chemical reaction engineeing

What is the definition of rate $$(−ra)=−\frac{dCa}{dt}$$ or $$(−ra)=−1/V\frac{dNa}{dt}$$ ? I think the general one is the second one and first one is for constant volume reaction system. Is the above written rate equation only valid to batch reactor? If not can we use this in a PFR or MFR? In PFR we know the rate comes out to be $$(−ra)=−\frac{dFa}{dV}$$ ,can we equate $$−1/V\frac{dNa}{dt}=−\frac{dFa}{dV}$$? If not then why? Is the rate equation not valid everywhere? Can we equate with CSTR as well ? eg $$-\frac{dCa}{dt}=\frac{Fa_o-Fa}{V}$$ (considering it a constant volume reaction system CSTR)

You are correct in saying that reaction rate $$(−ra)=−\frac{dCa}{dt}$$ is for constant volume systems and that the more general form is or $$(−ra)=−1/V\frac{dNa}{dt}$$.