0.33 2.33
snacks peanuts 3 0.33 2.33
packaging plastic 3 0.33 2.33
packaging carboard landfilled 2 0.5 3.50
drink milk 2 0.5 3.50
salad sweetcorn 2 0.5 3.50
beans baked beans 2 0.5 3.50
packaging steel (for cans) 2 0.5 3.50
dairy yoghurt 2 0.5 3.50
fruit strawberries 2 0.5 3.50
fruit raspberries 2 0.5 3.50
snacks almonds 2 0.5 3.50
snacks crisps 2 0.5 3.50
drink orange juice 2 0.5 3.50
grain rice 2 0.5 3.50
beans beans (tinned) 1.8 0.6 3.89
spread vegetable spread 1.5 0.7 4.67
salad lettuce 1.5 0.7 4.67
vegan vegan cheese 1.4 0.7 5.00
packaging carboard composted 1 1.0 7.00
vegan Quorn pieces 1 1.0 7.00
spices spices 1 1.0 7.00
drink beer on tap 1 1.0 7.00
drink wine on tap 1 1.0 7.00
drink plant milk 0.8 1.3 8.75
grain flour 0.8 1.3 8.75
staple bread 0.8 1.3 8.75
packaging re-cycled plastic 0.8 1.3 8.75
vegetables french/green beans 0.8 1.3 8.75
fruit bananas 0.7 1.4 10.00
vegetables potato 0.6 1.7 11.67
beans beans 0.6 1.7 11.67
packaging glass 0.6 1.7 11.67
vegetables carrots 0.6 1.7 11.67
fruit apples (local in season) 0.4 2.5 17.50
vegetables cabbage 0.4 2.5 17.50
transport anything from NZ by ship 0.3 3.3 23.33
fruit oranges (local!) 0.3 3.3 23.33
snacks fizzy drink on tap 0.2 5.0 35.00
transport anything 400 km by truck 0.05 20.0 140.00
drink tap water 0.001 1000.0 7000.00

A History of Bushy House

April 30, 2023

Friends, the other day I was fortunate enough to have dinner in the local landmark of Bushy House.

A view of Bushy House taken from Bushy Park this February.

At dinner, many people asked me – as a local – questions about the building which I was completely unable answer.

Wikipedia has a few words, but the best source by far is a history compiled by Peter Foster and Edward Pyatt for NPL in 1976. And by chance I came across a copy of this document while sorting through the library of my late father-in-law. And since I couldn’t see a copy on-line, I thought I would post a pdf of the document here. I do hope it is useful to some local Teddington historians.

You can download a low-resolution (2.9 Mb) copy from this link. If for some reason you feel the need for more resolution, please contact me and we can collectively figure out how to share the original 80 Mb scan.

Cover of the History of Bushy House




The Economics of Home Solar PV

April 30, 2023

Friends, you may find this hard to believe, but someone posted something incorrect on Twitter the other day. They suggested that home installations of solar PV will soon become uneconomic.

I commented that I didn’t agree. But to my surprise, several people commented further suggesting that Home Solar was not only uneconomic, it was tantamount to theft!

At first I was bewildered: How could these people be so wrong? But then it turned out these people were economists, and so were quite un-phased by being wrong.

But after an extended exchange, I began to understand their perspective, and that is what this article is about. I still think they are wrong, but the perspective shift was interesting.

Home Solar PV: Simple Economics

The economics of home solar PV are fairly straightforward. A system of 10 panels (~£5,000) and a 5 kWh battery (~£5,000) will conservatively generate around 3,500 kWh/year of electricity which is roughly the annual usage of electricity by a household. The system will generate (on average) about 15 kWh/day in summer and perhaps just 2 kWh/day in winter depending on local shading.

Typically around 2,000 kWh will be used within the home saving (at current prices) 2,000 × 34p/kWh ~ £680/year which would otherwise have been purchased. Additionally, the extra 1,500 kWh will be exported earning a much less impressive 5p/kWh or £75 /year. So a roughly £10,000 investment has a return on investment of ~£750/year, a nominal 7.5%/year return. It’s possible to do a bit better or a bit worse depending on panel orientation and battery size.

By any conventional economic assessment, this is a reasonable investment.

Home Solar PV: Simple Carbonomics

Considering the carbon dioxide emissions avoided, the home solar PV system above might involve roughly 2,100 kg (2.1 tonnes) of embodied carbon dioxide emissions. That’s based on:

  • Panels: ~400 kgCO2 per peak power (in kW) of a panel – leading to around 1.6 tonnes of emissions (Links 1, 2).
  • Battery: ~100 kgCO2 per kWh of storage – leading to around 0.5 tonnes of emissions for a 5 kWh battery (Link)

Each kWh of electricity generated might avoid nominally 0.23 kgCO2 emissions. And so the system would avoid 3,500 x 0.23kg ~800 kgCO2/year. Additionally, by using the battery to avoid consumption at peak hours, the system could also help reduce grid costs and the use of ‘peaker’ plants.

This is a pretty reasonable carbon investment.

Home Solar PV: How could this not make sense?

So from an economic and carbonomic point of view, Home Solar PV systems with or without batteries definitely make sense. So what was this Twitterista going on about?

Well it turns out that they were not talking about the UK but were instead referring to (if I recall correctly) Belgium or Holland. In these countries the majority of people do not pay fixed price tariffs on their electricity. Instead they pay tariffs which change every 30 minutes depending on market conditions. In the UK this practice is not at all common.

And the situation they were referring to was the situation where there was so much solar power being made available by large solar farms, that while the sun was shining, solar power would cover the majority of electricity required. At this point, the economic market value of any extra solar generation would be zero.

This is a situation that will become increasingly possible as we expand renewable generation and the market will need to evolve to cope with this reality. But in the UK it would not make much difference. Most of the electricity generated on a rooftop is used within the home, and this avoids paying the market rate, so the savings would be unchanged. However, the price paid for exporting electricity might possibly fall to zero, but since that was only worth £75/year, it doesn’t really significantly the economics.

If consumers were exposed to market electricity prices that varied every 30 minutes through the day, then the cost of buying electricity when the Sun shone might fall to zero, and so consumers would be able to have free electricity whether or not they had a solar PV system on their home. In this situation, having a home battery would make a lot of sense because one could fill it for free!

But that is not the situation in the UK. I think it is good to have relatively fixed tariffs so that people can budget for likely electricity costs. In this way, professional traders take calculated risks for which they earn a reward. I think that is better than exposing us to the risks of a market which when under stress can become extremely volatile, and potentially bankrupt people who keep their electricity on when the system is under stress. For example, in the 2021 power crisis in Texas, in between blackouts, the price for some customers rose to $9/kWh – up from a few cents per kWh resulting in some customers facing bills of $1,000/day.

So the situation in which half-hourly market prices sometimes falls to zero is unlikely to affect the UK market directly. And even it did, people with home solar would still be getting free electricity at times when the market cost was not zero.

At the heart of this persons argument was an economic rationale that any investment in an economic activity which is sub optimal – represents a waste. This is based on a hyper-capitalistic view of society in which optimal capital deployment will result in optimal outcome. This is patently, just not in correspondence with reality.

Home Solar PV: Theft?

Theft! Surely I was dealing with an idiot here? But here is their argument.

The tariffs we pay for electricity are divided into two parts:

  • a so-called ‘standing charge’ typically about £0.40/day and
  • a ‘unit’ charge of typically £0.34/kWh.

Originally the idea was that this reflected the cost structure of the electricity supply industry.

  • The ‘standing charge’ would pay for the costs of the electricity network that gave us the possibility of buying electricity, whether we used 1 kWh/day or 100 kWh.
  • The ‘unit charge’ would pay for the extra costs – notably the fuel – used to generate every extra unit of electricity.

So with this structure, using solar PV to go ‘off grid’, I would still pay the standing charge, and so contribute my fair share to the maintenance of the electricity network.

However, standing charges are no longer just a way to pay for the fixed costs of the electricity network. They now include costs of paying for the mass failure of electricity companies in 2021/22, and elements of subsidy for ‘greener’ generation. And some elements of the unit charge actually reflect fixed costs.

So if I avoid paying for units of electricity, I am avoiding paying for some of the fixed costs of the network, and thus forcing those costs to be paid by people who can’t install solar PV. In short, by using solar PV I am stealing from the community and increasing the cost of electricity for everyone else. At this point I would understand if you wanted to just stop reading – why read words by a social reprobate like me?

Except of course that this is just nonsense. There is nothing that I – or anyone else – can do about the assignment of fixed costs to standing/unit charges. The whole mess is the combined result of weak regulation, energy industry lobbying, and government meddling. All no doubt undertaken with the aim of ‘making things better’. But if the side-effect of these historical changes is to cast someone trying to reduce carbon dioxide emissions as a thief, then I think that view is non-sense.

From a wider perspective, we see that the costs of regulatory failure have been assigned to electricity bills rather than gas bills. This political choice drives people to continue to use gas for heating when using heat pumps would save the country money AND reduce carbon dioxide emissions. So by a similar argument, gas users are ‘stealing’ from electricity users.

In short, our energy supply market contains distortions. All the companies that went bust made large profits which were privatised, but their losses are now being spread over all our bills. In other words, the profits were privatised and the losses socialised: standard operating procedure in a mis-regulated monoply. This is a failure of market design and regulation and it’s not my fault!

Home Solar PV: But I’ve got no roof?

Of course if you don’t have a roof, you may feel excluded from this discourse. But by using Ripple, you can buy a fraction of a solar park, and a pro-rata share of the profits will be deducted from your energy bill.

Having previously built one wind turbine (Graig Fatha), and commenced construction of the 8-turbine Kirk Hill Wind Farm, Ripple are now (Spring 2023) looking for people to contribute money to build a solar park in Devon.

The deal is this:

  • You can buy a share of the solar park from £25 to a value equivalent to 120% of annual electricity consumption priced at roughly £1/kWh.
  • So if annual electricity usage is 2,900 kWh, then if you pay roughly £3,000, you will own a fraction of a solar park that will generate as many kWh as you use in a year.
  • Their financial projection is summarised below:

It’s clear the projected savings are modest (~ £180/year) which for a £3,000 investment amounts to about 6%/year.

But it is interesting to compare these cost with the costs of the home solar PV system described above. The Ripple investment is cheaper per kWh generated and gives you less to worry about. For example, you don’t have to worry about pigeons. Of course, none of this is financial advice: honestly: don’t listen to me. I only care about the carbon dioxide.

Keep your eye on the carbon

If you are fortunate enough to have a few thousand pounds to invest, then putting your money into renewable energy projects either on your roof or remotely via Ripple is – in my estimation – a pretty reasonable thing to do. Whatever the location, this reduces the demand for electricity generated by gas-fired power stations and so reduces our country’s carbon dioxide emissions.

Arguments about this being unfair are – I think – spurious. We live in a society in which almost all economic activity generates a ‘trickle-up’ effect that enriches the already wealthy and in general gives rise to net carbon dioxide emissions. In this context, spending resources on renewable energy projects is amongst the least worst things we can do – and helps to build a renewable energy infrastructure from which we will all benefit.


Hydrogen for Home Heating is a Scam.

April 20, 2023

Friends, you may have heard that using hydrogen for home heating is somehow a ‘green solution’ to the question of how we should heat our homes in the future. This is not the case, but fossil fuel companies are still promoting the idea (1 , 2):

  • Firstly they suggest that hydrogen heating for a home just replaces a familiar boiler with an outwardly similar device at lower upfront cost than a heat pump.
  • Secondly, they additionally spread fear, uncertainty, and doubt (FUD) about heat pumps.

Remember each year they delay the transition to heating our homes with renewable energy is another year of profits for their shareholders, and ongoing pollution of our atmosphere. And a world in which we use hydrogen for home heating is a world in which demand for methane (so-called ‘natural’ gas) will increase – not decrease as it must if we are ever to reach net zero.

This article is an explanation of why hydrogen is not any kind of a solution for home heating. It’s complex, but I’ll do my best to be as clear as possible.

But I urge you to keep in mind the key characteristics that any solution to the problem of home-heating must have in order to qualify as a solution:

  • It must have drastically reduced carbon dioxide emissions – with an ideal limit of zero emissions.
  • And it must have a way to begin that reduction right now: we really have no time left.

If a proffered solution does not meet these goals, it is not a solution at all: it’s a scam.

Shades of Hydrogen

When one combines hydrogen (H2) with the oxygen (O2) in the air to release heat, no carbon dioxide is produced. The exhaust gas is pure water, H2O. So at the point of combustion, all hydrogen is nominally free of harmful emissions.

But to understand its environmental impact one must take account of the amount of carbon dioxide emitted in the preparation of the hydrogen gas, and its transport to the point of combustion. The pre-history of the hydrogen gas is commonly summarised by a colour pre-fix. However, is not actually coloured and it behaves identically no matter how it is prepared.

  • Green HydrogenHydrogen which is prepared from water using renewable electricity is referred to as Green Hydrogen. Ideally, it has no associated carbon dioxide or methane emissions.
  • Grey Hydrogen: Hydrogen which is prepared by combining water with methane at high temperatures (so-called Steam Reforming) is referred to as Grey Hydrogen. This process produces carbon dioxide which is emitted into the atmosphere.
  • Blue Hydrogen: Hydrogen which is prepared by Steam Reforming but in which the emissions are captured is referred to as Blue Hydrogen. This process still produces carbon dioxide emissions because the capture process is never 100% efficient, and it is generally powered by burning methane.

A recent analysis (link) has estimated the  carbon dioxide emissions associated with the production of Grey and Blue Hydrogen. Its estimates of the carbon dioxide equivalent emissions associated with an amount of hydrogen gas which releases 1 kWh of heat are shown in the chart below:

Click on image for a larger version. Chart showing the carbon dioxide equivalent emissions from burning pure methane, greenblue and grey hydrogen. For blue and grey hydrogen, the emissions are shown with and without the effect of methane leaks. A methane leakage rate of 3.5% is assumed.

As discussed below, in this abbreviation the ‘eq’ stands for equivalent. This can be compared with the carbon dioxide emissions associated with simply burning the methane gas directly.

There are two contributory factors to this result. The first factor is the inefficiency of carbon capture and the fact that extra energy is required to process either grey or blue hydrogen.

The second factor is an assessment of rate of methane leaks – so-called ‘fugitive’ methane emissions. The author’s central estimate is that in the global supply chain, around 3.5% leaks directly into the atmosphere. Evaluated over 20 years, this fugitive methane has a heating effect of around 84 times as much as the same amount of carbon dioxide. The warming effect of the fugitive emissions is expressed in terms of the equivalent amount of carbon dioxide emissions which would produce the same warming.

So according to this study, if we convert methane to hydrogen assuming reasonable (3.5%) estimates of methane leakage, there are no reductions in emissions at all. In fact, there is an increase in emissions! If we unrealistically/optimistically assume no methane leakage, then grey hydrogen still has increased emissions, and blue hydrogen offers a maximum reduction in emissions of just 20%.  There is no path to zero emissions using either grey or blue hydrogen.

So the outcome of this research is that using methane  to prepare Blue or Grey Hydrogen may slightly reduce emissions, but even in the best circumstances, not by much. Only Green hydrogen offers the possibility of a fuel which would reduce emissions to zero.

Pure Green Hydrogen

It is not possible to send green hydrogen – or any other colour of hydrogen to our homes at the minute. Firstly, the gas distribution network is currently being used for methane! Secondly, there is not enough hydrogen to supply to the UK. And thirdly, compared to methane, hydrogen has a very low energy density i.e. energy per cubic metre. So to deliver the same heating power into our homes as methane currently does, we would need to operate the gas delivery system at roughly 3 times its current pressure.

Operating a hydrogen gas distribution system at high pressure is a bad idea for all kinds of reasons, but I don’t want to dwell on those reasons right now. All I want to point out is that even with the most ‘advantageous’ assumptions, we are decades away from switching to a pure hydrogen gas distribution system. In those decades, fossil fuel companies propose that we basically just keep burning methane – and delivering them their profits.

But referring back to the start of this article, if we can’t start now, then what is being proposed is not a solution. It’s a scam designed to keep us using methane gas for decades more.

A foot in the door: Hydrogen-Methane Mixtures

So the fossil-fuel industry’s plan to place themselves at the heart of future home-heating is the proposal to mix hydrogen with methane and distribute this through the existing gas infrastructure. Existing boilers can tolerate up to about 20% of hydrogen mixed into the methane, and their power output will only fall by about 7%.

The effect on carbon dioxide emissions per kWh of heating delivered is shown in the two figures below. The first graph is based on an assumption of 3.5% leakage of methane and the second assumes an unrealistic 0% leakage rate.

Click on image for a larger version. Graph showing the CO2-equivalent emissions as the fraction of hydrogen mixed into methane gas is varied from 0% to 20%. A methane leakage rate of 3.5% is assumed.

Click on image for a larger version. Graph showing the CO2-equivalent emissions as the fraction of hydrogen mixed into methane gas is varied from 0% to 20%. A methane leakage rate of 0% is assumed.

Assuming a 3.5% leakage rate, adding either Grey or Blue hydrogen to methane increases the so-called carbon intensity of the fuel mixture i.e. adding hydrogen increases the amount of carbon dioxide equivalent emissions per kWh of heating delivered.

Assuming a 0% leakage rate, adding Grey hydrogen to methane increases the carbon intensity of the fuel mixture but blue hydrogen could slightly reduce the carbon intensity, but only by around 1%.

So when it comes to mixtures of hydrogen in methane, adding blue or grey hydrogen generally results in an increase in the amount of carbon dioxide emissions rather than a reduction. So using blue or grey hydrogen does not represent a solution to the problem of carbon dioxide emissions. And of course, neither blue nor grey hydrogen are renewable – they still depend on endless mining of natural gas – and that is why they are being promoted: they allow fossil fuel companies to continue to carry on as before.

But what about green hydrogen?

Green Hydrogen

Looking at the graphs above one might think that green hydrogen looks like a possible solution to the home-heating problem: it does result in reduced carbon intensity of a green hydrogen/methane mixture. And in a hypothetical future world with a hydrogen grid, it might deliver heating with nominally zero associated emissions.

However, home-heating with green hydrogen is still a bad idea. To understand why one needs consider the renewable energy used to create the green hydrogen.

To create 1 kg of green hydrogen from water using electrolysis requires a minimum of 39.4 kWh of renewable electricity. When that hydrogen is later burned in air, all of that energy will be returned as heat.

But electrolysis is typically only 75% efficient, so more typically it requires 39.4/0.75 ~ 52 kWh of renewable electricity  to create 1 kg of  green hydrogen which will provide 39.4 kWh of heating. And since boilers are typically not 100% efficient, the amount of heat delivered into the home would be reduced further – to (say) 85% of 39.4 kWh – i.e. 33.5 kWh.

Is there something better that we could do with that renewable electricity?

With regard to home heating, Yes. If that 52 kWh of renewable electricity was used to power heat pumps, it would deliver approximately 156 kWh of heat to homes, more than 5 times as much heat as could be delivered by 1 kg of hydrogen.

Click on image for a larger version. Chart showing the amount of home-heating available from 1 kWh of renewable electricity.

This means that to create the same amount of renewable heat, heating homes with hydrogen would require five times as much renewable resource: five times as many wind and solar farms!

Now a hydrogen boiler is cheaper than a heat pump. In ‘ball park’ figures, let’s say that a hydrogen boiler might cost £3,000 to install and a heat pump might cost £10,000. These costs would be paid by the homeowner or landlord. This makes a hydrogen boiler look cheap at first sight.

But the cost to build five times the amount of renewable resource is very large

If we consider the cheapest renewable resource, onshore wind, a 10 MW turbine- big enough to generate on average around 3.5 MW of renewable electricity – this will likely cost around £10M. Nominally this single turbine would supply roughly 3,500 homes with 1 kW of electricity continuously, so one might guesstimate the cost as around £2,800 per household for 1 kW of continuous power.

So if we consider the total system costs, we have:

  • For a hydrogen boiler, the ‘local’ cost is £3,000 + 5 × £2,800 to build the required renewable electricity resource to create the hydrogen. So the total cost is ~£17,000.
  • For a heat pump, the ‘local’ cost is £10,000 + 1 × £2,800 to build the required renewable electricity resource. So the total cost is ~£12,800.

Now this is very much a ‘back of the envelope’ calculation – and there are many things I have not included, such as cost of building either a hydrogen capable gas grid, or improvements to the electricity grid. And I don’t put any store in the particular numbers in this calculation. But the calculation demonstrates that a green hydrogen ‘solution’ has very large costs that are not immediately apparent. And in the end, all those costs will be paid for by the consumers of the gas: us.

And friends, the UK is nowhere near having sufficient renewable capacity to generate these vast amounts of renewable green hydrogen. So the plan that the fossil fuel companies will try to sell is that they will start with blue hydrogen – and promise to slowly add green hydrogen to the mix. But of course, this will barely reduce emissions at all. But at its heart, the entire hydrogen for home-heating proposal is a scam to allow them to keep producing their toxic products.

In contrast, every home converted to using a heat pump immediately saves tonnes of CO2 emissions per year. So lowering the upfront cost of installing a heat pump through low-cost loans and grants is actually a national saving: it avoids the phenomenal costs of building the vast renewable resources required to produce green hydrogen.

So is Green Hydrogen pointless?

No! Green hydrogen is really important. If we want to live renewable lives then green hydrogen will be essential for some processes. But home-heating is just not one of those processes.

Michael Leibrich has produced a ‘Clean Hydrogen Ladder’ showing processes for which use of green hydrogen will be unavoidable, and processes for which green hydrogen will be uncompetitive.

Click on image for a larger version. The ‘Clean Hydrogen Ladder’. The use of green hydrogen is unavoidable in order to make fertiliser or feed stock for the chemical industry. But it is uncompetitive for applications such as domestic heating.

And we definitely need loads of green hydrogen to serve as feedstock for the chemical industry and for the manufacture of products like steel and fertiliser.


The solution to our home-heating problem is heat pumps: air source, ground source, air-to-air or air-to-water.

The idea of using hydrogen for home-heating is wasteful. It is a ruse of fossil fuel companies to allow them to keep producing their toxic products. Please don’t fall for this scam.

Perfect Solar Days

April 8, 2023

Friends, March may have been depressingly dull, but the start of April has been upliftingly sunny. And Tuesday April 4th was a perfect solar day.

Perfect solar days are days in which the sun shines unremittingly from dawn until dusk, with not a cloud in the sky: such days are rare: Typically there are around 10 per year and I try record the solar PV generation from each one. I do this using data from the Tesla App which records solar generation every 5 minutes via a current transformer (CT) clamp on the cable from the inverters.

The graph below shows 12 perfect (or near perfect) solar days from 2021 and 2022. The days are not evenly spaced because I can’t control the weather!

Click on image for a larger versions. Graph showing the daily hour-by-hour generation for a series of near-perfect solar days in 2021 and 2022.

Attentive readers will recall that in November 2022 I had eight extra solar panels installed on the east-facing roofs of Podesta Towers (link). I had expected that these would contribute nothing to solar generation in winter, but that generation would be significant in spring, summer and autumn.

The graphs below show the generation profile for each day for which there is reasonably well-corresponding day from before the new panels were installed. As expected the new generation is very weak in December and January, but by April has grown significantly.

As expected the extra generation from the panels on the North and East is in the morning. Happily, the maximum power looks like it will peak in summer at less than 5 kW – the maximum rating of the cable between the inverters and the consumer unit.

Click on image for a larger versions. Graph showing the daily hour-by-hour generation for a series of near-perfect solar days in 2021 and 2022.


The aim of the installing the new panels was to create extra generation in the spring and summer which would hopefully be enough to keep the house off-grid for 6 months. This goal has been hampered by the dullness of March, but things seem to be returning to normal now. However the weather is still cold enough to require the heat pump to stay running for another month or so, increasing domestic consumption.

The graphs below all have a vertical axis of kWh/day and the data are smoothed to highlight trends: They compare:

  • Domestic consumption and solar generation. One can see that solar generation is rising to be roughly equal to domestic consumption and should soon exceed it.
  • Domestic consumption and Grid Consumption. In winter, the two are practically equal, but in spring, grid use is falling as we rely more on solar energy.
  • Net Grid Consumption/Export and solar generation. As solar generation rises  we have become net exporters of electricity.

Click on image for a larger versions. Graphs variation of Daily Consumption, Daily Grid Consumption, Net Grid Consumption and Solar PV generation, all expressed in units of kW/day.


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