Thermodynamics without maths – Part 2

Thermal Conductivity

While we have covered a little on the heat capacity of substances as their ability to hold varying degrees of heat energy, the latent heat as the additional energy absorbed or expelled to change phase between solids, liquids and gasses. They don’t describe or relate to the “thermal conductivity” of materials. 

This describes the rate at which heat can transfer from one material to another via conduction. Again, it can be a counter intuitive concept, and unrelated to the specific heat capacity of a material. 

In the heating industry, you might have heard of a K-Value or U-Value, ways of measuring the thermal insulation properties of a material as used in heat loss calculations for a premises. 

The K-Value or Lambda, measured as W/m·K (Watts/meter Kelvin) is the quantity of heat transferred in a given time through a certain distance, at a set difference in temperature. The higher this number, the greater amount of heat a substance can absorb at a faster rate, making it a good conductor of heat, the lower the number then the better it is as a thermal insulator.

Some examples of Lambda (λ) values are shown below:

Silver – 428 W/mK

Copper – 401 W/mK

Aluminium – 236 W/mK

Iron – 83.5 W/mK

Stainless steel – 14 W/mK

Water – 0.609 W/mK

Modern foam insulation – 0.022 W/mK

These examples are rough approximations, the actual value is dependent on the current temperature of the material in question. From these materials you might be surprised to see Aluminium has over 16 times the thermal conductivity of Stainless steel, this is why gas fired stainless heat exchangers are often made up into narrow coils to massively increase the available surface area available to absorb heat.

Copper is an excellent conductor but unsuitable as a heat exchanger in modern boilers due to its low corrosion resistance to the acidic condensate produced in high efficiency appliances. 


In thermodynamics pressure and temperature are inescapably linked.  Put in simple terms, with a gas or liquid in a fixed volume, an increase in temperature will increase pressure, similarly a change in pressure will change the temperature of a volume. 

It helps to picture the atoms previously talked about, imagine a sealed container, pipe, tank etc, with molecules of a gas inside it. Every one of those particles is moving all the time, each one exerts a force anytime it strikes the wall of the container, with pressure being a measure of force over an area, the pressure can be seen to be directly affected by how often and how much force the particles are striking the container walls. 

As an example 

If we had a piston in a sealed sleeve with a gas inside, and compressed the gas into a much smaller area, you would still have the same number of gas particles as you started with, only now with a reduced volume they are striking a smaller area of the container wall with a higher frequency, thus an increase in pressure is observed, they are also striking each other more often now which means the temperature will also have risen. 

Scientifically pressure is measured in Pascals (Pa), in the heating industry we will more commonly use Bar and millibar. A Bar of pressure is equal to 100,000 Pascals, and a Bar is the same as 1,000mbar. As I mentioned previously, like heat, pressure always pushes from higher to lower pressure.

Pressure is also affected by height:

When talking about the pressure of a gas or a liquid, a contributing factor is always the height it reaches above its base.

This is the force of gravity pulling material towards the earth. In industry terms we often would say, an empty pipe has no pressure in it, however this is not accurate, we neglect the air pressure that is around us constantly. At sea level “atmospheric pressure” is approximately one bar, more accurately its defined as the equivalent of 1013.25 millibar.

The reason for this atmospheric pressure is that around sea level you are standing under a column of air approximately 50 kilometres tall, that pressure is the force you feel from the weight of this air above you. The higher mass and therefore higher weight of water on the other hand, would give the same one bar of pressure with a column of water only 10 meters in height.

For engineering terms, we normally refer to what is actually known as “Gauge” pressure, this is the pressure measured on a gauge above atmospheric pressure, so you take a gas pressure reading of 20mbar at a gas meter, this is 20mbar above atmospheric pressure, and not 20mbar “Absolute” pressure, which depending on the weather and height above sea level would be closer to 1023mbar. 

The volume of water at height has no bearing on the pressure at the base of a column, only the height. By this I mean that you could have an open system with a tank of water at the top, the pressure at the base of the system will be determined by the height of the level of the water in the tank from the base, regardless if this tank contains 10 litres or 10,000 litres. 

The image below, shows two instances of water filled pipework with pumps. If both were filled to the top, then the pressure at point A on both would be 5 bar (from the water height being at 50m above the base)

There is however a common misconception for some heating engineers that a larger pump is required for a higher system. If we look at system number 2 below, you can see the system pipework reaches 50m above the lowest level in the system. However that’s not the case, the system work on a counterbalance basis, the weight of the water is equal on both flow and return sides of the system, you are never pumping a mass of water up the flow pipework that gravity is not pulling down the return pipework, thus no energy is required by the pump to raise the height of the water.

The pump must still be able to overcome the resistance of the pipework its self, but the resistance would not change whether the system was 50m in height or all on one level and 50m horizontally in length. 

Conversely, on system 1 below, where you may be using a booster pump to raise water up to a tap, the pump must be able to raise the height of the water by 50m (5bar of pressure) to push the water up against gravity to the outlet, as there is no return circuit in a water supply line.

The only time this effect of raising the height of water in a heating circuit can be seen, is in cases of “pumping over” whereby a combination of poor design and a restriction in the pipework causes the pump to push water up and over the open vent, rather than circulate it around a balanced circuit. 

Other examples of thermodynamics at work in heating systems:

In an open vented heating system there is a feed and expansion tank, in sealed systems you will find an expansion vessel. We are aware that when we heat water it expands, this is the result of adding more energy to the water molecules, they gain an average increase in speed that they spin, move and collide with each other and the walls of their container, this higher energy behind the molecules is what makes them push against each other and their surrounding surfaces causing the liquid to expand, and in the case where the system is of a sealed volume, the result will be the pressure increasing. 

Heat pumps are a technology that have been used for decades in heating, cooling and refrigeration. However, are becoming slowly more popular in UK domestic heating systems. Many aspects of thermodynamics are taken advantage of to produce equipment that can bring heat into our homes with massive efficiency in electrical usage. 

As we talked about before, all matter has thermal energy. The problem we have had in the past is that to heat a house matter has to be a much higher temperature that the fabric of the building in order for heat transfer to occur.

With heat pumps, we can use a small amount of electrical energy, combine it in a process of pressurisation to create material phase changes utilising latent heat to extract the thermal energy from “cooler” materials and bring it to a useable temperature to heat the fabric of the building. 

The heat pump cycle 

The process starts in an evaporator, where a heat exchanger extracts the heat from either the outside air, the ground, or external water sources such as a lake.

  1. A compressor creates a suction in this heat exchanger causing a pressure drop which makes the refrigerant very cold allowing it to extract heat from the surrounding source, the heat drawn from the source will allow the refrigerant to boil change phase from a liquid to a gas again (from before, you now know that converting from liquid phase to gas phase takes a lot of energy)
  2. This refrigerant gas, still at a relatively low temperature is drawn into the compressor and compressed down into a high pressure gas, we know compressing a gas will increase its temperature.
  3. At high pressure and temperature, the refrigerant gas is now forced by the compressor into a condenser, a heat exchanger which will now allow the high-temperature gas to lose its heat to the lower temperature inside the property. In loosing heat energy, the gas cools and condenses then giving off the latent heat that was added to boil the gas. 
  4. The condensed gas now a liquid again, still has a relatively high pressure being on the positive pressure side of the compressor, moves to an expansion valve, which keeps the pressure high on the condenser side and allows the liquid refrigerant to slowly move through into the negative pressure side of the system still as a liquid at a cooler lower pressure to enter the evaporator again and repeat the cycle.

An important part to note here is that we are not just using the pressure-temperature relationship to exchange the heat energy, but also using phase-change energy. This means that we can take advantage of a primary source and where we are delivering the energy relatively close in temperature, as much of the energy is absorbed when the state change occurs, rather than actually increasing or dropping in temperature.

As you can see, nothing other than the electrical energy to run the compressor is put into the system as “chargeable energy”. We are simply taking the stored heat energy in our surroundings and manipulating it using the laws of thermodynamics to extract this energy and move it to create a more useable temperature for our chosen heat emitters that will heat our homes. 

Moving forward into a more sustainable future it is imperative that we look more to technology to utilise our environment in a more ecological way. With modern heat pumps being able to give out as much as 400-500% heat as the electricity we put into them, more innovative design ideas leading to better ways to reuse our waste heat, improving efficiency through solar thermal collectors, and the smart electronics revolution that is beginning to allow us to monitor and control every part of these processes, there has never been a better or more crucial time to pay attention and begin to implement this technology in our lives. 

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