## 3 Results and Discussion
### Heat Amplification Cycle \"Heat from Cold\" (HeCol)  
In the heat amplification cycle \"Heat from Cold\" (HeCol), recently suggested for upgrading the temperature of the environment heat in cold countries [43], two natural heat reservoirs, namely, the ambient air at low temperature \(T_{\rm L}\) and non-freezing water basins (or underground water) at middle temperature \(T_{\rm M}\), are used as the heat sink and heat source, respectively, to get a useful heat at higher temperature \(T_{\rm H}\) suitable for heating (Figure 7) [43]. The initial adsorbent state (point 1 in Figure 7) corresponds to the temperature \(T_{\rm M}\) and the pressure of the adsorbate vapor \(P_{\rm L}=P_{0}(T_{\rm L})\), where \(P_{0}(T_{\rm L})\) is the adsorbate saturation pressure at temperature \(T_{\rm L}\). Under these conditions, the equilibrium adsorbate content \(w\)min = \(w(T_{\rm M}\), \(P_{\rm L})\) is low due to the low adsorbate pressure \(P_{\rm L}\). Then, the adsorbent is heated up to temperature \(T_{\rm H}\) (stage 1-2) at constant uptake \(w\)min. At point 2, the adsorber is connected to an evaporator maintained at \(T_{\rm M}\) which generates the constant pressure \(P_{\rm M}=P_{0}(T_{\rm M})\) of adsorbate. This pressure jump causes the vapor adsorption that leads to an increase in the equilibrium uptake to \(w\)max = \(w(T_{\rm H}\), \(P_{\rm M})\) (point 3 in Figure 7). Figure 6: Boundary conditions (vertical lines) for the adsorption heat storage cycles (\(\rm Tev=\)\(Tn.\)av, \(T\)con = \(T\)d.av, \(\rm Tuh=\) 35 \({}^{\circ}\)C, \(\rm Treg=\) 90 \({}^{\circ}\)C) tested and the universal adsorption curves for: 1—LiBr/SiO\({}_{2}\), 2—MaxSorbIII, 3—TiO67, 4—LiCl/SiO\({}_{2}\), 5—LiCl/MWCNT. The refrigerant is methanol. Figure 7: P-T diagram of the isothermal “Heat from Cold” (HeCol) cycle [43]. The evaporation heat \(Q\)ev is absorbed in the evaporator at \(T_{\text{M}}\) and the useful adsorption heat \(Q\)ads is released at constant temperature \(T_{\text{H}}\) (isotherm 2-3) in the adsorber and supplied to the heating circuit of a consumer. Then, the adsorber is disconnected from the evaporator and cooled down to temperature \(T_{\text{M}}\) (isostere 3-4) at constant uptake \(w\)max. At point 4, the adsorber is connected to the condenser maintained at temperature \(T_{\text{L}}\) and pressure \(P_{\text{L}}\). The pressure drop results in the adsorbate desorption to restore the initial uptake \(w\)min = \(w(T_{\text{M}},P_{\text{L}})\) (point 1). The heat \(Q\)des needed for adsobate desorption is supplied to the adsorbent from the water basin at temperature \(T_{\text{M}}\) (isotherm 4-1). The desorbed vapor is collected in the condenser releasing the heat \(Q\)con to the ambient, and the cycle is closed. The work is required to pump the liquid adsorbate from the low pressure level in the condenser to the high pressure level in the evaporator. This work is small as compared to the latent heat in the cycle [45]. This process can be realized in regions with a cold climate, where the difference (\(T_{\text{M}}-T_{\text{L}}\)) = 30-50 \({}^{\circ}\text{C}\). Therefore, the analysis is carried out for Yakutsk (IV climatic zone) and Oimyakon (Special zone, Figure 1). We assume that \(T_{\text{L}}\) equals the average temperature \(T\)av during winter months. For Yakutsk \(T_{\text{L}}\) = \(T\)av varies from \(-\)28.9 \({}^{\circ}\text{C}\) (November) to \(-\)40.7 \({}^{\circ}\text{C}\) (January); for Oimyakon from \(-\)32.3 \({}^{\circ}\text{C}\) (March) to \(-\)47.1 \({}^{\circ}\text{C}\) (January). The reservoir at \(T_{\text{M}}\) = 3 \({}^{\circ}\text{C}\) (non-freezing water under ice) or 10 \({}^{\circ}\text{C}\) (ground water) is used as a heat source for evaporation and desorption, and \(T_{\text{H}}\) of useful heat varies from 30 to 50 \({}^{\circ}\text{C}\) (Table 4).