Questioning the Efficiency of a Heating/Cooling System as a Heat Engine

[wakko101]

Attached is a graph of a system that has undergone heating/cooling, expansion/compression. The question is: Suppose now that this system is being used as a heat engine, to convert the heat added into mechanical work. Estimate the efficiency of this engine.

I'm confused...in this system, there is external work being done on it and heat is being taken away from it, so how can it be used as a heat engine?

Please help...

Cheers,
W.

 

[Mapes]

That's common to all heat engines, because they rely on cyclic processes. After the engine does work on the environment (by expanding, for example), the volume must be restored to its original value to start the cycle anew. Thus, the environment must do some work on the system, but in a properly working engine the net work done on the environment is still positive.

There's a related argument for heat: thermal energy entering the system carries entropy, but no entropy is removed when the system performs work. We therefore need to transfer some thermal energy to a low-temperature reservoir to avoid a buildup of entropy.

 

[wakko101]

alright...that makes sense.

The thing that is confusing me, I guess, from what I can tell from the diagram, the amount of heat being put into the system (ie. the left hand line going up) is less than the total amount of work that is being done on the environment. But, in the heat engine, Qh = W + Qc, where all of these quantities are positive, so how is that possible? Also, the waste heat that is being dumped into the cool reservoire (ie. the right hand line going down) is more than the heat that is being put into the system. At least, that's the way it looks to me, but I must be seeing it wrong, because that doesn't make sense.