Heat pumps

Figure 1

As noticed at reference 3, I was prompted by Davies on the information content of life to inquire into how exactly heat pumps worked. Pumps which seem to swing in and out of fashion among the eco-warriors; at least in the sense that one hears about them for a while then it all goes quiet again. And a quick peek at the Internet suggests that they are, indeed, still quite expensive. See reference 9.

Figure 2

Not being online at the time, I tried my telephone and turned up a useful manual prepared by some Naval branch of the US military. Saved it to OneDrive on the telephone OK, but then had some difficulty getting it from there to my laptop. Provincial broadband just can’t cope when all the boys are off school and playing with their computer games. But I got there in the end.

What we have is Chapter 6 – refrigeration – and Chapter 7 – air conditioning – of a TRAMAN, US Navy speak for a training manual. Possibly the training manual which has to be studied in order to get the Utilitiesman rating of reference 5. 90 pages of text and figures.

An accessible blend of theory and practise, complete with diagrams of the important components of refrigeration systems – systems which look to be mainly, if not exclusively, intended for refrigerators, of various sizes, to hold food and drink. There are a modest number of typing and printing errors. Probably quite an old book although these isolated chapters include no dates and I cannot now find where my telephone got it from.

However, what we have it the the product of a large bureaucracy, with every diagram carrying what is probably a unique diagram reference number. So, for example, UTB2f601 is Figure 6-1 showing the three states of matter, that is to say solid, liquid and gas. Bing does not find anything useful with this search string, but Google turns up something which leads to what appears to be an updated version of the manual from which my download was taken. To be found at reference 6, properly described as at reference 7 and from which the opening illustration is taken. 

Figure 3

But I struggled for a while with the Figure 6-9, the pressure temperature chart, a two dimensional array of numbers with temperature down the page and something across the page. The top part of which is snapped above. Eventually I learned from a later section, a bit of which is snapped below, that the numeric column headers were actually the numbers of commonly used refrigerants, so 12 for R12, otherwise dichlorodifluoromethane. I think it says somewhere that this particular one is no longer much used because of global warming issues. For which see reference 10.

Figure 4

The basic theory seems to be that first, if you increase the pressure, a gas will eventually turn into a liquid and release latent heat to its cooler surroundings. The higher the temperature of the gas, the more pressure is needed to achieve this. Then second, if you then decrease the pressure, the liquid will eventually turn back into a gas, taking the necessary latent heat from its warmer surroundings – in the case of a refrigerator, this being now the interior where the food is being kept. Most of the heat involved here is the latent heat of the state change, of the transition from liquid to gas or from gas to liquid. With the sequence of events being roughly as follows.

Cool gas comes out of the evaporator inside into the condenser outside.

Arrives in the high temperature outside. Absorbs some heat.

Compressed until its condensing point is higher than the temperature.

Gas condenses and releases its latent heat of condensation to the now slightly cooler outside. This latent heat is large relative to the amount of heat needed, for example, to heat a liquid which is comfortably between its melting and boiling points, through a few degrees Centigrade.

Warm liquid goes into the evaporator inside from the condenser outside.

Arrives in the low temperature inside. Gives out some heat.

Pressure goes right down until the boiling point is lower than the temperature.

Liquid evaporates and takes its latent heat of boiling – equal and opposite to the latent heat of condensation – from the now slightly warmer inside.

Presumably, if one does this in reverse, that is to say if one has a heat pump  rather than a refrigerator, the amount of heat or energy required to drive the compressor and the other bits and bobs is much less than the heat you get out. And, intuitively, it is not unreasonable that one has to use energy to pump energy against the natural gradient.

Figure 5

Presumably also, one gets more heat like this, than if the mechanical energy that went into driving the compressor was put instead into some contraption for converting motion to heat more directly. With such a contraption usually involving friction, the of contraption one used in physics classes at school when attempting to measure the mechanical equivalent of heat. An updated version of that snapped above – although I have no idea now why that one would not have done. It looks a lot simpler than the contraption I remember using – and getting a rather bad answer from. Or at least, a good deal further off the mark than some of my fellow pupils.

The leaking of refrigerant seems to be an issue and one does not want long gas lines. Which might mean that one goes for a primary-secondary system in which (for example) refrigerant cooled brine (secondary) is used to cool the inside of the refrigerator, rather than using the cooled refrigerant (primary) direct.

We learn that the four or five main components making up the cooling cycle – condenser, liquid receiver (optional), expansion valve, evaporator and compressor – are supplemented by a number of control components and refinements. With more and more of them as the refrigerator gets bigger. Lots of bells and whistles.

Figure 6

 More fun and games trying to play spot the difference with the two figures above. Rotate central valve 90° to get from one to the other. I cheated by flipping the right hand element right to left in Powerpoint.

In sum, this sort of heat pump works by using trickery with the pressure of the refrigerant, to move the latent heat of evaporation or condensation from one place to another. With part of the trickery being to find a refrigerant, the pressure of which can be manipulated so that its boiling point varies from below the temperature of the cold side to above that of the high side, and the latent heat of which is large relative to its specific heat. Without heating up the planet too much when it leaks away.

Other matters

Figure 7

By analogy of the potential energy of water with thermal energy, in option 1 we convert the potential energy of the water in the upper tank to work with the round magenta gadget between them, perhaps a simple paddle wheel, by allowing the water to flow though it to the lower tank. In option 2, we do work with the magenta gadget, now a pump, a rather more complicated gadget, to move water from the lower tank to the upper tank. In option 3, we get work out of the overshot (water) wheel by allowing the water to fall into the wheel’s buckets. Note first, that the water needs to drop onto the overshot wheel slightly to the right of centre (as illustrated above and below); and second, that this simple arrangement does not work in reverse and turning the wheel with a horse (or whatever) does not result in water going up, at least not without introducing a rather more complicated wheel. In option 4, we get work out of the flowing water by harnessing the flow to turn the much simpler undershot wheel – much the same, in principle, as a paddle in a paddle boat. Note first, that such a flow usually arises in the first place from flow from high ground to low ground; second, that the same wheel can turn in either direction, clockwise or anticlockwise; and third, that this arrangement can be reversed with little alteration. It can either use the flow of water to turn the wheel or turn the wheel to make the water flow. 

Figure 8

The overshot wheel at Buckfast Abbey, last noticed at reference 4. The leat runs away to the right for a couple of hundred yards, and may be fed by the holy brook running down from Holne, where we stay, as suggested in the snap from Ordnance Survey which follows. Although, to complicate the story, the building concerned was probably once a commercial woollen mill, nothing to do with the monastery, but now gathered into its conferencing business.

Figure 9

Not altogether clear what exactly happens above Buckfast, but it seems likely that Holy Brook, which one supposes to be so named for the abbey of old, supplies the leat one way or another, before running down into the Dart, right.

Figure 10

The diagrammatic version, with both timber bucket and steel bucket options shown.

Nature, on the whole, does not use large gadgets of this sort. It cannot manage these sorts of tricks. But according to Davies at reference 1 (page 56), it can do them at the scale of living cells and the complex molecules in them. And it can do chemical exchanges across the large surface areas of lungs and intestines.

Conclusions

The physics details of a refrigerator are tricky and I dare say the differential equations involved are even more so. But refrigerators do work, and worked before those details got worked out, so maybe the interested amateur does not need to worry about them.

And if you are semi-literate scientifically and want to know about a bit of technology that a navy might use, go along to the US Navy training operation, that is to say the Naval Education and Training Professional Development and Technology Centre, which may well be able to help.

References

Reference 1: https://en.wikipedia.org/wiki/Gas_laws. All about the relationship between temperature, pressure, volume and mass of a gas.

Reference 2: The demon in the machine – Paul Davies – 2019.

Reference 3: https://psmv5.blogspot.com/2021/10/back-to-demonology.html.  

Reference 4: https://psmv5.blogspot.com/2021/10/the-rule-of-st-benedict.html. 

Reference 5: https://www.navycs.com/navy-jobs/utilitiesman.html. I don’t know who these people are: an unusually anonymous website.

Reference 6: https://www.academia.edu/44398759/Utilitiesman_Basic_Volume_2. 

Reference 7: Utilitiesman Basic Volume2: NAVEDTRA 14279 – Naval Education and Training Professional Development and Technology Centre – 1999. NAVSUP Logistics Tracking Number 0504-LP-026-9110.

Reference 8: https://en.wikipedia.org/wiki/Ideal_gas_law. More background for the curious.

Reference 9: https://www.worcester-bosch.co.uk/heat-pumps. 

Reference 10: https://www.ccacoalition.org/en/slcps/hydrofluorocarbons-hfcs.