## 1 Introduction
Thus, the transition can very well take place using the available 80-90 \({}^{\circ}\)C from the collector with the pool condenser at 20 \({}^{\circ}\)C. For heat regeneration during winter, the pool will be somewhat colder, say 10 \({}^{\circ}\)C, giving a pressure of about 12 hPa for evaporation, according to the horizontal blue line in Figure 2. From the intersection with the pT-line of K\({}_{2}\)CO\({}_{3}\)-(1\(\%\)-0)H\({}_{2}\)O, it follows that the maximum achievable hydration temperature is then about 60 \({}^{\circ}\)C. Thus, apart from some sensible heat to preheat the salt for hydration or dehydration, all heat is recovered, although at a somewhat lower temperature due to the difference in condenser and evaporator temperatures during summer and winter. Figure 1: Elementary thermochemical heat storage (THS) system. The core of the system is a reactor containing modules with thermochemical material (TCM), e.g., a hydrated salt. The salt is dried by solar heat of, e.g., 80–90 \({}^{\circ}\)C, captured by a solar collector, buffered in hot water storage and transferred by a heat exchanger (HX). Process water from dehydrating the salt is captured in a pool which acts as a condenser during dehydration and as an evaporator during hydration. Process water is kept at 10–20 \({}^{\circ}\)C by an HX with a reservoir which may be a borehole energy storage (BES). We see that in order to estimate dehydration and hydration temperatures at given operation conditions, it is sufficient to have the pT-line of a candidate transition. In literature, [10], pT-lines of salt hydrate transitions are often represented by the entropy and enthalpy differences \(\Delta s_{0}\) and \(\Delta h_{0}\) of the transition at reference pressure \(p_{0}=1\) atm. The pT-line is then obtained by the relation [10; 11]  
\[\ln\frac{p}{p_{0}}=\frac{\Delta s_{0}}{R}-\frac{\Delta h_{0}}{RT}. \tag{1}\]  
Here, \(R=8.314\) J/mol\(\cdot\)K is the gas constant. In the following section, we discuss the assumptions on which the derivation of this formula is based. Besides dehydration temperature at operating pressure, heat storage density \(Q/V\) (J/m\({}^{3}\)) is an important parameter, determining the system volume for a given amount of stored heat. The heat storage density follows by  
\[\frac{Q}{V}=\frac{n\rho\Delta h}{M}. \tag{2}\]  
This is the amount of heat per volume of hydrate, where \(\Delta h\) is the transition enthalpy, \(n\) the amount of water molecules involved in the transition, and \(\rho\) (kg/m\({}^{3}\)) and \(M\) (kg/mol) are the density and molar mass of the hydrate. For instance, for the transition K\({}_{2}\)CO\({}_{3}\)-(1%-0)H\({}_{2}\)O with \(\Delta h=\Delta h_{0}=63.6\) kJ/mol, \(n=1\%\), \(\rho=2181\) kg/m\({}^{3}\), and \(M=0.1652\) kg/mol, we obtain \(Q/V=1.26\) GJ/m\({}^{3}\) = 350 kWh/m\({}^{3}\). Fortunately, tables of \(\Delta s_{0}\) and \(\Delta h_{0}\) have been published for many salt hydration transitions [5; 10; 12], as well as for salt ammoniate transitions [11]. However, hydration states as well as \(\Delta s_{0}\) and \(\Delta h_{0}\) values of different references are sometimes contradictory, and hydration states are not always confirmed by X-ray diffraction data from, e.g., the online database of the ICDD (International Centre for Diffraction Data) [13]. Besides, behind every pT-line is an article describing the measurements and the analysis of the obtained data to arrive at the fitted \(\Delta s_{0}\) and \(\Delta h_{0}\). Collecting and verifying all this information is not easy. Often sources are difficult to find and the reports sometimes lack sufficient completeness. Therefore, a rule obeyed by \(\Delta s_{0}\) and \(\Delta h_{0}\) data of certain classes of transitions would be valuable. For that purpose, we consider [PERSON]'s rule [14] that asserts the proportionality of transition enthalpy \(\Delta h_{0}\) with transition temperature \(T_{0}\) at given reference pressure \(p_{0}\) for a certain class of transitions.