In a cyclic process,

$\Delta U = 0$

In a cyclic process work done is equal to the area under the cycle and is positive if the cycle is clockwise and negative if anticlockwise.

$\therefore \Delta$W = – Area of rectangle ABCD = – P(2V) = – 2PV

According to first law of thermodynamics

$\Delta Q = \Delta U + \Delta W \Rightarrow \Delta Q = \Delta W$
    (As $\Delta U = 0$)

i.e., heat supplied to the system is equal to the work done

So heat absorbed, $\Delta$Q = $\Delta$W = – 2PV

$\therefore$ Heat rejected by the gas = 2PV