## 2 Thermodynamic and Transport Properties
Thus, the initial temperature of the fluid entering a cooling device depends on the Joule-Thomson coefficient, the pressure and temperature in the high-pressure container, and the pressure of the flow path. It is clear that when a fluid expands from a high-pressure reservoir into a lower-pressure flow network, since \(\partial P<0\), it is cooled down if \(\mu_{JT}\) is positive and it is heated if \(\mu_{JT}\) is negative. The coefficient \(\mu_{JT}\) depends on the type of gas being used and, on the temperature, and pressure of the gas before the expansion. The point at which the coefficient \(\mu_{JT}\) changes its sign is called the inversion point, and the temperature of this point also depends on the pressure of the gas before expansion. From the correlations reported by [PERSON] and [PERSON] [20] for CO\({}_{2}\) and the correlations reported by [PERSON] et al., [24] and by [PERSON] et al., [25; 26] for air, we calculate the Joule-Thomson temperature inversion curves for CO\({}_{2}\) and air (the temperature inversion curve is the curve that connects the inversion point at which the value of the Joule-Thomson coefficient changes sign). The results are shown in Figure 3. The curve divides the graph into two regions: the cooling and the heating regions. If the pressure and temperature before the expansion of a fluid fall into the cooling region, the fluid will be cooled down if it expands at constant enthalpy, and if they fall into the heating region, heating of the fluid ensues. The cooling region for air covers a range of temperature from about 100 K to 650 K and a pressure range up to 42.5 MPa. The cooling region associated with CO\({}_{2}\) has a much bigger range in both pressure and temperature. Let us assume that both gaseous CO\({}_{2}\) and air are stored in a container with pressures ranging from 1 to 5 MPa and are in thermal equilibrium with the surroundings so that the temperature of the stored gas can be somewhere from 35 \({}^{\circ}\)C (308 K) to 40 \({}^{\circ}\)C (313 K). These conditions fall into the cooling regions of both CO\({}_{2}\) and air as shown in Figure 3. Thus, as these gases expand, the temperature of the expanded streams entering a cooling device will be lower than their temperatures in the storage container. However, the values of \(\mu_{JT}\) of CO\({}_{2}\) are 4.9 to 5.6 times higher than those of air as shown in Figure 4, and the temperature of the CO\({}_{2}\) entering a cooling device, as given by Equation (2), depends on the storage tank temperature and the pressure, and it is 7 to 40 K lower than that of air. The data are based on the correlations reported by [PERSON] and [PERSON] [20] for CO\({}_{2}\) and the correlations reported by [PERSON] et al. [24] and by [PERSON] et al. [25; 26] for air. Figure 3: The Joule–Thomson temperature inversion curve for CO\({}_{2}\) and air. As an example, we use Equation (2) to calculate the fluid temperature entering a cooling device which is operated at a constant pressure of 0.1 MPa after the expansion from a high-pressure container. The container pressures are from 1 to 5 MPa, and the surrounding temperatures are at 35 \({}^{\circ}\)C (308 K) and 40 \({}^{\circ}\)C (313 K). The results are tabulated in Table 1. For the same conditions, the temperature of the CO\({}_{2}\) stream is significantly lower than that of air while the mass flux of the CO\({}_{2}\) stream is significantly larger than that of air. These results indicate that using CO\({}_{2}\) for cooling is much more effective than using air.