The arrow OA in the PV diagram shown in the figure represents a reversible adiabatic expansion of an ideal gas. The same sample of gas, starting from the same state $O,$ now undergoes an adiabatic free expansion to the same final volume. What point on the diagram could represent the final state of the gas?

a$.$ none of these choices

b$.$ any of these choices

c$.$ the same point $A$ as for the reversible expansion

d$.$ point $C$

e$.$ point B