$930$Hydrogen is considered a potential energy storage and transportation medium for renewable energy. The surplus electric power from the renewable resources such as solar and wind energy is used to produce hydrogen usually by the electrolysis of water. Because gaseous hydrogen requires a large volume of storage, it is sometimes liquefied using a liquefaction system in order to store a large mass of hydrogen in a small volume.

Consider a Carnot refrigeration system used to liquify hydrogen which enters at $100$ kPa and $20\backslash$deg C and leaves at $253\backslash$deg C as a liquid, as shown in the figure. Determine the work input, in kWh$/$kg and the COP of this ideal liquefaction system. If the same liquefaction process is carried out by an actual liquefaction system with a COP of $0\mathrm{.}055,$ determine the second$-$law efficiency and the actual work input, in kWh$/$kg$,$ of that system. Various properties of hydrogen before and after the liquefaction process are h$1=4128\mathrm{.}2$ kJ$/$kg$,$ h$2=270\mathrm{.}67$ kJ$/$kg$,$ s$1=70\mathrm{.}228$ kJ$/$kg$$K$,$ s$2=17\mathrm{.}066$ kJ$/$kg$$K$.$ The solutions are: $3\mathrm{.}3$kWh$/$kg$,0\mathrm{.}33$ COP, $16\mathrm{.}7\%,19\mathrm{.}5$kWh$/$kg