Thermodynamic Cycles and Heat Engines -- Where does heat enter and leave?

Factual Questions
1

I’m studying for a physics test and I think I’m mostly good, I can draw PV diagrams and do heat calculations etc, but my one trouble is thermodynamic cycles. I don’t really understand how to gauge where heat enters and leaves.

On the practice test, there’s a question that has a thermodynamic cycle, it starts at STP, goes through an adiabatic step where pressure increases and volume decreases, an isochoric step where pressure decreases, and an isothermal step where pressure decreases and volume increases (at which point it’s at STP again). The answer says that heat leaves during the isochoric step and leaves during the isothermal step.

I hate to say that I can’t even articulate my misunderstanding, I mostly just look at it and go “… okay, if you say so”. I understand heat and the equations for the most part, so I could probably work out why heat increases or decreases during those steps by crunching the math, but the way the problem is set up you’re supposed to figure that out before anything else. I don’t really get how you just intuit where heat enters and leaves.

ETA: Now that I really think, my intuition is that in the isochoric step, pressure decreases while vol is constant so temp decreases and it doesn’t do any work, so therefore heat must decrease. For isothermal, it does work with no change in temp so heat increases. Adiabatic does no work with no internal energy change so it must not have any heat change. But I don’t see how you could intuit what would happen in a cycle if you had an isobaric step, it seems that you’d be required to work out the math before you determined whether heat entered or left.

2

I think you could intuit that, if you had an impermeable and loose bag of air, and you heated the bag and the air expanded, that heat had entered the bag (which is still at the same atmospheric pressure and so isobaric).

3

For the isobaric case it’s as simple as: if PV increases (i.e. isobaric expansion) you are adding heat, whereas if PV decreases (isobaric compression) you are rejecting heat from the system.

Is that not intuitive?

4

Sorry, that didn’t come out the way I intended. I didn’t mean to sound insulting and patronising. This stuff isn’t easy or intuitive at all.

What I meant was, did my reply correctly address what you were asking, or did I miss something?

5

No, that makes sense. What got me is that since the direction of the volumetric change affects the sign of the work and the sign of the internal energy change in the same way you don’t have to calculate what happens to each one and add them up to get a total.

Thanks!