Why can gas nitrogen be used to cool liquid nitrogen in liquid nitrogen supercooler?

The liquid nitrogen supercooler uses the low temperature gas nitrogen from the upper tower to cool the liquid nitrogen from the lower tower, so as to reduce the gas rate when the liquid nitrogen throttling enters the upper tower.
Why is the temperature of gas nitrogen lower than that of liquid nitrogen? This is because for the same substance, phase change temperature (saturation temperature) is related to pressure. The lower the pressure is, the lower the corresponding saturation temperature is (see Figure 8 ). On the top of the tower, it is in the saturated state of the coexistence of gas nitrogen and liquid nitrogen, both of which have the same saturation temperature. The absolute pressure of nitrogen going out of the tower is about 0.13MPa, and the corresponding saturation temperature is-193℃, which is also the temperature of the nitrogen saturated vapour going out of the tower. The absolute pressure on the top of the lower tower is about 0.55MPa, and the corresponding nitrogen saturation temperature is about-177℃. The extracted saturated liquid nitrogen is also the temperature. The temperature of this liquid nitrogen is about 16 ℃ higher than that of the gas nitrogen in the upper tower. Therefore, when two streams of fluid flow through the liquid nitrogen supercooler, after heat exchange, the liquid nitrogen will release heat and be cooled into supercooled liquid, gas and nitrogen become superheated steam due to heat absorption.