Heat pump study project

Hi, my name is Vitalys and I'm creating this blog to give you a presentation of my project on heat pumps. I'm not an expert in this field, I'm a student in "Classe préparatoire aux Grandes Écoles" (CPGE) in France and I have to do a TIPE (Personal initiative work). At first, I was going to do a computer science program on zero-knowledge proofs, but finally this project on thermodynamics interests me much more. I will try to post an article every week, knowing that the free time of a student is not huge (especially since I'm entering my second year and I have to prepare for the competitive exams). If you wish to contact me to discuss the study, whether you are a specialist or not, I will be happy to reply. My email is : vitalys@rougetet.com Image : Sadi Carnot (1796 - 1832)

Pure substances

A pure substance is one that contains only one type of atom or chemical molecule (the opposite of a mixture).

Pure substances such as water (H2O) can be found in 3 forms

  • solid
  • liquid
  • gaseous

Water has the advantage of being naturally present on Earth in these 3 forms, because its properties allow it to be at ambient temperature. This is not the case for other substances, which require extreme conditions to change state, such as :

  • copper: solid
  • oxygen : gaseous
  • ethanol: liquid

For example, for oxygen to become solid, it requires a temperature lower than -218.79°C!

Thermodynamics is concerned with the conditions required to change from one form to another and the way this transition takes place, which requires a significant exchange of heat.

An important tool for determining the stable form of a pure substance is the equilibrium phase diagram.

To name the homogeneous state of a pure substance, we use the concept of phase. We will thus have the liquid, solid and gaseous phase.

  • Solid: the particles are in contact with each other around a defined position. They make small oscillations and the solid keeps a well defined shape.
  • Liquid: no fixed shape, the particles are in contact, but can move.
  • Gaseous: the particles are not in direct contact and are distant from each other.

When the particles are in permanent contact (which is the case of the liquid and gaseous phase), we speak of a condensed phase.

Those whose compound can flow and which do not have their own form are called fluid phases (this is the case of the liquid and gaseous phase).

The phase diagram

It allows to predict the state of a given pure substance at equilibrium thanks to the temperature and pressure.


Logically, at high temperature and low pressure, the stable state is the gaseous form. At very low temperatures, the solid appears as the stable state. The liquid is stable only in an intermediate zone between the two other zones, there is a minimum pressure and a minimum temperature for the existence of the liquid state.

The shape of a phase diagram is almost the same for each pure substance.

Several phases can coexist if the pressure and temperature conditions are on the phase separation curve. The most common example is an ice cube in a glass, if the temperature between the liquid and the solid is precisely 0°C and the air is also at 0°C, then their state will remain frozen ad vitam æternam since there is no more heat transfer.

Thus, we realize that to store a gas in liquid form, we often have the choice between increasing the pressure or lowering the temperature.

The triple point is the coexistence of these three phases (here, it is θ)

The critical point (here, the point C), when we exceed this point, the notion of liquid or gas loses its meaning, there is no more boiling or temperature plateau. This area of the phase diagram is called the "zone of continuity of the fluid state".

Latent heat of change of state

Enthalpy of change of state

When water is boiled, its temperature increases continuously until it boils. Then, the temperature remains constant as the heating continues. Why does this happen?

According to the phase diagram, the temperature of the water cannot increase any more, because after this temperature it is no longer in a stable state. Thus, the amount of heat supplied is used for the transformation of the water into steam. In order for the temperature to continue to rise, all the water must have become steam.

This is how we define :

The latent heat of change of state is the amount of heat required to move a pure substance from one state to another reversibly, with the pressure held constant.

To melt an ice cube, it takes as much heat as to raise the temperature of the same amount of liquid by 80°C. As for the transformation of this same quantity of liquid into gas, it requires no less than 5.4 times the amount of heat necessary to make the liquid go from 0°C to 100°C! For example, if it took 5 minutes to boil, it will take more than 25 minutes to turn all the water into gas. Thus, there is no point in keeping the heating at maximum for cooking pasta, the temperature remains the same, it is enough to keep the boiling time to a minimum to save energy.

Here is a diagram to name the passage from one state to another, for example to pass from a liquid state to a solid state, it is the solidification:


    The latent heats of change of state are always positive values and correspond to the passage of lower enthalpy to that of higher enthalpy. That is to say from solid to liquid or from liquid to gas.

    We will see soon: the chemical potential and the mixtures.

    The second principle

    The second principle of thermodynamics allows us to know if a system will evolve spontaneously. It introduces a new concept: entropy. It is a rather abstract notion, often seen as a measure of disorder.

    First of all, it is important to define the state of equilibrium: a system is said to be in equilibrium when it is stable and invariant, for an indefinite period of time as long as an external event does not intervene.

    • A transformation is said to be reversible if at any time there is equilibrium between the internal elements of the system and equilibrium with the external elements of the system considered.
    • To show that a transformation is irreversible, it is sufficient to point to an instant during the transformation when an equilibrium condition is not verified. Often, the simplest way is to analyze the situation at the initial moment: in most cases, the evolution is induced by a break of equilibrium.
    • A transformation will be said to be quasi-static if there is an equilibrium at any time between the internal elements of the system.

    Statement of the second principle

    During a transformation of a quantity of heat into an energy which is macroscopically ordered, it is never possible to have an efficiency of 100%, a part remains in disordered form. Thus, as the transformations proceed, there is an irreversible evolution towards an increase of disorder.

    The second principle then introduces the notion of entropy which allows to quantify the tendency to go towards a disordered state. Thus, to any system is associated a state function S, called entropy. When the isolated system and the seat of an irreversible transformation, its entropy increases. When the maximum is reached, the system is in equilibrium.

    To use the concept of entropy, it is fundamental that the system is isolated, otherwise if it is not isolated, its entropy can very well increase or decrease or remain invariant.

    To calculate its entropy, we use the relation of the second principle: dS = 𝛅Q/T

    In reality, the measurement of entropy is more a notion of probability.

    For heat pumps, we will use several notions, including that of the heat source: it is a system that has a constant temperature, and whatever interactions it may have with the system under study, the temperature does not vary, it can only exchange heat. To designate this heat source, we often use the term thermostat.

    This second principle also allows us to obtain Laplace's law: during an adiabatic transformation (when heat exchange with the outside is negligible) and reversible, a fixed quantity of perfect gas, the quantity PV𝜸 is constant.

    We will see in the next chapters why all these notions are important and in what context we can use them. In particular, we will see the properties of the pure body.

    The conservation of energy

    Thermodynamics is based on three principles:

    • temperature (or the zero principle)
    • the first principle
    • the second principle

    If we say that temperature is the zero principle, it is because this notion has often been used without being really defined.

    The first principle, which we are going to see today, is neither more nor less than the conservation of energy. It may seem trivial, but it allows us to see properties that are not so obvious.

    To apply the first principle of thermodynamics, we start by studying a system and determining the parameters that define its state. We can take the example of the system of a thermal engine with pistons whose gas we study. Thus, the parameters that can vary are: temperature, pressure and volume. The transformations will thus exchange energy with the outside. In the case of the engine, it will exchange a mechanical work thanks to the pistons. Thus, the gas will exert on the piston a driving force on the wheels of the car.

    The various forms of energy

    Energy comes in many forms and it is often possible to convert one energy into another. The goal of thermodynamics is to optimize this conversion and to obtain a maximum of this energy in a reusable form.

    Mechanical energy

    The different forms of mechanical energy are :

    • kinetic energy : due to a movement
    • gravitational potential energy : due to its position in a gravitational field (ex.: hydroelectric dam)
    • elastic potential energy (e.g. a compressed or extended spring)

    Electrical energy

    It can be seen as a special case of mechanical energy, because it is interpreted as resulting from the action of electrostatic forces. It is the movement / transfers induced by differences in electrical potential.

    It is an energy difficult to store, it passes through inductances or capacitors, but this stores only a small amount of energy. It is then necessary to use batteries, but it is then necessary to use chemistry.

    The chemical potential energy

    The energy is stored by the chemical bond in the molecules. It is the main source of energy. It is used in batteries and in the combustion of coal, wood, oil or gasoline. Combustion converts chemical potential energy into heat.

    Electromagnetic energy

    This energy is moved by electromagnetic waves. For example, filament bulbs convert the heat produced by passing an electric current into light (electromagnetic energy).

    Energy conversions

    All conversions between different forms of energy are possible, but the efficiency is not always 100%. During a transformation where there is an exchange of heat, it is not possible to convert the entire amount of heat into a macroscopically ordered form of energy.

    Final form \ Initial formDisordered microscopic energyMechanicalElectricalChemicalElectromagnetic

    Disordered microscopic energy

    -Friction force Efficiency = 100%Joule effect Efficiency = 100%Reaction
    chemical yield 100%
    Absorption by a black body = Efficiency close to 100%
    MechanicalThermal engines (engines of very large boats) Max efficiency = 55%-Electric motor Efficiency close to 100%.Micromotors, biology (muscles: efficiency of the order of 10%)No simple direct conversion except for solar sails in space (about 10% efficiency)
    ElectricalThermoelectric effect Very low efficiency (a few %)
    Alternator, dynamo Efficiency close to 100%
    Batteries and cells Efficiency above 90% for some batteries
    Photovoltaic cell Efficiency ≈ 20% (even over 45% for some technologies).
    Displacement of chemical equilibria
    Shift of chemical equilibrium due to pressure
    Reaction induced by photons (example: photosynthesis)
    Hot body radiation in the visible range Efficiency = 2-3%.
    No simple direct conversion
    Antenna, diodes Efficiency 10 to 20 % for diodes

    Statement of the first principle

    Every system has an associated state function U, called internal energy, which characterizes the stored energy and which depends only on the state of the system. During any transformation, the variation of U is equal to the energy received by the system, which can be translated as:

    ΔU = Q + W, where Q is the amount of heat received by the system, W is the sum of work received, and ΔU = Ufinal - Uinitial.
    U is a state function, i.e. only the final state counts, we are not interested in the intermediate transformations that served to arrive at this state.

    For example, for thermal machines that we will study later in the context of heat pumps, the systems undergo cycles and go through the same states. When the system returns to the initial state, its internal energy must be identical. So after a complete cycle, the internal energy must be zero.

    The thermal capacities

    • Cp : is the coefficient which relates the quantity of heat exchanged to the temperature increase, the pressure being invariant.
    • Cv : is the coefficient which relates the quantity of heat exchanged to the temperature increase, the volume being invariant.

    The enthalpy

    From the internal energy, we can form other state functions.

    The enthalpy function, generally noted H, is H = U + PV.
    Since pressure P, volume V and internal energy U are state functions, H is also a state function.

    This function is very useful for isobaric transformations (at constant pressure), because its variation is identified with the amount of heat exchanged.

    It remains only: ΔH = Q


    All these notions (I passed some of them in order not to weigh down the text, if you want more precision send me an email or Wikipedia is your best friend!) are essential for the study of thermodynamic systems.

    Tomorrow, we will discuss the second principle of thermodynamics.

      Pressure and temperature

      Pressure and temperature are the basis of thermodynamics. Pressure allows us to calculate the forces exerted on the object and thus to account for the work and energy exchanged. While the temperature gives an account of the energy stored. 

      Over time, several tools have been developed to measure pressure and temperature in a relative way. From the manometer or barometer for pressure to the thermometer for temperature. For the temperature, the absolute zero was fixed as the passage from the solid state to the liquid state of water while for the degree Fahrenheit, its reference was based on the temperature of a horse (100°F), which is very relative.

      This allows the temperature to take all its importance and surely the law of perfect gases. This law tells us that at a given temperature, the product of pressure and volume remains constant (PV = f(T)). The problem is that now there is not really an absolute 0 for the degree Celsius in the sense that the melting temperature of ice can change according to the pressure. Today, the reference frames for these temperatures have fortunately changed. And science uses the kelvin for the temperature with a real absolute zero in the sense that it is the lowest temperature that can exist.

      Gases can be seen at two different levels:
      • From a microscopic point of view, they are particles moving in all directions and separated by empty space
      • From a macroscopic point of view, it is only a continuous fluid which exerts a pressure on walls
      Statistical physics will study from a microscopic point of view the particles and calculate their forces on the walls to deduce a new parameter which will be studied from a macroscopic point of view which is the pressure.

      Tomorrow, we will approach the first principle of thermodynamics, i.e. the conservation of energy.

      A brief history

      In the middle of the 20th century, home heating was mainly based on the combustion of low-cost fossil fuels.

      How did heat pump heating develop at that time?

      The history of heat pumps began in the 20th century with the development of fluid compression refrigeration machines.

      In France, it was only in 1950 that households installed refrigerators on a massive scale. Incredible when you think about it, it is extremely recent, we wonder how people did to live before. It is the symbol of the comfort of food hygiene.

      The refrigerator is the same principle as the heat pump, but in reverse. It will draw the calories present inside to lower the temperature and reject it outside (in the kitchen). 

      It is also during this period that the main air-conditioning devices for cars, buildings, etc. were developed, especially in the United States.

      However, the development of heat pumps in the domestic sector remained slow and did not convince households. The oil crises gave a boost to the installation of heat pumps (1973 and 1979). Several programs were launched by groups such as EDF (1980: PERCHE program, during the second oil crisis).

      What slows down its development is :
      • the bad insulation of the houses (which also caused the failure of the development of the heating floors, because a bad insulation requires more power)
      • the lack of reliability of the material used (poor adaptation for domestic use)
      • the price and complexity of installation
      • the lack of training of installers
      • the low cost of fossil fuels (individuals are not encouraged to invest in these systems)
      • no ecological awareness
      At the beginning of the 1980's, houses started to be properly insulated, which allows to need less power to heat the house, which allows the installation of low temperature floor heating systems. This lowering of temperature also allows a better performance of heat pump systems.

      In the 2000s, its development in France was driven by the following factors :
      • the appearance of high-performance equipment and new technologies (ground source collectors / Scroll compressors, etc.)
      • the contribution of heat pumps to renewable energy
      • the creation of quality labels (QUALIPAC) and associations (AFPAC)
      • long-term savings
      • the obtaining of tax credits
      • the objective of the Grenelle de l'environnement
      If the installation is done correctly, it does not require any maintenance and does not represent any danger. 
      The search for new refrigerants is permanent, so that they are less dangerous for the environment in case of leaks, also less dangerous for the inhabitants (risk of explosions), as well as a better thermal power. We will see it in an article dedicated to refrigerants.

      I will mainly talk about "traditional" heat pumps, but there are several variants. Like magnetic heat pumps which would allow to obtain a spectacular efficiency ratio, but which, for the moment, is not feasible on a reasonable scale.

      The value of heat pumps in our society

      An energy issue

      Facing increasing shortages and rising fossil fuel prices, better energy management is becoming essential. We are facing a climate crisis linked to human activity. The level of CO2 in the atmosphere is constantly increasing, the oceans are storing a lot of heat and releasing it only very gradually.

      The rise in temperature is causing :

      • the rise of the sea level
      • the melting of glaciers and ice floes
      • the increase of extreme events such as wildfire
      Climate change has already begun, and it compromises the future of evolved life on Earth.

      What are the solutions?

      To try to solve these different problems, we can already act on two factors
      • reduce our energy consumption
      • make better use of available renewable energies
      Heat pump systems meet these two criteria. Indeed, they allow to extract economically the calories available in abundance in nature, in an efficient way. They can heat, cool and produce hot water for the home.

      To produce heat, instead of burning raw materials such as oil, gas, coal... which drains resources and requires a high temperature, the heat pump will use the principles of thermodynamics to raise the temperature level of the energies available in nature in order to make them usable.  

      Nowadays, they are the most economical and ecological way to ensure the heating/cooling and hot water production of homes. They allow to answer the new thermal regulations (RT2012 or RE2020 for France). 

      In addition, the State provides several grants to finance the installation of these machines, which can make real savings and return on investment in just a few years. 

      Are all installations equal?

      Several types of installations exist, some are more relevant than others, we will see them in the next articles. There are also different refrigerants, most of which are extremely harmful to the planet if leaked. 

      Some systems also appear more practical than others, they allow reversibility (having warmth in winter and cold in summer). Some are more disturbing (noise) than others (e.g. drawing calories from the air instead of water through a borehole). In addition, climatic conditions have a significant influence on the efficiency ( performance factor ) of the heat pump. 
      Some installations are particularly interesting, such as geothermal heat pumps or thermodynamic water heaters. 
      All these conditions show us that it is difficult to take just one example of a system, and that in order to have a more global view of these installations, it is necessary to take several "typical" examples.

      In conclusion

      It is obvious that heat pumps alone will not be able to respond to the climate crisis, but they are a real advantage. Other solutions must be combined with them, like drastically reducing global emissions, which requires a change in our lifestyles (not only insulation of our homes...), other discoveries will probably also help us like CO2 absorption ("negative emissions").

      Tomorrow, we will see how the first heat pumps appeared and why they had so much difficulty to impose themselves.

      Why this subject and not another one?

      The main reasons I chose this topic are:
      • I had to find a topic! (and here, I was at the limit in terms of timing, I write this text on August 1st knowing that I should have had it in April)
      • This is one of the chapters where I was the least bad in physics (and physics is probably one of the subjects where I failed the least this year)
      • It's a more easily accessible subject (compared to my first choice in computer science on zero-knowledge proofs where I would have had to type 20000 lines of code and with only English theses)
      And there are probably a lot of other reasons that my brain refuses to put on paper for having chosen this path and not another one...

      During the next few days, I will publish several articles. I will try to mix "pure" thermodynamics with very concrete cases of heat pumps. It's not going to be easy and I hope I'll be as clear as possible.

      I will start by explaining the interest of these machines in our societies, I will make for that a brief history. Then, before showing you the general functioning of a heat pump, I will explain you the basics of thermodynamics to be able to understand why it is fantastic!

      Finally, even if this subject was not my favorite at the beginning, I must admit that thermodynamics is essential. Without it, we wouldn't have had the industrial revolution, we wouldn't have all the scientific principles that are the basis of our current societies. By taking an essentially macroscopic point of view, we can explain many natural phenomena, and design many objects that impact our daily life such as cars, refrigerators, heat pumps, thermal power plants to produce electricity and so on.

      In the next article, I will explain why thermodynamics is not only the science of the past or the present, but especially why it is the science of the future!