Q$1.(20$ marks$)$ One mole of a monatomic gas goes through the cyclic process ABCA. It starts at point $A$ of pressure $p_0=6$kPa and volume $V_0=4m^3.$ Firstly, the pressure is reduced, with constant volume, to half at point B$.$ Then, it is compressed with a constant temperature to half its volume at point C$.$ Finally, the gas expands at constant pressure back to point A$.$

a$)$ Sketch the cyclic process ABCA in the $p-V$ plane.

b$)$ Compute the energy transferred as heat through the whole cycle.