Understanding the Carnot Cycle: Heat Pumps & Engines

[mayer]

Greetings,
Here is my thought process on the carnot cycle, regarding heat pumps and engines. I'd much appreciate it if you can clear up any misconceptions and answer my question at the very end.
So my book states that there is no change in internal energy in a heat engine, but neither confirm nor denies that fact when describing the heat pump. Judging from its omission I assume that heat pumps do have a change in internal energy which makes sense since heat is added and subtracted in different parts of the cycle. But I am having trouble seeing that heat engines have no change in internal energy. Is it because it involves isothermal and adiabatic processes? I can understand how an adiabatic process would lead to no internal energy change but I am still stuck on the isothermal part. Heat is being added during this segment of the cycle yet its internal energy change is zero. Is the volume increase produced by the heat added so instantaneous that the energy from the heat is never considered part of the system? I guess what my question boils down to is, when is the heat that is added considered to produce a change in internal energy?

Thank You

 

[mayer]

Ah, I apologize I should've made the title more descriptive, I lost my train of thought while writing the question.

 

[Zeppos10]

when the carnot cycle has come full circle, it returns to the same state, hence dU=0. During the cycle, this is different ie dU ><0.