Example: Carnot Engine with External Irreversibility
Fully reversible (e.g., Carnot) engines cannot be build since any real process is associated with some irreversibilities. These can be reduced, but not avoided. For instance, heat transfer requires finite temperature differences, which are accompanied by entropy generation, i.e., work loss. As an example we study a reversible Carnot heat engine with external irreversibilities that occur in transferring heat in and out of the engine, see Fig. 11.2.
We compare a fully reversible engine (I), which does not require tem- perature differences for heat transfer, and an engine (II) that requires finite temperature differences. When both engines take in the same amount of heat, their power outputs are
While the internally reversible engine II has the optimum efficiency with respect to its boundary temperatures TL + ΔT and TH − ΔT , the engine does not have optimum efficiency with respect to the available boundary temperatures TL and TH , due to external irreversibilities in heat transfer.
This simple example shows once more the importance of considering external losses. In order to obtain a comprehensive picture of thermodynamic performance, one cannot restrict the attention to the performance of an isolated system, say a heat engine, but one has to account for the interaction of the system with its surroundings as well.
A perfect heat exchanger, which operates at infinitesimal temperature difference, and hence does not generate entropy, requires an infinite exchange surface, and thus can only be thought of, but not be build. Thus, in any existing heat exchanger the temperature difference is finite, and entropy is generated. The art of building heat exchangers, or choosing heat exchangers for a particular system, is to make the temperature difference, and thus the work losses, as small as technology and purchase or construction costs allow.