# Can the Efficiency Be Greater Than One?

This is one of the perennial top search terms for this blog.

Anticlimactic answer: Yes, because input and output are determined also by economics, not only by physics.

Often readers search for the efficiency of a refrigerator. Its efficiency, the ratio of output and input energies, is greater than 1 because the ambient energy is free. System’s operators are interested in the money they pay the utility, in relation to the resulting energy for cooling.

If you use the same thermodynamic machine either as a refrigerator or as a heat pump, efficiencies differ: The same input energy drives the compressor, but the relevant output energy is either the energy released to the ‘hot side’ at the condenser or the energy used for evaporating the refrigerant at the ‘cool side’:

The same machine / cycle is used as a heat pump for heating (left) or a refrigerator or AC for cooling (right). (This should just highlight the principles and does not include any hydraulic details, losses etc. related to detailed differences between refrigerators / ACs and heat pumps.)

For photovoltaic panels the definition has sort of the opposite bias: The sun does not send a bill – as PV installers say in their company’s slogan – but the free solar ambient energy is considered, and thus their efficiency is ‘only’ ~20%.

Half of our generator, now operational for three years: 10 panels, oriented south-east, 265W each, efficiency 16%. (The other 8 panels are oriented south-west).

When systems are combined, you can invent all kinds of efficiencies, depending on system boundaries. If PV panels are ‘included’ in a heat pump system (calculation-wise) the nominal electrical input energy becomes lower. If solar thermal collectors are added to any heating system, the electrical or fossil fuel input decreases.

Output energy may refer to energy measured directly at the outlet of the heat pump or boiler. But it might also mean the energy delivered to the heating circuits – after the thermal losses of a buffer tank have been accounted for. But not 100% of these losses are really lost, if the buffer tank is located in the house.

I’ve seen many different definitions in regulations and related software tools, and you find articles about how to game interpret these guidelines to your advantage. Tools and standards also make arbitrary assumptions about storage tank losses, hysteresis parameter and the like – factors that might be critical for efficiency.

Then there are scaling effects: When the design heat loads of two houses differ by a factor of 2, and the smaller house would use a scaled down heat pump (hypothetically providing 50% output power at the same efficiency), the smaller system’s efficiency is likely to be a bit lower. Auxiliary consumers of electricity – like heating circuit pumps or control systems – will not be perfectly scalable. But the smaller the required output energy is, the better it can be aligned with solar energy usage and storage by a ‘smart’ system – and this might outweigh the additional energy needed for ‘smartness’. Perhaps intermittent negative market prices of electricity could be leveraged.

Definitions of efficiency are also culture-specific, tailored to an academic discipline or industry sector. There are different but remotely related concepts of rating how useful a source of energy is: Gibbs Free Energy is the maximum work a system can deliver, given that pressure and temperature do not change during the process considered – for example in a chemical reaction. On the other hand, Exergy is the useful ‘available’ energy ‘contained’ in a (part of a) system: Sources of energy and heat are rated; e.g. heat energy is only mechanically useful up to the maximum efficiency of an ideal Carnot process. Thus exergy depends on the temperature of the environment where waste heat ends up. The exergy efficiency of a Carnot process is 1, as waste heat is already factored in. On the other hand, the fuel used to drive the process may or may not be included and it may or may not be considered pure exergy – if it is, energy and exergy efficiency would be the same again. If heat energy flows from the hot to the cold part of a system in a heat exchanger, no energy is lost – but exergy is.

You could also extend the system’s boundary spatially and on the time axis: Include investment costs or the cost of harm done to the environment. Consider the primary fuel / energy / exergy to ‘generate’ electricity: If a thermal power plant has 40% efficiency then the heat pump’s efficiency needs to be at least 2,5 to ‘compensate’ for that.

In summary, ‘efficiency’ is the ratio of an output and an input energy, and the definitions may be rather arbitrary as and these energies are determined by a ‘sampling’  time, system boundaries, and additional ‘ratings’.

It is the the duty of a Webmaster to allocate URIs which you will be able to stand by in 2 years, in 20 years, in 200 years. This needs thought, and organization, and commitment. (https://www.w3.org/Provider/Style/URI)

Joel Spolsky did it:

I’m bending over backwards not to create “linkrot” — all old links to Joel on Software stories have been replaced with redirects, so they should still work. (November 2001)

More than once:

I owe a huge debt of gratitude to [several people] for weeks of hard work on creating this almost perfect port of 16 years of cruft, preserving over 1000 links with redirects… (December 2016).

Most of the outgoing URLs linked by Joel of Software have rotted, with some notable exceptions: Jakob Nielsen’s URLs do still work, so they live what he preached – in 1998:

… linkrot contributes to dissolving the very fabric of the Web: there is a looming danger that the Web will stop being an interconnected universal hypertext and turn into a set of isolated info-islands. Anything that reduces the prevalence and usefulness of cross-site linking is a direct attack on the founding principle of the Web.

No excuses if you are not Spolsky- or Nielsen-famous – I did it too, several times. In 2015 I rewrote the application for my websites from scratch and redirected every single .asp URL to a new friendly URL at a new subdomain.

I am obsessed with keeping old URLs working. I don’t like it if websites are migrated to a new content management system, changing all the URLs.

I checked all that again when migrating to HTTPS last year.

So I am a typical nitpicking dinosaur, waxing nostalgic about the time when web pages were still pages, and when Hyperlinks Subverted Hierarchy. When browsers were not yet running an OS written in Javascript and hogging 70% of your CPU for ad-tracking or crypto-mining.

The dinosaur is grumpy when it has to fix outgoing URLs on this blog. So. Many. Times. Like every second time I test a URL that shows up in my WordPress statistics as clicked, it 404s. Then I try to find equivalent content on the same site if the domain does still exist – and had not been orphaned and hijacked by malvertizers. If I am not successful I link to a version of this content on web.archive.org, track down the content owner’s new site, or find similar content elsewhere.

My heart breaks when I see that it’s specifically the interesting, unusual content that users want to follow from here – like hard-to-find historical information on how to build a heat pump from clay tablets and straw. My heart breaks even more when the technical content on the target site gets dumbed down more and more with every URL breaking website overhaul. But OK – you now have this terrific header image with a happy-people-at-work stock photo that covers all my desktop so that I have to scroll for anything, and the dumbed down content is shown in boxes that pop up and whirl – totally responsive, though clunky on a desktop computer.

And, yes: I totally know that site owners don’t own me anything. Just because you hosted that rare and interesting content for the last 10 years does not mean you have to do that forever.

But you marketing ninjas and website wranglers neglected an important point: We live in the age of silly gamification that makes 1990s link building pale: I like yours and you like mine. Buy Followers. Every time I read a puffed up Case Study for a project I was familiar with as an insider, I was laughing for minutes and then checked if it was not satire.

In this era of fake word-of-mouth marketing you get incoming links. People say something thoughtful, maybe even nice about you just because they found your content interesting and worth linking not because you play silly games of reciprocating. The most valuable links are set by people you don’t know and who did not anticipate you will ever notice their link. As Nassim Taleb says: Virtue is what you do when nobody is looking.

I would go to great lengths not to break links to my sites in those obscure DIY forums whose posts are hardly indexed by search engines. At least I would make a half-hearted attempt at redirecting to a custom 404 page that explains where you might the moved content. Or just keep the domain name intact. Which of course means not to register a catchy domain name for every product in the first place. Which I consider bad practice anyway – training users to fall for phishing, by getting them used to jumping from one weird but legit domain to another.

And, no, I don’t blame you personally, poor stressed out web admin who had to get the new site up and running before April 1st, because suits in your company said the world would come to an end otherwise. I just think that our internet culture that embraces natural linkrot so easily is as broken as the links.

I tag this as Rant, but it is a Plea: I beg you, I implore you to invest just a tiny part of the time, budget and efforts you allocated to Making the Experience of Your Website Better to making some attempt at keeping your URLs intact. They are actually valuable for others – something you should be proud of.

# Consequences of the Second Law of Thermodynamics

Why a Carnot process using a Van der Waals gas – or other fluid with uncommon equation of state – also runs at Carnot’s efficiency.

Textbooks often refer to an ideal gas when introducing Carnot’s cycle – it’s easy to calculate heat energies and work in this case. Perhaps this might imply that not only must the engine be ‘ideal’ – reversible – but also the working fluid has to be ‘ideal’ in some sense? No, it does not, as explicitly shown in this paper: The Carnot cycle with the Van der Waals equation of state.

In this post I am considering a class of substances which is more general than the Van der Waals gas, and I come to the same conclusion. Unsurprisingly. You only need to imagine Carnot’s cycle in a temperature-entropy (T-S) diagram: The process is represented by a rectangle for both ideal and Van der Waals gas. Heat energies and work needed to calculate efficiency can be read off, and the – universal – maximum efficiency can be calculated without integrating over potentially wiggly pressure-volume curves.

But the fact that we can use the T-S diagram or the fact that the concept of entropy makes sense is a consequence of the Second Law of Thermodynamics. It also states, that a Perpetuum Mobile of the Second Kind is not possible: You cannot build a machine that converts 100% of the heat energy in a temperature bath to mechanical energy. This statement sounds philosophical but it puts constraints on the way real materials can behave, and I think these constraints on the relations between physical properties are stronger than one might intuitively expect. If you pick an equation of state – the pressure as a function of volume and temperature, like the wavy Van der Waals curve, the behavior of specific heat is locked in. In a sense the functions describing the material’s properties have to conspire just in the right way to yield the simple rectangle in the T-S plane.

The efficiency of a perfectly reversible thermodynamic engine (converting heat to mechanical energy) has a maximum well below 100%. If the machine uses two temperature baths with constant temperatures $T_1$ and $T_2$, the heat energies exchanged between machine and baths $Q_1$ and $Q_2$ for an ideal reversible process are related by:

$\frac{Q_1}{T_1} + \frac{Q_2}{T_2} = 0$

(I wrote on the related proof by contradiction before – avoiding to use the notion of entropy at all costs). This ideal process and this ideal efficiency could also be used to actually define the thermodynamic temperature (as it emerges from statistical considerations; I have followed Landau and Lifshitz’s arguments in this post on statistical mechanics and entropy)

Any thermodynamic process using any type of substance can be imagined as being a combination of lots of Carnot engines operating between lots of temperature baths at different temperatures (see e.g. Feynman’s lecture). The area in the p-V diagram that is traced out in a cyclic process is being split into infinitely many Carnot processes. For each process small heat energies $\delta Q$ are transferred. Summing up the contributions of all processes only the loop at the edge remains and thus …

$\oint \frac{\delta Q}{T}$

which means that for a reversible process $\frac{\delta Q}{T}$ actually has to be a total differential of a function $dS$ … that is called entropy. This argument used in thermodynamics textbooks is kind of a ‘reverse’ argument to the statistical one – which introduces  ‘entropy first’ and ‘temperature second’.

What I  need in the following derivations are the relations between differentials that represent a version of First and Second Law:

The First Law of Thermodynamics states that heat is a form of energy, so

$dE = \delta Q - pdV$

The minus is due to the fact that energy is increased on increasing volume (There might be other thermodynamics degrees of freedom like the magnetization of a magnetic substance – so other pairs of variables like p and V).

Inserting the definition of entropy S as the total differential we obtain this relation …

$dS = \frac{dE + pdV}{T}$

… from which follow lots of relations between thermodynamic properties!

I will derive one the them to show how strong the constraints are that the Second Law actually imposes on the physical properties of materials: When the so-called equation of state is given – the pressure as a function of volume and temperature p(V,T) – then you also know something about its specific heat. For an ideal gas pV is simply a constant times temperature.

S is a function of the state, so picking independent variables V and T entropy’s total differential is:

$dS = (\frac{\partial S}{\partial T})_V dT + (\frac{\partial S}{\partial V})_T dV$

On the other hand, from the definition of entropy / the combination of 1st and 2nd Law given above it follows that

$dS = \frac{1}{T} \left \{ (\frac{\partial E }{\partial T})_V dT + \left [ (\frac{\partial E }{\partial V})_T + p \right ]dV \right \}$

Comparing the coefficients of dT and dV the partial derivatives of entropy with respect to volume and temperature can be expressed as functions of energy and pressure. The order of partial derivation does not matter:

$\left[\frac{\partial}{\partial V}\left(\frac{\partial S}{\partial T}\right)_V \right]_T = \left[\frac{\partial}{\partial T}\left(\frac{\partial S}{\partial V}\right)_T \right]_V$

Thus differentiating each derivative of S once more with respect to the other variable yields:

$[ \frac{\partial}{\partial V} \frac{1}{T} (\frac{\partial E }{\partial T})_V ]_T = [ \frac{\partial}{\partial T} \frac{1}{T} \left [ (\frac{\partial E }{\partial V})_T + p \right ] ]_V$

What I actually want, is a result for the specific heat: $(\frac{\partial E }{\partial T})_V$ – the energy you need to put in per degree Kelvin to heat up a substance at constant volume, usually called $C_v$. I keep going, hoping that something like this derivative will show up. The mixed derivative $\frac{1}{T} \frac{\partial^2 E}{\partial V \partial T}$ shows up on both sides of the equation, and these terms cancel each other. Collecting the remaining terms:

$0 = -\frac{1}{T^2} (\frac{\partial E }{\partial V})_T -\frac{1}{T^2} p + \frac{1}{T}(\frac{\partial p}{\partial T})_V$

Multiplying by $T^2$ and re-arranging …

$(\frac{\partial E }{\partial V})_T = -p +T(\frac{\partial p }{\partial T})_V = T^2(\frac{\partial}{\partial T}\frac{p}{T})_V$

Again, noting that the order of derivations does not matter, we can use this result to check if the specific heat for constant volume – $C_v = (\frac{\partial E }{\partial T})_V$ – depends on volume:

$(\frac{\partial C_V}{\partial V})_T = \frac{\partial}{\partial V}[(\frac{\partial E }{\partial T})_V]_T = \frac{\partial}{\partial T}[(\frac{\partial E }{\partial V})_T]_V$

But we know the last partial derivative already and insert the expression derived before – a function that is fully determined by the equation of state p(V,T):

$(\frac{\partial C_V}{\partial V})_T= \frac{\partial}{\partial T}[(-p +T(\frac{\partial p }{\partial T})_V)]_V = -(\frac{\partial p}{\partial T})_V + (\frac{\partial p}{\partial T})_V + T(\frac{\partial^2 p}{\partial T^2})_V = T(\frac{\partial^2 p}{\partial T^2})_V$

So if the pressure depends e.g. only linearly on temperature the second derivative re T is zero and $C_v$ does not depend on volume but only on temperature. The equation of state says something about specific heat.

The idealized Carnot process contains four distinct steps. In order to calculate efficiency for a certain machine and working fluid, you need to calculate the heat energies exchanged between machine and bath on each of these steps. Two steps are adiabatic – the machine is thermally insulated, thus no heat is exchanged. The other steps are isothermal, run at constant temperature – only these steps need to be considered to calculate the heat energies denoted $Q_1$ and $Q_2$:

Carnot process for an ideal gas: A-B: Isothermal expansion, B-C: Adiabatic expansion, C-D: isothermal compression, D-A: adiabatic compression. (Wikimedia, public domain, see link for details).

I am using the First Law again and insert the result for $(\frac{\partial E}{\partial V})_T$ which was obtained from the combination of both Laws – the goal is to express heat energy as a function of pressure and specific heat:

$\delta Q= dE + p(T,V)dV = (\frac{\partial E}{\partial T})_V dT + (\frac{\partial E}{\partial V})_T dV + p(T,V)dV$
$= C_V(T,V) dT + [-p +T(\frac{\partial p(T,V)}{\partial T})_V] dV + p(T,V)dV = C_V(T,V)dT + T(\frac{\partial p(T,V)}{\partial T})_V dV$

Heat Q is not a function of the state defined by V and T – that’s why the incomplete differential δQ is denoted by the Greek δ. The change in heat energy depends on how exactly you get from one state to another. But we know what the process should be in this case: It is isothermal, therefore dT is zero and heat energy is obtained by integrating over volume only.

We need p as a function of V and T. The equation of state for ideal gas says that pV is proportional to temperature. I am now considering a more general equation of state of the form …

$p = f(V)T + g(V)$

The Van der Waals equation of state takes into account that particles in the gas interact with each other and that they have a finite volume (Switching units, from capital volume V [m3] to small v [m3/kg] to use gas constant R [kJ/kgK] rather than absolute numbers of particles and to use the more common representation – so comparing to \$latex pv = RT) :

$p = \frac{RT}{v - b} - \frac{a}{v^2}$

This equation also matches the general pattern.

Van der Waals isotherms (curves of constant temperature) in the p-V plane: Depending on temperature, the functions show a more or less pronounced ‘wave’ with a maximum and a minimum, in contrast to the ideal-gas-like hyperbolas (p = RT/v) for high temperatures. (By Andrea insinga, Wikimedia, for details see link.)

In both cases pressure depends only linearly on temperature, and so $(\frac{\partial C_V}{\partial V})_T$ is 0. Thus specific heat does not depend on volume, and I want to stress that this is a consequence of the fundamental Laws and the p(T,V) equation of state, not an arbitrary, additional assumption about this substance.

The isothermal heat energies are thus given by the following, integrating $T(\frac{\partial p(T,V)}{\partial T})_V = T f(V)$ over V:

$Q_1 = T_1 \int_{V_A}^{V_B} f(V) dV$
$Q_2 = T_2 \int_{V_C}^{V_D} f(V) dV$

(So if $Q_1$ is positive, $Q_2$ has to be negative.)

In the adiabatic processes δQ is zero, thus

$C_V(T,V)dT = -T(\frac{\partial p(T,V)}{\partial T})_V dV = -T f(V) dV$
$\int \frac{C_V(T,V)}{T}dT = \int -f(V) dV$

This is useful as we already know that specific heat only depends on temperature for the class of substances considered, so for each adiabatic process…

$\int_{T_1}^{T_2} \frac{C_V(T)}{T}dT = \int_{V_B}^{V_C} -f(V) dV$
$\int_{T_2}^{T_1} \frac{C_V(T)}{T}dT = \int_{V_D}^{V_A} -f(V) dV$

Adding these equations, the two integrals over temperature cancel and

$\int_{V_B}^{V_C} f(V) = -\int_{V_D}^{V_A} f(V) dV$

Carnot’s efficiency is work – the difference of the absolute values of the two heat energies – over the heat energy invested at higher temperature $T_1$:

$\eta = \frac {Q_1 - \left | Q_2 \right |}{Q_1} = 1 - \frac {\left | Q_2 \right |}{Q_1}$
$\eta = 1 - \frac {T_2}{T_1} \frac {\left | \int_{V_C}^{V_D} f(V) dV \right |}{\int_{V_A}^{V_B} f(V) dV}$

The integral from A to B can replaced by an integral over the alternative path A-D-C-B (as the integral over the closed path is zero for a reversible process) and

$\int_{A}^{B} = \int_{A}^{D} + \int_{D}^{C}+ \int_{C}^{B}$

But the relation between the B-C and A-D integral derived from considering the adiabatic processes is equivalent to

$-\int_{C}^{B} = \int_{B}^{C} = - \int_{D}^{A} = \int_{A}^{D}$

Thus two terms in the alternative integral cancel and

$\int_{A}^{B} = \int_{D}^{C}$

… and finally the integrals in the efficiency cancel. What remains is Carnot’s efficiency:

$\eta = \frac {T_1 - T_2}{T_1}$

But what if the equation of state is more complex and specific heat would depends also on volume?

Yet another way to state the Second Law is to say that the efficiencies of all reversible processes has to be equal and equal to Carnot’s efficiency. Otherwise you get into a thicket of contradictions (as I highlighted here). The authors of the VdW paper say they are able to prove this for infinitesimal cycles which sounds of course plausible: As mentioned at the beginning, splitting up any reversible process into many processes that use only a tiny part of the co-ordinate space is the ‘standard textbook procedure’ (see e.g. Feynman’s lecture, especially figure 44-10).

But you could immediately see it without calculating anything by having a look at the process in a T-S diagram instead of the p-V representation. A process made up of two isothermal and two adiabatic processes is by definition (of entropy, see above) a rectangle no matter what the equation of state of the working substance is. Heat energy and work can easily been read off as the rectangles between or below the straight lines:

Carnot process displayed in the entropy-temperature plane. No matter if the working fluid is an ideal gas following the pv = RT equation of state or if it is a Van der Waals gas that may show a ‘wave’ with a maximum and a minimum in a p-V diagram – in the T-S diagram all of this will look like rectangles and thus exhibit the maximum (Carnot’s) efficiency.

In the p-V diagram one might see curves of weird shape, but when calculating the relation between entropy and temperature the weirdness of the dependencies of specific heat and pressure of V and T compensate for each other. They are related because of the differential relation implied by the 2nd Law.

# The Subtle Power of the Top Snippet. A New Sub-Genre of Google Poetry.

New game, new rules!

I have tried to make the rules tougher! Here is some context and history.

2. Pick the first search result in the language of your site[*]
3. Pick a chain of words, a contiguous snippet from this Google search result (use only the snippet on the results page – don’t click on it). This becomes the title of your poem.
4. Copy your chosen snippet and search again, now for this phrase.
5. Pick the first snippet from the new search results, choose a phrase. This is the next line of the poem; re-arrangement, editing or skipping search results is not allowed.
6. Goto 4.

[*] The major challenge in this game is one strange attractor: All the poetic chaos is finally is sucked into this black-hole: Dictionaries and thesauruses. I’ve used a private browser window with both preferred language and display language set to English. Yet Google knows my IP address and keeps showing me translations to German as the first search result.

Unless you want to pick a term like German-English translation, your worm-hole out of the dictionary attractor is the innocuous reference to the web page in Cache. Fortunately, when searching for Cache there was a ‘reasonable’ English snippet on the first results page, and I felt entitled to choose it, according to rule 2. The poem shows that I was stuck in the potential well of the cache. The same happened with less severe attractors, and eerily enough these events always had a self-referential flavor. I was also leading and pacing, leading and pacing, leading and pacing… until I was in sync. And the pop-up, pop-up, pop-up was hard to get rid of, as in the real world.

I also had to appeal to Google themselves, and the poem describes itself correctly as a treasure hunting game – to find hidden objects or places.

Enough of the meta-analysis and over-explanations, this is no Worstward Ho!

________________________________________

Combine Just Anything

your transactions are now in one beautiful place
anywhere in Europe

search engine for
facts and stats. Oh and Gifs

Reaction
Cache
Cache
Cache
Cache
How to clear
If you don’t want a record

switch to another program
You don’t have to close
The Virus of Life

I want governance of all worlds

negotiating responses to problems
strategies to solve
The comprehensive nature of the list

all elements or aspects of something
denoting a system of
powers of ten

people both nationally and internationally
gain real credibility
as content creators can attest

state that something is true or real
of a satisfactory standard
engaged for an indefinite period

sentences containing
gold coins

and Backdates
To mark or supply
Trailers for Sale

Cache

fix issues
Cache
temporarily stores
temporary stores
Pop-up-Store
Pop-up-Store
pop up
pɒpˌʌp

a treasure hunting game
find hidden objects or places
throughout hundreds of custom designed maps
in just a few seconds
a few seconds
a few
‎Quite a few

Day 10 of the Doodle
a fluttering glimpse of today’s action

hoping to prove themselves best in class
With such fierce competition
Im Cache

# Bots, Like This! I am an Ardent Fan of HTTPS and Certificates!

This is an experiment in Machine Learning, Big Data, Artificial Intelligence, whatever.

But I need proper digression first.

Last autumn, I turned my back on social media and went offline for a few days.

There, in that magical place, the real world was offline as well. A history of physics museum had to be opened, just for us.

The sign says: Please call XY and we open immediately.

Scientific instruments of the past have a strange appeal, steampunk-y, artisanal, timeless. But I could not have enjoyed it, hadn’t I locked down the gates of my social media fortresses before.

Last year’ improved’ bots and spammers seem to have invaded WordPress. Did their vigilant spam filters feel a disturbance of the force? My blog had been open for anonymous comments since more than 5 years, but I finally had to restrict access. Since last year every commentator needs to have one manually approved comment.

But how to get attention if I block the comments? Spam your links by Liking other blogs. Anticipate that clickers will be very dedicated: Clicking on your icon only takes the viewer to your gravatar profile. The gravatar shows a link to the actual spammy website.

And how to pick suitable – likeable – target blog posts? Use your sophisticated artificial intelligence: If you want to sell SSL certificates (!) pick articles that contain key words like SSL or domain – like this one. BTW, I take the ads for acne treatment personally. Please stick to marketing SSL certificates. Especially in the era of free certificates provided by Let’s Encrypt.

Please use a different image for your different gravatars. You have done rather well when spam-liking the post on my domains and HTTPS, but what was on your mind when you found my post on hijacking orphaned domains for malvertizing?

Did statements like this attract the army of bots?

… some of the pages contain links to other websites that advertize products in a spammy way.

So what do I need to do to make you all like this post? Should I tell you that have a bunch of internet domains? That I migrated my non-blogs to HTTPS last year? That WordPress migrated blogs to HTTPS some time ago? That they use Let’s Encrypt certificates now, just as the hosting provider of my other websites does?

[Perhaps I should quote ‘SSL’ and ‘TLS’, too.]

Or should I tell you that I once made a fool of myself for publishing my conspiracy theories – about how Google ditched my blog from their index? While I actually had missed that you need to add the HTTPS version as a separate item in Google Webmaster Tools?

So I despearately need help with Search Engine Optimization and Online Marketing. Google shows me ads for their free online marketing courses on Facebook all the time now.

Or I need help with HTTPS (TLS/SSL) – embarrassing, as for many years I did nothing else than implementing Public Key Infrastructures and troubleshooting certificates? I am still debugging of all kinds weird certificate chaining and browser issues. The internet is always a little bit broken, says Sir Tim Berners-Lee.

[Is X.509 certificate a good search term? No, too nerdy, I guess.]

Or maybe you are more interested in my pioneering Search Term Poetry and Spam Poetry.  I need new raw material.

Like this! Like this! Like this!

Maybe I am going to even approve a comment and talk to you. It would not be the first time I fail the Turing test on this blog.

Don’t let me down, bots! I count on you!

Update 2018-02-13: So far, this post was a success. The elkemental blog has not seen this many likes in years.… and right now I noticed that the omnipresent suit bot also started to market solar energy and to like my related posts!

Update 2018-02-18: They have not given up yet – we welcome another batch of bots!

It is not a paradox – it is a straight-forward relation between a heat pump system’s key data:

The lower a heat pump’s performance factor is, the smaller the source can be built.

I would not write this post, hadn’t I found a version of this statement with a positive twist  used in an advert!

In this post I consider a heat pump a blackbox that converts input energy into output heat energy – it ‘multiplies’ energy by a performance factor. A traditional mechanical heat pump uses electrical input energy to drive a mechanical compressor. The uncommon Rotation Heat Pump utilizes the pressure gradient created by centrifugal forces and thus again by electrical power.

But a pressure difference can also be maintained by adsorption/desorption processes or by changing the amount of one fluid dissolved in another; Einstein’s famous refrigerator uses a more complex combination of such dissolution/evaporation processes. Evaporation or desorption can be directly driven by heat: A gas heat pump thus ‘multiplies’ the energy from burning natural gas (and in addition, a heat pump and a gas boiler can be combined in one unit).

The overall performance factor of a gas heat pump – kWh heating energy out over kWh gas in – is about 1,5 – 2. This is lower than 4 – 5 available with mechanical compressors. But the assessment depends on the costs of kWh gas versus kWh electrical energy: If gas is four times cheaper (which nearly is the case in Germany) than burning natural gas in a traditional boiler without any ‘heat pump multiplication’, then the classical boiler can be more economical than using a heat pump with an electrical compressor. If gas is ‘only’ two times as cheap, then a gas heat pump with an overall performance number of ‘only’ 2 will still beat an electrical heat pump with a performance factor of 4.

While the gas heat pump may have its merits under certain market conditions, its performance number is low: For one kWh of gas you only get two kWh of heating energy. This  means you only need to provide one kWh of ‘ambient’ energy from your source – geothermal, water, or air. If the performance factor of an electrical heat pump is 4, you multiply each kWh of input energy by 4. But the heat source has to be able to supply the required 3 kWh. This is the whole ‘paradox’: The better the heat pump’s performance is in terms of heating energy over input energy, the more energy has to be released by a properly designed heat source, like ground loops sufficiently large, a ground-water well providing sufficient flow-rate, an air heat pump’s ventilator powerful enough, or our combination of a big enough solar/air collector plus water tank.

Illustration of the ‘heat source paradox’: The lower the performance number (ratio of output and input energy), the lower is the required ambient energy that has to be provided by ‘the environment’. The output heating energy in red is the target number that has to be met – it is tied to the building’s design heat load.

If you wish to state it that way, a heat pump with inferior performance characteristics has the ‘advantage’ that the source can be smaller – less pipes to be buried in the ground or a smaller water tank. And in an advert for a gas heat pump I found it spelled out exactly in this way, as a pro argument compared to other heat pumps:

The heat source can be built much smaller – investment costs are lower!

It is not wrong, but it is highly misleading. It is like saying that heating electrically with a resistive heating element – and thus a performance number of 1 – is superior because you do not need to invest in building any source of ambient energy at all.

# Things You Find in Your Hydraulic Schematic

Building an ice storage powered heat pump system is a DIY adventure – for a Leonardo da Vinci of plumbing, electrical engineering, carpentry, masonry, and computer technology.

But that holistic approach is already demonstrated clearly in our hydraulic schematics. Actually, here it is even more daring and bold:

There is Plutonium – Pu – everywhere in the heating circuit and the brine circuit …

I can’t tell if this is a hazard or if it boosts energy harvest. But I was not surprised – given that Doc Emmett Brown is our hero.

Maybe we see the impact of contamination already: How should I explain the mutated butterflies with three wings otherwise? After all, they are even tagged with M

Our default backup heating system is … Facebook Messenger!

So the big internet companies are already delivering heating-as-a-service-from-the-cloud!

But what the hell is the tennis ball needed for?