In a cylinder and piston system, $0\mathrm{.}1$ kg of air is compressed from $100$ kPa and $300$K to $10$L$.$ The environmental temperature is $300$K$.(1).$ If the process is isothermal, find the net entropy change.

$(2).$ If the process is isentropic$,$ find the work. The heat capacity of air is NOT constant.

$(3).$ If the process is adiabatic, and the entropy change is $0\mathrm{.}01$ kJ$/$K$,$ find the work. The heat capacity of air IS constant.