Carbon dioxide $($CO$2)$ at $1$ bar, $300$ K enters a compressor operating at steady state and is compressed adiabatically to an exit state of $10$ bar, $580$ K$.$ The CO$2$ is modeled as an ideal gas, and kinetic and potential energy effects are negligible. For the compressor, determine: $($a$)$ the work input, in kJ per kg of CO$2$ flowing, $($b$)$ the rate of entropy production, in kJ$/$K per kg of CO$2$ flowing, and $($c$)$ the percent isentropic compressor efficiency.