The state of an ideal gas with and is changed frombar andtobar andby the following mechanically reversible process: $($a$)$ Isothermal compression. $($b$)$ Adiabatic compression followed by cooling at constant pressure. $($c$)$ Adiabatic compression followed by cooling at constant volume. $($d$)$ Heating at constant volume followed by cooling at constant pressure. $($e$)$ Cooling at constant pressure followed by heating at constant volume. Calculate Q$,$ W$,,$ andfor each of these processes, and sketch the paths of all processes on a single PV diagram.