Air humidity in rooms – thermodynamics and enthalpy

Unlike with temperature, we humans are not able to feel changes in relative humidity immediately, only its effects. If it is too low (well below 30% relative humidity), our mucous membranes and skin start to feel dry after a while. If it is too high, on the other hand, we perceive it as feeling muggy and at some point we start to perspire uncomfortably. A healthy body temperature is around 37 °C. As ambient temperatures are usually lower, we give off heat continuously. This is the second law of thermodynamics, which states the reverse: “Heat never transfers on its own from a colder body to a warmer body.” This means that our body's own heat transfer is based on the principles of physics. through “conduction” when we come into contact with colder surfaces, through “convection” when air passes over our skin or through “radiation exchange” between surfaces of different temperatures.

In addition to our clothing, however, we regulate our temperature in another way, i.e. to a large extent through the evaporation of moisture via our largest organ, the skin. This process of evaporation is directly aided by convection processes. When air, which has not yet reached its saturation point, flows over the skin, it can absorb water vapour, which is released by the body. So when our own body heat evaporates the water in our body through the pores and the sweat is absorbed by the air and transported away, we experience this process as heat loss, we feel a change in temperature, we feel cold. When one kilogram of water evaporates through our skin, the body is deprived of just under 700 Wh per hour, in other words about 600 kilo calories. Dry warm air absorbs the water vapour we give off, causing it to evaporate very quickly on the skin. A good example is what happens if we go in a sauna. We can easily withstand a temperature of 90 °C with very low relative humidity because the body can cool itself for a certain amount of time. However, if the relative humidity in the room was 100% at the same temperature as in a steam bath, we would not last a minute and it could even be life-threatening.

In addition to conduction, radiation, convection and clothing, temperature and indoor air humidity therefore play a decisive role for human comfort and well-being. Since both of these variables depend on each other and our bodies rely on them, we even feel the “enthalpy” (abbreviated to “h”) of the air surrounding us to a certain extent. In the field of air conditioning technology, it is used to determine the amount of heat that is added to or removed from the air during a process. This is the same process in our body. It registers the heat content of the air-water mixture that constantly surrounds us. If there are any deviations, we unconsciously try to adapt the heat balance of our bodies to the enthalpy of the indoor air in order to ensure a healthy body temperature. But what happens when temperature and humidity change?

We can all imagine what the state variable of temperature means. However, it is a little more difficult when it comes to the common terms air humidity or air moisture. What is meant is the proportion of water vapour – i.e. not droplets, fog, rain or ice – in the gas mixture in rooms or in the air we breathe. This proportion depends on temperature and air pressure. For example, a certain volume of air can absorb a precisely determinable mass of water vapour, measured in grams of water vapour per kilogram of dry air. This value expresses absolute humidity and is indicated by the symbol “x”. If the air is saturated, it is at the so-called saturation or dewpoint. It is unable to absorb any more water vapour, and the relative humidity “ϕ” is then at 100%. As a matter of fact, this condition hardly ever occurs in nature. This is why the volume percentage of relative water vapour present in the air fluctuates between 0 and 100% when the temperature or pressure changes. This value is of great importance for air conditioning technology. On the one hand, this value, together with the temperature, provides information about the level of comfort in rooms. On the other hand, it allows processes to be calculated and quantities of energy to be determined that are required for evaporation and condensation or that are necessary for evaporation. The correlations are complex, but calculable. This is why computer programs can help in the design of adiabatic and isothermal air humidification processes in rooms or ventilation units. Adiabatic means the atomisation and evaporation of water at a constant temperature. In this process, the smallest water droplets immediately turn into steam and the thermal energy required for this is extracted from the ambient air. A cooling effect occurs. For isothermal humidification, on the other hand, water is heated to boiling point and reaches an enthalpy of h = 419 kJ/kg. At sea level, it then evaporates at 1,013 mbar and 100 °C.

Richard Mollier, Professor of Applied Physics and Mechanical Engineering at the Universities of Göttingen and Dresden in Germany (1897 to 1931), recognised the relationships between the state variables of temperature, absolute and relative humidity, water vapour pressures, enthalpies and densities at the beginning of the 20th century. Without the use of a computer, he combined these with great expertise in the h-x diagram for humid air, which was later named after him. With the help of this diagram, it is still quite easy to depict changes in the state of humid air, such as heating, cooling, humidifying, dehumidifying and mixing, and to quickly read out the thermal power required for air conditioning. Let us consider a simple example to illustrate this.

Thanks to Mollier's h-x diagram, a specialist planner or ventilation system engineer can check whether a humidification or dehumidification system has been correctly dimensioned. The diagram shown in Fig. 3 can also be applied to “The Squaire” multi-complex at the ICE mainline train station at Frankfurt Airport. The building with 140,000 m2 of total rental space for offices, conference rooms, hotels, retail and catering is equipped with a ventilation and air conditioning system with supply air cooling. The outside air of state 1 (32 °C, 40% relative humidity, h = 62.5 kJ/kg) is drawn into a central supply air conditioning unit where it is filtered. The fresh air is then cooled to supply air (state 2) in two coupled heat exchangers with a closed circuit system (CCS).

The water leaving the CCS heat exchanger in the central exhaust air unit at 21.5 °C is cooled to 13 °C in an intermediate heat exchanger using 10 °C cold water (from a refrigeration unit). This water first flows through heat exchanger 2 and then through heat exchanger 1 in the supply air unit before returning to the central exhaust air unit at a temperature of 28 °C. As a result of this pre-cooling and post-cooling, the outdoor air is cooled and dehumidified from 32 °C to state 2 with 15.5 °C, 10 g/kg humidity and an enthalpy of 40 kJ/kg.

After flowing through further air filters and the fan unit (temperature increased by 1.5 K), the supply air in state 3 has a temperature of 17 °C, a relative humidity of 82% and an enthalpy of h = 41.5 kJ/kg, which is introduced into the rooms of the building. The exhaust air heated to 26 °C (state 4) is then drawn in again by the central exhaust air unit and flows through an adiabatic evaporative cooling system after filtering. At this point, the exhaust air is humidified to almost 100% relative humidity and thus cooled to around 18.5 °C (h = 52 kJ/kg) (state 5). The 18.5 °C air then cools the 28 °C warm water in the exhaust air heat exchanger of the CCS system to a flow temperature of 21.5 °C. Finally, the exhaust air with a temperature of about 26 °C (state 6) flows outdoors as exhaust air.

In winter, the system technology of the ventilation and air conditioning systems remains as before, but several operating parameters are changed: The outside air now has a temperature of -12 °C and a relative humidity of 90%. The target temperature of the supply air processed in the central air conditioning units remains at 17 °C even in winter. The adiabatic evaporative cooling in the exhaust air units is switched off. Instead of the refrigeration unit, heating water (district heating with a flow temperature of 85 °C) is now used to temper the water in the CCS system to a maximum flow temperature of 60 °C for heating the supply air. If the outside air is too dry, it is humidified in the central supply air unit. Incidentally, systems for moisture recovery, such as membrane heat exchangers or sorption rotors, also represent an alternative to active humidification in ventilation units. They extract heat (enthalpy) from the exhaust air and a large part of the air humidity and then feed this into the supply air. The advantage of this is that every gram of water vapour required, which does not have to be generated by a technical process, not only saves energy, but also reduces costs and CO2 emissions. However, this process cannot be regulated as easily as active humidification.

Fig. 3: h-x diagram illustrating supply air (1 to 3) and exhaust air treatment including adiabatic evaporative cooling in summer (4 to 6). The lower part of the figure illustrates the coupling of the supply air and exhaust air units with the circulating compound heat recovery system (Fig. 2C: Content + communication)