## 3 Working Principles and _Cop_ Limit of Adsorption Systems
The key parameters often used in judging the efficacy of an adsorption system are the specific cooling capacity (_SCP_) and the coefficient of performance (_COP_). Both _SCP_ and _COP_ strongly depend on the heat source temperature. On the other hand, the performance of the adsorption systems depends on the choice of the working pairs. Regardless of the working pairs, the theoretical limit of an adsorption heat pump can be calculated using the Carnot _COP_. The Carnot _COP_ of an adsorption cycle operating among three temperature reservoirs (heat source at \(T_{d}\), the intermediate temperature reservoir, \(T_{c}\), for the rejection of condensation and adsorption heat, and the cooling load at low temperature, \(T_{e}\)) is given as [20; 21]  
\[COP_{C}=\frac{T_{e}}{T_{c}-T_{e}}\bigg{(}1-\frac{T_{c}}{T_{d}}\bigg{)} \tag{1}\]  
Figure 3 shows the Carnot _COPs_ of the adsorption cycle for various temperatures of the heat source and the intermediate reservoir. Here, the temperature of the evaporator is kept constant at 5 \({}^{\circ}\)C. In automobile applications, the heat source temperature can be classified as the engine coolant below 100 \({}^{\circ}\)C and the exhaust gas above 100 \({}^{\circ}\)C. It is noted that the effect of the temperature for the heat rejection (adsorption and condensation heat) on the _COP_ is less significant for a heat source temperature below 100 \({}^{\circ}\)C as compared to those above 100 \({}^{\circ}\)C. The Carnot _COP_ is independent of the working pair and irreversibilities associated with the cycle. Hence, the _COPs_ of practical adsorption  
Figure 2: The Clapeyron diagram of an adsorption cycle. cycles are lower than the Carnot _COP_. The _COP_ of a typical single-effect adsorption cycle without the recycling of heat is approximately 0.3-0.4 [22]. [PERSON] and [PERSON] highlighted that the _COP_ could be improved to around 0.65 by recovering \(\sim\)40% in a two-bed device using uniform temperature heat recovery [6]. As highlighted by [PERSON] et al., 40% recovery is the practical limit while the theoretical ceiling is \(\sim\)50% [23]. On the other hand, the system _COP_ of 1.2 was demonstrated by 75 to 80% in a thermal wave regeneration scheme [24; 25]. As mentioned before, the _COP_ of the adsorption heat pumps varies depending on the choice of a working pair. The performance of adsorption heat pumps for several working pairs based on the equilibrium cycle analysis can be found elsewhere [26; 27; 28; 29; 30]. The specific cooling power (_SCP_) is often expressed as (i) mass-based in kW/kg and (ii) volume-based, i.e., kW/m\({}^{3}\). The mass-based _SCP_ is usually employed for solid adsorbents in pellet forms while the volume-based _SCP_ is adopted for very fine powder and composite adsorbents. It should be highlighted here that two different kinds of denominator of _SCP_, i.e., the mass or the volume, are usually encountered in the literature depending whether the \"dead mass\" is counted or not. Here, the \"dead mass\" refers to other structural components such as heat exchanger and the shell of the chamber which do not participate in the adsorption process. When assessing the performance of a particular adsorbent, the _SCP_ using the dry mass of the adsorbent is convenient since it is sometimes problematic to estimate the total mass of the adsorber heat exchanger. Dry mass- or volume-based _SCP_ is the preferred performance parameter for the studies based on isotherm properties of the adsorbent. However, dry mass- or volume-based _SCP_ might provide an erroneous impression when the adsorption system is investigated for the replacement of other systems such as a mechanical vapour compression (MVC) system or an absorption system. For such scenarios, the total mass- or volume-based _SCP_ should be employed for a fair comparison. Thus, herein, the dry mass- or volume-based specific cooling power will be termed as _SCP\({}_{d}\)_, while the total mass- or volume-based specific cooling power will be termed as _SCP\({}_{t}\)_.