When the transportation of natural gas in a pipeline is not feasible for economic reasons, it is first liquefied using nonconventional refrigeration techniques and then transported in super$-$insulated tanks. In a natural gas liquefaction plant, the liquefied natural gas $($LNG$)$ enters a cryogenic turbine at $\frac{30}{b}ar$ and $160C$ at a rate of $20k\frac{g}{s}$ and leaves at $\frac{3}{b}ar.$ If $110\mathrm{.}0kW$ power is produced by the turbine, determine the efficiency of the turbine. Take the density of LNG to be $423\mathrm{.}8k\frac{g}{m^3}.$

The efficiency of the turbine is $\%$