In these two time-dependent diagrams it is also obvious that the engine cannot generate any power when operated at Carnot efficiency.
The black solid circles in the lower graphs indicate the instantaneous time, the blue dashed line in the lower right graph indicates the Carnot efficiency, and the red dashed line indicates the Curzon-Ahlborn efficiency.
(1) Why do most power plants and engines have an efficiency that is so far from the Carnot efficiency? After all students had written their answers, the papers were collected and the visualization tool was demonstrated.
Following the demonstration, we again looked at the power plant data and we explained to the students that the observed efficiencies match very well the Curzon-Ahlborn efficiencies and that no power plant will operate at the Carnot efficiency since the output power in this case will approach zero.
Many of these students appear to believe that the reason that real power plants do not operate at Carnot efficiency is that the Carnot process is ideal and thus not possible to reach in practice, because of heat losses.
They seem to understand that Carnot efficiency can in principle be reached, but that it would require a very long cycle time and a minimum of heat losses, which is not practically feasible.
This student knows that there is a timing issue but somehow misunderstands and believes that the time in the isotherms should approach zero instead of infinity in order to reach Carnot efficiency.