Thermodynamic states#
In the technical systems investigated in this workshop fluids (liquids or gases) flow through individual components and therefore change their state continuously. By determining the thermodynamic state of a fluid at the inlet and at the outlet of every component in the technical system and knowing all components’ properties we can determine the performance of the complete system. Therefore, this section outlines how to determine the state of a fluid.
Note
To simplify things, we are only considering pure fluids. The fluid might be gaseous and liquid at the same time (in the two-phase state), but we will not consider mixtures of different fluids.
Describing the thermodynamic state#
We can describe the state of a fluid through various properties, for example
pressure \(p\),
temperature \(T\) and
density \(\rho\) or specific volume \(v=\frac{1}{\rho}\).
In many cases it is sufficient to measure two of these three properties to determine the third using physical models. For example, if you measure the pressure and the temperature of water, you can mathematically determine the density. Or, if you measure density and pressure, you can determine the temperature. However, pressure and temperature are not sufficient to determine every state of the fluid. The Fig. 4 shows the change of the state of a fluid when heat is added continuously in an isobaric (at constant pressure) process.
Fig. 4 States of the evaporating fluid.#
Assume, the cylinder only contains liquid water. While transferring energy to your system, the temperature of the water has reached the boiling point at some point (the boiling point temperature depends on the pressure of the system). At that point, the water is in the so-called saturated liquid state. If you continue to transfer heat to the water, you will notice, that the temperature does not change, but part of the water will evaporate. This state is called two-phase because both liquid and gaseous state are present. Only when the last drop of water evaporated (this state is called saturated vapor) the temperature of the steam will start to increase again if you transfer more energy to the fluid.
Note
These physical models for fluid properties can be very simple, i.e. for so-called ideal gases, or they can be very complex. In our course we will use complex models, but the good news is: Others have implemented the algorithms and shared them as open source software, e.g. CoolProp [3], iapws [4] or pyromat [5].
pvT phase diagram#
It is possible to visualize the fluid property models in different types of states diagrams. For example, a log(p),log(v),T-surface is plotted for water in Fig. 5. \(v\) is the mass specific volume, the inverse of density. The Fig. 6 shows the pT-projection of the same fluid. The colors indicate the different phases of the fluid:
red: two-phase region
blue: subcooled liquid
turquoise: overheated gas
yellow: supercritical state
Fig. 5 Pressure, specific volume, temperature space of water.#
In the pT-projection we can see, that pressure and temperature are linearly dependent in the two-phase region. We cannot determine the state of the fluid completely without knowing specific volume or vapor mass fraction here.
Fig. 6 Pressure, temperature plane of water.#
The shape of the pvT space is different for every individual fluid. Note the changes in the scales in the pvT space of ammonia compared to water in Fig. 7.
Fig. 7 Pressure, specific volume, temperature space of ammonia.#
More state variables#
Apart from the three state variables pressure, temperature and density, other state variables can be of interest. For a number of connected open systems, as they are typically present in technical plants for heat provision, it is important what amount of energy is transported into the system and what amount is transported out of each subsystem to assess the overall performance. A fluid itself always transports energy, therefore we need another state variable to account for energy in such systems. For open systems, this property is the mass-specific enthalpy \(h\). The enthalpy describes the energy required per mass of a fluid to change the state while flowing through an open system.
On top of that, mass specific entropy \(s\) is used to describe the state of a fluid. The entropy is useful for detecting whether processes are reversible or irreversible or for component benchmarking. First, there are three fundamental principles for entropy:
Entropy can never be destroyed.
Entropy is generated in thermodynamic non-ideal (irreversible) processes.
Entropy can be transferred together with heat.
With these relations we can use the entropy for process benchmarking. For example, in a component with an adiabatic process, the entropy does not change if the process is thermodynamically ideal because neither is it generated nor can entropy be transferred with heat transfer. You would find such a process in a compressor or in a turbine. We can now benchmark our real world component with this ideal process and assess the optimization potential in our component.
Or, we can prove, why heat transfer can never be reversible: To transfer heat from one object to another object or from one fluid stream to another fluid stream, a temperature difference must be present, since heat always is transported from high temperature to low temperature. The entropy transported together with heat depends on the temperature level of the heat.
If we transfer a specific amount of heat e.g. from a stream of water to a stream of air, the total amount of heat delivered by the water would be received by the air stream. Therefore, \(|\dot Q_\text{water}| = \dot Q_\text{air}\). Since the temperature of the water must be higher than the temperature of the air, we can see that the entropy removed from the water stream is lower than the entropy received by the stream of air.
Similar to enthalpy, entropy can be expressed as function of pressure and temperature or pressure and specific volume.
For reversible processes an easy relationship can be made between entropy, enthalpy and the other state variables can be made: