How Heat Pumps work
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. |
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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) |
| 5 | 13.2 |
| 10 | 46.8 |
| 14 | 66.1 |
| 16 (use) | 74.47 (use 74°C ) |
| 20 | 89 |
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. |
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