If you accept that the 2nd law of thermo tells you that the

$$Work_{net} = Q_{in} - Q_{out}$$

it's easy to see why 2 adiabatic processes cannot cross on a PV diagram when connected by an isothermal process.

however, why is the 2nd law true without taking a statistical approach?
Why must we have heat flow in order to get work out of an engine?

isn't that a restatement of the conservation of energy?

how do you define heat? in wikipedia it says "the energy transfer due to a difference in temperature", and temperature is a statistical definition. so there would be no sense to state such a law without the statistical approach.

you mean to tell me you cannot explain why 2 adiabatic processes cannot cross without doing a statistical approach to temperature?

I'm sure one can explain why heat flow is necessary for work inside an engine without statistics.

I haven't gotten to statistical and thermal physics yet...

no, what i'm telling you is that in order to define heat, you need to define temperature, and temperature is just a way of forgetting about certain degrees of freedom and collapse them into what we call 'temperature'. So to define adiabatic, you need to define heat, so you need to define temperature, and to do this, you collapse this whole mess of particles interacting with each other into one statistical definition, which is i think, the average kinetic energy or something like that.
that is, heat makes no sense at all just like friction makes no sense at all when you are taking into account every degree of freedom your system has.

EDIT: i haven't got to statystical physics yet neither.