Where do you want to go ?

Is this Process Possible?

Just because a cycle obeys the 1st Law does not guarantee that the cycle will occur.

Heat flow from a hot reservoir to a cold reservoir requires only a medium for the heat to flow through.
This process obeys the 1st Law and occurs spontaneously.

Lesson 6C: page 1 of 11

Because there is no net heat transfer to or from the cold reservoir, we can lump it into our system.
The system behaves just as if the heat rejected by the HE flowed right into the HP.
Do you see what I mean ? Both of these heat flows have the same magnitude.
Now, step back and take a look at the new system within the dashed line.
This system takes in a net amount of heat, QH – QC and converts all of it into work.
So,, what can we conclude ?
Well, systems that violate the Clausius Statement of the 2nd Law are able to exchange heat with a single thermal reservoir and produce a net amount of work.
I think we are on the brink of making a different, but equivalent statement of the 2nd Law.