## 2 Experiment
### Experimental Procedure and Data Reduction  
Many researchers have already analyzed several hypothetical adsorption isotherms and kinetics models to estimate the behavior of adsorbate-adsorbent working pairs. For example, [PERSON] et al. [37] presented the adsorption isotherms and kinetics of CO\({}_{2}\)-CSAC pair for cooling applications. In their study, the rate of R1234 yf adsorbed by CSAC (coconut shell-based activated carbon) was evaluated by a similar CVVP experimental setup with a starting pressure of around 0.01 kPa.  
Here, we placed the adsorption cell (1) and the load cell (2), in Figure 3, in a constant-temperature bath while we implemented the liquid cell (3) for charging of the refrigerant.  
Figure 3: Constant-volume–variable-pressure experimental apparatus.  
The temperature of the bath in the case of the Liquid cell (3) was regulated using a constant temperature circulator (CTP-3000, EYELA Co., Ltd., Tokyo, Japan) to control the initial charging pressure of the refrigerant (adsorbate). The actual charging pressure of the refrigerant (adsorbate) was regulated by adjusting the control valve (V-3). A ribbon heater (E16, Sakaguchi E.H VOC, Tokyo, Japan) was utilized to maintain the tube temperature at a constant temperature of about 5 \({}^{\circ}\)C above the saturation point at the given isothermal conditions. Before starting the measurement, the experimental system was thoroughly evacuated for around 12 h to ascertain constant initial conditions for each isothermal experiment.  
During the individual experiments, we first charged the refrigerant (adsorbate) into the Load cell (2) from the Liquid cell (3) at the targeted pressure. The amount of refrigerant in the load cell at the constant temperature was calculated using the volume of the cell, equilibrium pressure data, and temperature data. The adsorption of the refrigerant started by opening the valve (V-1), separating the adsorption and the load cell. The adsorption uptake was subsequently estimated, as explained before, from the calculated amount based on the pressure change before and after the adsorption step at constant temperature and volume. For further details about this procedure, interested readers may refer to the works of [PERSON] et al. [38], [PERSON] et al. [39], and [PERSON] [29].  
The amount of refrigerant(adsorbate) \(m_{i}\) in the load cell with constant volume \(V_{Load\_cell}\) before the adsorption step \(i\) can then be estimated as:  
\[m_{i}=\rho_{ref,i}(P,T)V_{Load\_cell} \tag{4}\]  
where \(\rho_{ref,i}(P,T)\) is the density of the refrigerant at a given temperature \(T\) and pressure \(P\).  
The void space of the adsorption cell can be calculated by the following formula:  
\[V_{Void}=V_{ads\_cell}-\frac{m_{ads}}{\rho_{ads}}-v_{\mu}m_{ads} \tag{5}\]  
where \(v_{\mu}\) and \(\rho_{ads}\) are the micropore volume and the density of the adsorbent, and \(m_{ads}\) is the mass of the adsorbent. Hence, the mass of refrigerant in the adsorption cell (in the void space) is estimated:  
\[m_{Void}=\rho_{ref}(P,T)V_{Void} \tag{6}\]  
Finally, the net uptake \(m_{Update}\) by the adsorbent at the adsorption step can be calculated by Equation (7), and the specific adsorption amount \(c\) is obtained simply by Equation (8):  
\[m_{Update}=m_{i}-\rho_{ref}\big{(}V_{Load\_cell}+V_{Void}\big{)} \tag{7}\]  
\[c=\frac{m_{Update}}{m_{ads}} \tag{8}\]  
We performed the measurement for four different isothermal conditions applicable to the intended heat pump cycles. All procedures were identical for all the isotherm measurements. The data measurements were performed from 20 \({}^{\circ}\)C to 70 \({}^{\circ}\)C with a step of 10 \({}^{\circ}\)C. In the range of 20 \({}^{\circ}\)C to 40 \({}^{\circ}\)C, the measurements were performed two times to evaluate the consistency and accuracy.