How Heat Pumps work

Andrew on September 2, 2024

Hot water heat pump diagram

The example heat pump

I show how heat pumps work using an example heat pump, including the refrigerant temperatures and pressures. This heat pump:

  • uses propane as the refrigerant,
  • draws heat from the 17°C air outside the house,
  • moves the heat into the 50°C water in a hot water tank outside the house,
  • has a target hot water temperature of 60°C, and
  • warms 15°C tap water.

The heat pump works by repeatedly moving the propane refrigerant through this anti-clockwise cycle of processes:

Condensation:
Propane at 16 atm condenses at 74°C, releasing heat to warm 50°C water.
 
Throttling/Expansion Compression
Evaporation:
Propane at 4 atm evaporates at 3°C, energised by air at 17°C.

Figure 1: The Heat Pump Cycle

.

How can 17°C air heat 50°C water? Below, I detail this seemingly magical process, but in brief, this heat pump cycle works because:

  • the expansion valve drops the pressure to 4 atmospheres (4 atm), which decreases the temperature at which propane evaporates to 3°C. The heat pump then uses 17°C air to harvest energy by evaporating 3°C propane, and
  • the compressor increases the pressure to 16 atm, which increases the temperature at which propane condenses and releases heat to 74°C. The heat pump then uses the heat released by condensing propane at 74°C to heat 50°C water.

I’ve written this because I’ve noticed that even those of us with a science background often have only a basic understanding of how heat pumps operate. Given the crucial role heat pumps play in advancing renewable energy and improving energy efficiency, I wanted to know how they worked – and still want to know more about them. For example, I’d welcome your opinions about the last section of this page headed “speculation”.

The equipment

Here is the equipment for heating water with a heat pump.

Figure 2: Hot water heat pump equipment: Source: everydayplumbing.com.au

The diagram shows:

  • The hot water tank, a cold-water inlet and a hot-water outlet.
  • The electric fan which blows air over the evaporator.
  • The evaporator: a heat exchanger where the heat from the air passes into the propane.
  • The compressor takes low-pressure propane from the evaporator, compresses it and pushes high-pressure propane into the condenser.
  • The condenser: a second heat exchanger where the heat from the propane passes into the water. The heat exchange coils wrap around the water tank. On the tank’s left and right sides, you can see the brown sausage-like cross-section of the condenser pipes.
  • Propane gas moves from the compressor via the red pipe and enters the condenser near the top left of the tank.
  • Propane liquid leaves the condenser via the blue pipe near the bottom left of the tank. Under high pressure, this propane briefly dams in the pipe, waiting to move through the expansion valve.
  • The accumulator prevents liquid propane from entering the compressor.
  • The expansion valve releases the high-pressure propane from the condenser into the low-pressure evaporator.

Propane boiling points

Heat pumps work because the refrigerant’s boiling point increases with the pressure around the liquid. The table shows this for propane. I use the four marked values in the table in the example heat pump.

Pressure
(Atmospheres: atm)  		Propane boiling points
(Degrees C)
1 – 43°C
3-7.4
3.92 (use 4 atm)3°C (use)
513.2
1046.8
1466.1
16 (use)74.47 (use 74°C )
2089
 
The boiling points come from the Internet Omni Calculator.

Pressure & volume change during each cycle

The four thick black lines on the pressure-volume diagram show what happens to one gram of propane as it cycles around the heat pump. The lines show how the propane’s pressure, volume and temperature change during the cycle. In the diagram, the heat pump cycle is anticlockwise.

Figure 3: The Pressure-Volume Diagram

Diagram Source: Wikipedia: Vapour-Compression Refrigeration page

The following table shows the temperatures and pressures of the example propane heat pump. The layout of the table follows the layout of the pressure-volume diagram. The temperatures and pressures are rough estimates.

Heat Sink: Hot water
Temperature 50°C
Target 60°C
Propane after condenser
Saturated liquid
High Pressure 16 atm
High Temperature 74°C.  		Condenser
heat exchanger

Propane after compressor
Superheated vapour
High Pressure 16 atm
High Temperature 78°C  

 Expansion Valve
 
Compressor
Propane after expansion
Liquid & vapour
Low pressure: 4 atm
Low temperature: 3°C  		Evaporator
heat exchanger


Propane after evaporator
Saturated vapour
Low pressure: 4 atm
Low temperature: 3°C  

Heat Source: Air
Temperature 17°C.
Figure 4: The Example Heat Pump

Please consider printing the diagrams so you can view them as you read.

Evaporation

The thick black evaporation line on the pressure-volume diagram shows that evaporation occurs at a constant low pressure, in my example, 4 atm, as the liquid propane turns into vapour and takes up a larger volume.

(Note that the pressure-volume diagram neglects the small pressure drop across the evaporator, which drives the propane through the evaporator.)

The evaporation line partly hides the blue, cold temperature line marked Tc. This blue line shows that evaporation occurs at a constant temperature; in my example, 3°C, which is propane’s boiling temperature at 4 atm.

Propane enters the evaporator as a mix of liquid and vapour at 3°C, and an electric fan blows 17°C air over the evaporator. The evaporator is a heat exchanger with many coiled tubes and metal fins. The air can transfer its heat to the propane through this large metal surface area. The air warms the evaporator’s metal, heating the propane liquid and giving it the energy to vaporise.

As the low-volume liquid propane evaporates, becoming high-volume vapour, the pressure in the fixed-volume evaporator does not increase because the compressor keeps sucking gas out of the evaporator. Also, the compressor removing gas does not cause low pressure because the expansion valve keeps moving refrigerant into the evaporator.

Latent heat

The air heating the propane in the evaporator does not change the propane’s temperature. It changes the propane’s state from a liquid to a vapour. The air provides the propane liquid molecules with the energy needed to escape the liquid and become a gas. This energy is the latent heat of vaporisation, for propane, 426 joules per gram. The propane gas gains this latent heat in the evaporator and later condenses, transferring this latent heat into the hot water.

To give the propane latent heat context, consider the energy needed to boil water. Boiling 15°C tap water uses 355 joules per gram of water. So, the energy needed to vaporise propane, 426 joules per gram, is 20% more than the energy used to boil tap water.

Compression

The compressor draws propane vapour out of the evaporator at 4 atm, compresses it, and pushes it into the condenser at high pressure, 16 atm. As the pressure builds, the gas gets hotter, just as a bicycle pump gets hot while you pump up the tyres. The compressor also provides the pressure differences that drive the propane around the whole cycle.

The compressor is a scroll compressor. These do not have the pulsing output of a piston compressor but produce a continuous stream of compressed gas.

(See Scroll compressors in the Engineering Encyclopedia: enggcyclopedia.com)

Condensation

The thick black condensation line on the pressure-volume diagram shows that condensation occurs at a constant high pressure, in my example, 16 atm, as the propane vapour turns into liquid taking up a smaller volume.

(Note that the pressure-volume diagram neglects the small pressure drop across the condenser, which drives the propane through the condenser.)

The condensation line partly hides the red, hot temperature line marked Th, which shows that condensation mainly occurs at the constant temperature. In my heat pump, this is 74°C, which is propane’s boiling temperature at 16 atm.

After compression, the propane is in the condenser as a superheated vapour, in my example, at 78°C. It is “superheated” by 4°C as the 78°C is 4°C above the 74°C boiling temperature at 16 atm.

The condenser is a second heat exchanger, where the propane heats the water in the hot water tank. The propane is between 74°C and 78°C so it heats the heat exchanger’s metal, which heats the 50°C water in the tank.

The propane loses heat energy to the water from:

  • the superheat of 4°C as it cools from 78°C to 74°C, and
  • the latent heat as it condenses into a liquid at 74°C.

The propane becomes a liquid at 74°C and 16 atm pressure.

As the high-volume propane vapour meets the colder metal of the condenser, it condenses into a low-volume liquid. The compressor replaces this vapour, keeping the pressure at 16 atm. The small pressure drop pushes the liquid towards the expansion valve. Under this 16 atm pressure, the liquid briefly dams in the pipe in front of the expansion valve, like water under pressure in a dribbling hose.

Expansion

The expansion valve releases propane liquid from the condenser at 16 atm into the evaporator at 4 atm. On the pressure-volume diagram, this is the “throttling” line.

The pressure drop causes some propane to vaporise. In vaporising, the propane absorbs latent heat, which cools the mixture of liquid and vapour, lowering it from 74°C to 3°C.

After the expansion, the propane is a mixture of liquid and vapour at 4 atm and 3°C. It’s back where it started in the evaporator, ready to repeat the heat harvesting cycle.

This completes the heat pump cycle, which causes the propane refrigerant to change state several times and transfer heat from the outside air to the hot water tank,

Steady-state continuous cycle

At first, I thought the heat pump ran through its cycle by stopping and then starting each operation, e.g., starting and stopping the evaporation, then starting and stopping the compression. While writing this, I learned that this is wrong.

After the heat pump starts up, it comes into a slowly moving steady state, with each heat pump process running continuously.

The refrigerant comes into a different steady state after each of the four processes. At each point in the cycle, we see constant pressure, temperature, and mass flow rates with these steady states depending on:

  • the external air temperature
  • the target hot water temperature,
  • the current hot water temperature,
  • the refrigerant used, and
  • the design of each component.

The saturation curve

On the pressure-volume diagram,

  • The “saturation curve” is the dashed line that passes through the “critical point”.
  • To the left of the critical point on the saturation curve, the propane is a saturated liquid, i.e., a liquid at boiling temperature where any heating generates vapour.
  • To the right of the critical point on the saturation curve, the propane is a saturated vapour, i.e., a vapour at boiling temperature where any cooling generates liquid.
  • On the saturation curve and within the dome formed by that curve, the propane is at its boiling temperature for that pressure. For example, along the dark black evaporation line, the propane is at its boiling temperature, 3°C, for that constant pressure of 4 atm.

Estimating temperatures and pressures

Here’s how I got the temperatures and pressures for the heat pump scenario. My estimates are rough guesses, and I’ll update this page if someone lets me know of more rational estimates.

The evaporator estimation

The pressure-volume diagram shows that to describe the propane in the evaporator, we need:

  • a low-pressure (Pc), and
  • the cold temperature (Tc) which is the propane boiling point at pressure Pc.

To efficiently transfer heat from the 17°C air to the propane, you need a significant temperature difference, so say the propane is 14°C cooler than the air. That makes the propane temperature 3°C. Then, the pressure Pc will be the pressure at which 3°C propane boils. My propane boiling point table shows this is 4 atm, so Pc = 4 atm.

Here I ignore:

  • the small pressure drop across the evaporator, and
  • propane entering the compressor is slightly above boiling temperature to prevent liquid from entering and damaging the compressor.

The condenser estimation

The pressure-volume diagram shows that to describe the propane in the condenser, we need:

  • the high-pressure (Ph)
  • the hot temperature (Th), which is the propane boiling point at pressure Ph, and
  • a superheated temperature (Ts), which is higher than Th.

This propane needs to heat the hot water to 60°C, so the propane temperature needs to be significantly hotter than that, say 74°C.

The pressure will be the pressure at which 74°C propane boils. My propane boiling point table shows this is 16 atm, so Ph = 16 atm.

The pressure-volume diagram shows that, after compression, the propane is at the same pressure during condensation, but it is now a superheated vapour. That is, its temperature is higher than the 74°C propane boiling point at that pressure. Assume the temperature of the superheated vapour, Ts is 78°C.

Here I ignore the small pressure drop across the condenser.

Heat pumps are in most houses.

Electric heat pumps are an essential part of other household equipment too:

  • Refrigerators have a heat pump that moves heat from “inside the fridge” to “outside the fridge”.
  • Air-conditioners have a heat pump that can (1) cool a room by moving heat from the room to outside the house or (2) heat a room by doing the reverse.

Heat pumps are efficient.

Heat pumps are remarkably efficient, offering a significant advantage over other heating systems.

A heat pump hot water service (HWS) has an electric fan and compressor that harvest energy from the air outside a house. They can use one unit of electrical energy to move three times as much heat energy into your hot water, an efficiency of 300%.

By comparison:

  • Heaters with an electric element, like a hot water jug, put all their electric energy into heating the water, so they have an efficiency of 100%, and
  • Gas heaters have an efficiency of between 50% and 95%, as heat escapes via the heater’s flue.

So, a heat pump hot water service is usually far more efficient than alternatives and can reduce your power bills. They can cut these bills even more when you have solar panels and run your heat pump predominantly during the day, using electricity from your panels.

Acknowledgements

I got a lot of help from a physics forum (www.physicsforums.com).

I still have much to learn about heat pumps. If you can see some improvements to this page, please let me know.

Some speculation

In writing this, I learned that I had a few significant misunderstandings about heat pumps – and I’m still uncertain about some things.

Do the following sections make sense to you? If some sections need modification, please let me know.

The condenser

In the steady state considered here, both the compressor and the expansion valve move propane continuously at the same rate, let’s say 14 grams per second. (I did some rough heat flow calculations to estimate this.)

In the condenser, as the 74°C propane vapour contacts the condenser metal close to the hot water temperature of 50°C, the propane vapour condenses around the inner circumference of the pipe. This state change from a vapour to a gas drastically lowers the volume taken by the propane. The compressor feeds propane gas into the condenser at 14 grams per second, keeping the pressure at about 16 atm, replacing the vapour that has condensed, and pushing propane liquid through the expansion valve at 14 grams per second. A small pressure drop across the condenser pushes the propane liquid and gas towards the expansion valve also at 14 grams per second.

Under this 16 atm of pressure, the liquid propane briefly dams in the pipe, held up by the expansion valve, like water in a dribbling hose. (The propane is different from the water in a hose because the propane only gathers in the pipe near the expansion valve, whereas with a hose, the water fills the hose all the way to the tap and beyond.)

The heat pump diagram (Figure 2) shows the pipe carrying the propane out of the bottom of the condenser, separated entirely from the hot water tank, up to the expansion valve at the top of the heat pump.

This heat pump works efficiently with all the propane vapour condensing in the condenser and passing its latent heat to the water, leaving no propane vapour in the upward pipe to the expansion valve. The upward pipe carries liquid propane close to 74°C and 16 atm. (When propane vapour does get into this pipe, the accumulator removes it to prevent damage to the compressor.)

With the heat pump in a quasi-steady state, the position in the piping at which all the propane becomes liquid is one of the constants of the quasi-equilibrium.

Estimate the propane flow rate.

Here is the rough calculation, which gives the propane flow rate of 14 grams per second.

  • Hot water tank size = 250 litres = 250,000 ml
  • The heat pump can heat the water from 50C to 60C, 10C in one hour.
  • Water needs 4.186 joules of energy to heat one gram by one degree.

Heat needed = 10C x 250,000 ml x 4.186 = 10,475,000 joule in 60 minutes

= 2,910 joule per second

  • Propane needs 426 joules to heat one gram by one degree C.

Propane flow rate needed to perform this heating = 2910 / 426 = 6.8 gram / second

Doubling this, to allow for inefficiency, gives 14 grams per second.

Updated: 25 Sep 2024

Australia’s strong sun

Andrew on April 30, 2018

Australia could become a renewable energy superpower.  One factor behind this is that Australia gets stronger sun than most developed countries.

Two world maps superimposed

Here is a fascinating map that demonstrates this.
http://www.dailymail.co.uk/sciencetech/article-4707544/Antipodes-Map-lets-dig-virtual-tunnel-Earth.html

It is two maps superimposed on one another. The first is a normal map of the world.  The second map shows, for each point on the first map, where you would be if you drilled straight down through the centre of the Earth to the other side.

The closer a place is to the equator: (1) the more the sun is directly overhead, (2) the more sunshine it gets, (3) the more electricity is generated from each solar panel, and (4) the cheaper it is for that place to generate electricity from the sun.  This is ignoring other factors like how cloudy a place is.

From this map you can see that:

  • Australia is closer to the equator than the developed countries in northern Europe, northern Asia and northern America.
  • Northern Greenland, Canada, Alaska and Russia are as far from the equator as northern Antarctica
  • Melbourne is as far from the equator as southern Spain, so most of Australia gets stronger sun than Spain and most of Europe.
  • Northern Australia is as far from the equator as the border between the Sudan and Egypt.
  • The southern border of the USA is about the same distance from the equator as Port Macquarie (halfway between Sydney and Brisbane). So northern Australia gets more sun than the south of the USA.

Manchester in England is as far north as Macquarie Island is south

Look at this yet another way. Australia gets far stronger sun than most of Europe because we are closer to the equator.

People often think of Macquarie Island as being in the Antarctic as it lies far south of New Zealand at latitude 55 degrees south. Well, Manchester in England lies at latitude 54 degrees north, so Manchester is as far north as Macquarie Island is south – and both experience a similar level of sun exposure.

Northern America and northern Europe get very weak sun compared to most of Australia. Europe would be very cold without the Gulf Stream.

Australia has quality solar resources

So, considering only the factor of sun strength (closeness to the equator), Australia has better solar resources than most developed countries – and we have other advantages too, which mean that Australia could become a renewable energy superpower.

Updated: 21 June 2024

Warm is Not Cool: A Musical Protest

Andrew on June 22, 2016

warm-is-not-cool-350

Musical Protests Against Inaction on Global Warming: 2016 & 2019.

THE GLORIOUS RABBLE, with
THE HORNS OF INFINITE JUSTICE, and
THE DRUMLETARIAT.

Stephen Taberner organised this protest.

(As you might already be able to tell, on this page I have used lots of “dirty funky” words from Stephen’s event promotion.)

Our long-awaited first public outing was on Sunday 19 June 2016.

A marvellous experiment in public protest, inspired by the New Orleans brass bands, the English football crowds, and the Brazilian samba.  We brought our delicious hybrid to the streets.

It was highly enjoyable, highly effective and downright dead, dirty funky. The three contingents of voice, horns and drums intersected in every cool way possible as we protested the woeful lack of attention in these election weeks to the elephant in the policy room: CLIMATE CHANGE.

To get people started, we rehearsed in public on the steps outside the Victorian State Library.  Here we are, learning and brushing up on our songs, chants, and grooves.

Video 1: (1) watcha gonna do (2) Warm is not cool

After the warm-up,  we strutted our stuff at the old shot tower in the Melbourne Central Arcade.  (Sorry, you may need to be on Facebook to see the next two links.)

Video 2: (1) warm is not cool (2) watcha gonna do

https://web.facebook.com/Nancy.a.casa/videos/10206440165870954

Video 3: (1) warm is not cool (No longer available: 9/8/2023)

Later we were in the Melbourne City Square

Video 4: (1) warm is not cool (2) Whatcha gonna do

Then we did our thing in Federation Square.
And then called it a day.

Warm is not Cool: The Sequel: 26 June 2016:

Video 5: In Melbourne Central again: (1) Warm is Not Cool (2) Whatcha Gonna Do.
https://www.youtube.com/watch?v=ZS0b37BoZOw

“Vote the Bastards Out” 2019

We sang this in the streets prior to the 2019 election – to no avail.

Vote the bastards out: Spooky Men’s Chorale

The songs and chants: Lyrics and tunes

Not too many words.  Lots of repetition, harmony and jive.

(The lyrics and tunes are no longer where they were on the web. 9/8/2023)

****** Song: Warm is not cool

You can hear this on the sound cloud links and videos

Warm’s not cool

Warm is not cool
Warm is not
Warm is not
Is not

Yo de aye
Warm is not cool

Did you know that’s the case so
We got to fix up this place

We don’t want to mess up the future

***** Song :  A message to you Turnbull

You can hear this on the sound cloud links and videos

Stop your messing around
Better think of our future
Time to straighten right out
This problem in town

Turnbull, a message to you Turnbull
, a message to you Turnbull
, a message to you Turnbull
, a message to you Turnbull

22 percent of the reef is gone
Turn the coal off.  Turn the solar on

***** Song 3: Malcolm

You can hear this on the sound cloud links and videos.
Each part: bass, mid and top is separate on sound cloud.

Words:
Malcolm Turnbull’s got a very nice face
So let’s find him a lovely job in another place

***** Whatcha gonna do:  Call and Response Chant

Whatcha gonna do                  What
When the world gets hot      What
Whatcha going to do               Whatcha going to do
What                                                  When the world gets hot
What                                                  Whatcha going to do

Then Repeat

Try this chant while listening to the above video of us outside the State Library.

***** Chant: Coal Don’t Dig it

Coal don’t dig it
Leave it in the ground
You’ve gotta get with it

Origin

Stephen Taberner taught us these songs and chants
www.stephentaberner.com

He knows how to work a group!
Here he is leading the Spooky Men’s Choir at a folk festival in Shrewsbury, England.  Good song.  You might even laugh.

Another top song

We Are Not a Men’s Group – The Spooky Men’s Chorale

Andrew Gunner

A solar-powered winery on Sikinos

Andrew on August 5, 2015

A remote winery on the island of Sikinos in Greece has a spectacular view and more.  It has solar panels on the roof and battery storage, along with the expected large stainless steel wine vats.  Across the world, it’s happening more, away from the grid, it’s economical to be self-sufficient.

The winery is 2.5 kilometres away from the main village, perched high over its terraced vineyard with views of steep island peaks. There’s a tiny church on one peak and, out of view in a valley below, there’s an ancient Roman temple that became a church.  The wine-dark seas of Odysseus are spread in front of you, with islands dotting the broad sweeping horizon.  You can walk the old footpaths of Sikinos, and most of the ancient agricultural terraces are crumbling, but at the winery, the terraces are in repair, and the vines thrive on the moisture from the morning mists. 

Manalis Winery Sikinos

Temperature, CO2 and Sea Levels move together

Andrew on June 6, 2015

Sea levels, Carbon dioxide concentrations, and Global temperatures have moved together over the last 450,000 years.

graph-co2-temp-sea-level-450k-years

The graphs show the movement over the last 420,000 years of:

  • Carbon dioxide concentrations in the air (the green line),
  • Global temperatures (the red line), and
  • Sea levels (the blue line).

The carbon dioxide concentrations have fluctuated between about 180 and 280 parts per million (ppm) over this period of 420,000 years, but in the last 50 years, it has rocketed to above 410 ppm. (See the red circle on the green carbon dioxide graph.)  

The sea levels and temperatures have moved with carbon dioxide levels in the past.  This suggests that the recent increase in carbon dioxide will lead to large rises in sea level and temperature.

The graph shows five periods of high temperatures. We are living in one of those warm periods. During the previous warm period, about 120,000 years ago, the temperature was a few degrees warmer than at present, and the sea level rose about 8 meters higher than the present – and carbon dioxide levels were a lot lower than they are now.

The work of Hansen and Sato provided the basis of this graph

(John Englander: Oceanographer)
https://johnenglander.net/420000-years-of-temp-co2-and-sea-level-what-a-coincidence/

Glaciers in retreat:

Andrew on May 31, 2015

Glaciers around the world are in retreat. Out of 250 alpine glaciers studied, the Taku Glacier in Alaska was the only glacier not retreating until, in 2019, it too began retreating. At 1,500 metres thick, it’s one of the world’s thickest mountain glaciers, now retreating by up to 390 billion tons of snow and ice a year.

(This is a big deal. Mighty glacier finally succumbs to climate change: The Age: 8 Nov 2019)

The glacier altitude feedback cycle

This feedback occurs because the average temperature at the top of a mountain is lower than at sea level – and this is relevant because we have some thick ice sheets, for example:

  • up to 4,900 meters deep in Antarctica,
  • up to 3,000 metres in Greenland, &
  • up to 1,500 meters for mountain glaciers.
More glacial surface meltingA drop in the altitude of the glacier surface
*A rise in average temperature at the glacier surface

When the “glacier altitude feedback” is dominant:

  • more glacial surface melting causes
  • the altitude of the glacial surface to drop, causing
  • higher temperatures at the glacial surface, which closes the cycle by causing
  • more glacial surface melting.

This feedback cycle indirectly increases global temperatures. As the “glacier altitude feedback cycle” decreases the area of reflective glacial ice, the area will absorb more heat from the sun. So, another feedback, the “ice reflection feedback cycle“, will increase global temperatures.

The Extreme Ice Survey

The Extreme Ice Survey collects visual evidence of the impact of global warming on our planet, like time-lapse photos of the contraction of the glaciers.  Outside of the Antarctic, 95% of the world’s glaciers are retreating. See:

  • the film “Chasing Ice”, produced in cooperation with National Geographic. It won an Emmy award as an outstanding nature program, or
  • the TED talk by James Balog in July 2009.

Related pages

Updated 28 March 2022