Question $4(20$ points$)$

Air is compressed adiabatically in a piston$-$cylinder assembly from $\frac{1}{b}ar,380K$ to $\frac{10}{b}ar,680K.$ The air can be modeled as ideal gas and kinetic and potential energy effects are negligible. Determine the amount of entropy produced, in $K\frac{J}{K}$ per $kg$ of air, for the compression. What is the minimum theoretical work input, in $kJ$ per $kg$ of air, for an adiabatic compression from the given initial state to a final pressure of $10$ bar?