CHEF has a 5 liter hydrogen liquefaction chamber with a maxi

CHEF has a 5 liter hydrogen liquefaction chamber with a maximum pressure of 100 psig and a minimum attainable temperature of 7.8 Kelvin. Before CHEF can be used to liquefy hydrogen it is necessary to pressure test the liquefaction chamber with helium. The condenser is initially filled with helium at 14 K and 100 psig (g stands for gauge, since this is gauge pressure you need to add 14.7 psi to this to convert to absolute pressure). Helium does not liquefy until near 4 Kelvin, so Ron assumes that the ideal gas law is valid. The pressure test was successful and no leaks appeared in the cryogenic seals. However it is all ready the end of the day and Ron plans to let the system warms up over night. He knows that the pressure in the system will increase as the system warms up. He decides to vent the helium in the condenser down to a pressure of 2 psig with the condenser at 60 K to prevent from blowing the pressure relief valve. With the pressure test out of the way, Ron vents the helium remaining in the condenser and proceeds with the hydrogen liquefaction test. He connects a 23.8 gallon rigid steel tank to serve as a reservoir for the system and fills the tank to 100 psig with hydrogen at room temperature. Hydrogen flows from the reservoir to the condenser as it cools down in a process called cryopumping. Cryopumping occurs because the hydrogen that flow into the condenser is cooled and liquefies such that it does not escape back to the reservoir. As the reservoir is cryopumped down the pressure drops. Later in the day the pressure in the reservoir has dropped all the way to atmospheric pressure (14.7 psi absolute) but remains at room temperature. e) Find the mass of hydrogen that left the reservoir and cryopumped into the condenser (in kilograms). f) What are the temperature and quality of the hydrogen in the condenser if it is now at the same pressure as the reservoir? g) How many liters of liquid hydrogen should be in the condenser?

Solution

To exist as a liquid, H₂ must be cooled below hydrogen\'s critical point of 33 K. However, for hydrogen to be in a fully liquid state without boiling at atmospheric pressure, it needs to be cooled to 20.28 K^[3] (423.17 °F/252.87 °C).^[4][5] One common method of obtaining liquid hydrogen involves a compressor resembling a jet engine in both appearance and principle. Liquid hydrogen is typically used as a concentrated form of hydrogen storage. As in any gas, storing it as liquid takes less space than storing it as a gas at normal temperature and pressure. However, the liquid density is very low compared to other common fuels. Once liquefied, it can be maintained as a liquid in pressurized and thermally insulated containers.

The product of its combustion with oxygen alone is water vapor (although if its combustion is with oxygen and nitrogen it can form toxic chemicals), which can be cooled with some of the liquid hydrogen. Since water is harmless to the environment, an engine burning it can be considered \"zero emissions.\" Liquid hydrogen also has a much higher specific energy than gasoline, natural gas, or diesel.^[8]

The density of liquid hydrogen is only 70.99 g/L (at 20 K), a relative density of just 0.07. Although the specific energy is around twice that of other fuels, this gives it a remarkably low volumetric energy density, many fold lower.

Liquid hydrogen requires cryogenic storage technology such as special thermally insulated containers and requires special handling common to all cryogenic fuels. This is similar to, but more severe than liquid oxygen. Even with thermally insulated containers it is difficult to keep such a low temperature, and the hydrogen will gradually leak away (typically at a rate of 1% per day^[8]). It also shares many of the same safety issues as other forms of hydrogen, as well as being cold enough to liquefy (and possibly solidify) atmospheric oxygen which can be an explosion hazard.

The triple point of hydrogen is at 13.81 K^[3] 7.042 kPa