Problem $08\mathrm{.}089-$ Cryogenic energy storage $($CES$)$ system

Consider a cryogenic energy storage $($CES$)$ system in which nitrogen is liquefied during off$-$peak hours using surplus electricity generated by wind turbines and stored in a $475-m^3$ cryogenic tank at $T_1=-200C$ and $P_1=0\mathrm{.}12$MPa. During peak times, the entire liquid nitrogen is pumped to $P_2=15$MPa and is heated by ambient air to $T_3=20C$ at that pressure before it is routed to a nitrogen turbine where it expands to a pressure of $P_4=100$kPa. The properties of nitrogen are $h_1=-440\mathrm{.}1k\frac{J}{k}g,{}_1=825\mathrm{.}9k\frac{g}{m^3},h_3=-33\mathrm{.}36k\frac{J}{k}g,$ and $h_{4s}=-245\mathrm{.}5k\frac{J}{k}g($enthalpy at turbine exit for the case of isentropic $$xpansion$).$

Problem $08\mathrm{.}089.$b $-$ Fraction of work consumed during the liquefaction process

What fraction of work consumed during the liquefaction process is recovered when the stored liquid nitrogen is used to generate work? Assume that it takes $0\mathrm{.}8$ kWh of electricity to liquefy a unit mass of nitrogen. $($Round the final answer to four decimal places.$)$

The fraction of work consumed during the liquefaction process is