P$4\mathrm{.}8$ An adiabatic compressor is used to continuously compress nitrogen $(\frac{C_p}{R}=\frac{7}{2})$ from $2$ bar and $300K$ to $\frac{15}{b}ar.$ The compressed nitrogen is found to have an outlet temperature of $625K.$ How much work is required $)?$ What is the efficiency of the compressor? $($ANS$.9\mathrm{.}46k$J$/$mol $72\%$