Exercise Problem

$*$

An ideal gas undergoes the following sequence of mechanically reversible processes in a closed system:

$($a$)$ From an initial state of $70C$ and $1$ bar, it is compressed adiabatically to $150C.$

$($b$)$ It is then cooled from $150$ to $70C$ at constant pressure.

$($c$)$ Finally, it is expanded isothermally to its original state.

Calculate $W,Q,U,$ and $H$ for each of the three processes and for the entire cycle. Take $C_V=(\frac{3}{2})R$ and $C_P=(\frac{5}{2})R.$

If these processes are carried out irreversibly but so as to accomplish exactly the same changes of state $($i$.$e$.$ the same changes in $P,T,U,$ and $H),$ then different values of $Q$ and $W$ result. Calculate $Q$ and $W$ if each step is carried out with an efficiency of $80\%.$