## 3 Thermal Transformations and Parameters Describing the TES Phenomena  
The physical thermal transformations associated with the TES process, regardless of prevailing conditions, occur according to specific rules. They are systematized as shown:  
* the amount of heat given out by the body is equal to the amount of heat absorbed by the environment of the body during the cooling,
* the amount of heat stored by the body during its heating is equal to the heat removed from the body during cooling (only if two changes occur in the same temperature range),* the amount of heat \(\Delta Q\) stored by the body during its heating or removed during the cooling is proportional to the body's weight \(m\) and the difference of the body temperature \(\Delta T\) before and after the thermal conversion; this rule can be written as: \[\Delta Q=c\cdot m\cdot\Delta T\qquad(J)\] (1)  
The \(c\) parameter in Equation (1) is called as the specific heat. A simplified, commonly-quoted definition of this quantity is: the specific heat is the energy which enhances (or decreases) the temperature of a unit mass body by a unit temperature. Another parameter which characterizes materials in terms of the thermal properties is the heat capacity. Its value \(b\) is calculated using the specific heat \(c\) and density of the material \(\rho\) of which the body is made:  
\[b=c\cdot\rho\qquad(J/(m^{3}\cdot K)) \tag{2}\]  
The heat capacity is, therefore, the amount of the energy which is adopted while heating, or returned while cooling by 1 m\({}^{3}\) of the material, changing its temperature by one degree. Alternatively, the heat capacity is the energy which lifts (or decreases) the temperature of the unit volume material, by a unit temperature. Table 1 shows the values of the specific heat, density, and the heat capacity of various materials, including building materials. It can be stated that the best TES materials are not the materials of the highest bulk density--metals with bulk density of 7000-900 kg/m\({}^{3}\) are characterized by an average heat capacity of approx. 1.5 to 3.5 MJ/(m\({}^{3}\cdot\)K). The very good heat capacity, at low density, shows water at approx. 4.2 MJ/(m\({}^{3}\cdot\)K), and at even lower density, benzene (15.1 MJ/(m\({}^{3}\cdot\)K)). Granite, used as an aggregate in concrete, has a lower heat capacity than metals. Brick and river sand show even less heat capacity, at approx. 1.2 MJ/(m\({}^{3}\cdot\)K). The heat capacity value is not sufficient to describe the maximum energy that can be stored in a unit volume of the material. In Equation (1), the \(\Delta T\) is the difference between the temperature to which the body was heated, and the initial temperature before heating; assuming that the base temperature is \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Material**} & **Specific Heat** & **Bulk Density** & **Heat Capacity** \\  & & **(J/(kg\(\cdot\)K))** & **(kg/m\({}^{3}\))** & **(MJ/(m\({}^{3}\cdot\)K))** \\ \hline
1 & Benzene & 17,200 & 880 & 15.136 \\
2 & Water & 4190 & 998 & 4.181 \\
3 & Ice & 2100 & 880 & 1.848 \\
4 & Gasoline & 2100 & 700 & 1.470 \\
5 & Air & 1005 & 1.29 & 0.001 \\
6 & iron & 449 & 7875 & 3.535 \\
7 & Copper & 385 & 8933 & 3.439 \\
8 & Brass & 377 & 8400 & 3.166 \\
9 & Zinc & 389 & 7130 & 2.773 \\
10 & Aluminum & 902 & 2720 & 2.453 \\
11 & Concrete & 1130 & 2450 & 2.769 \\
12 & Granite & 670 & 2670 & 1.788 \\
13 & Brick & 850 & 1400 & 1.190 \\
14 & River sand & 800 & 1550 & 1.240 \\
15 & Ceramics & 880 & 2640 & 2.323 \\
16 & Terracotta & 920 & 2000 & 1.840 \\
17 & Glass & 840 & 2500 & 2.100 \\
18 & Styrofoam & 1200 & 20 & 0.024 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specific heat, bulk density, and heat capacity of different materials [38; 39].