Figure Q$1$ below shows the cycle followed by one mole of a perfect gas. Assuming each process is carried out reversibly:

a$)$ Name each process and calculate the pressure at each state

$(10$ marks$)$

b$)$ Write down the expression of the heat flow $q,$ work done, $w,$ and the change in internal energy, $U,$ and entropy change $S,$ for each process.

$(15$ marks$)$

c$)$ Calculate q$,$ w$,U$ and $S$ for the complete cycle.

$(20$ marks$)$