## 2 Operation of a Geothermal Thermoelectric Generator (GTEG)  
As exposed in the introduction, thermoelectric generators are devices based on solid state physics whereby heat (i.e., temperature difference) is directly transformed into electricity by means of the Seebeck effect. This transformation is held in the so-called thermoelectric modules, the efficiency of which is proportional to the temperature difference between their sides. In order to maximize this temperature difference, the introduction of heat exchangers with low thermal resistances becomes indispensable, so that the temperature of the hot side of the thermoelectric modules approaches to the temperature of the heat source, and the temperature of the cold side does the same with respect the dissipation sink (normally the environment). An 8% higher generation can be obtained with a reduction of 10% in the thermal resistance of the heat exchangers [40]. Fin dissipators, heat exchangers with a fluid as heat carrier, heat pipes, and thermosyphons are the most common heat exchangers used in thermoelectric generators [41]. Thanks to these devices, it is possible to generate electricity directly, avoiding the intermediate conversion of thermal energy into mechanical energy; regardless of the source temperature, only a temperature gradient is required; durably, as demonstrated in spatial applications; with scalability possibilities, increasing the installed power just by adding more thermoelectric modules; and without moving parts, working fluids and noise in the operation of their main element, the thermoelectric modules [42]. As a drawback, they present a very low efficiency, which can be rated between 2 and 5% depending on the temperature range. Nevertheless, as derived from the introduction, there exist some applications in which the benefits of thermoelectric generators counteract their main disadvantage, becoming the best alternative. This is the case of supplying power to volcanic monitoring stations, the application under consideration in the present paper. In this application, fumaroles represent the heat source. These fumaroles, in their emergence to the surface, heat up and moisten the soil. Hence, due to the low heat transfer coefficient of gases, the thermoelectric generator responsible for the power supply will be directly in contact with the hot and wet soil. For depths higher than 10% it is considered that the temperature of the soil equals the fumaroles' one and that the soil moisture is close to 90%, thus a good heat transfer from the soil is expected [35]. The purpose of the hot side heat exchanger consists of absorbing the volcanic heat underground and transmitting it, with a minimal temperature difference to the thermoelectric modules located overground, so that the hot side of the thermoelectric modules approaches the temperature of the fumaroles. [PERSON] et al. demonstrated that heat exchangers based on phase change are the most adequate ones for this task [43], and therefore, will be the ones considered in this paper. As depicted in Figure 1, this type of heat exchanger is made of one or several tubes with an internal fluid in their interior. In contact with the heat source, the internal fluid vaporizes, occupying all the available space. Afterward, this vapor condensates releasing heat to the thermoelectric modules. If the condensed fluid returns to the evaporator part only due to gravity, the heat exchanger is known as thermosyphon, while if a wick material is introduced so that it can work in any position, the term heat pipe is used. [PERSON], [PERSON] et al., and [PERSON] et al. also used phase change heat exchangers, specifically heat pipes, to absorb heat from the soil and transfer it to the thermoelectric modules [27; 33; 34; 35]. The heat that is not transformed into electricity by the thermoelectric modules needs to be dissipated into the environment, again with a heat exchanger with a minimal thermal resistance so that the cold side of the thermoelectric modules approach the ambient temperature.