Because gas and liquid nitrogen are in a coexisting saturated state and have the same saturation temperature. However, saturated liquid and saturated vapour at the same temperature belong to different states. A saturated vapour gives off heat to condense into a saturated liquid, and when the temperature remains constant, the saturated liquid absorbs heat to evaporate into a saturated vapour. For the same substance, at the same pressure, the latent heat of condensation and the latent heat of evaporation are numerically equal. So there is both liquid and gas nitrogen at the top of the air separation tower.
The liquid nitrogen subcooler is used to reduce the liquid nitrogen throttling vapourisation rate by using the low temperature gas nitrogen induced from the upper tower to cool the liquid nitrogen induced from the lower tower. For the same substance, the phase change temperature (saturation temperature) is related to the pressure, so that gas nitrogen has a lower temperature than liquid nitrogen. The lower the pressure the lower the saturation temperature. The liquid nitrogen leading from the lower tower is about 16°C hotter than the gas nitrogen in the upper tower, therefore, when the two fluids flow through the liquid nitrogen subcooler, after heat exchange, the liquid nitrogen gives up heat and is cooled to become a supercooled liquid, while the gas nitrogen becomes a superheated vapour due to heat absorption. The liquid nitrogen can therefore be cooled by the gas nitrogen in the liquid nitrogen subcooler.
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