# Reversible engines with different efficiencies

1. Aug 21, 2014

### AbhiNature

Is is possible to have 2 different engines with all the following criterion?

1) Are reversible
2) Work differently (different cycles)
3) At the same working temepratures have different efficiencies.

E.g.
Working temperatures 100K and 50K.
Engine 1: Carnot's
Efficiency - 50%

Engine2: Some cycle
Efficiency - 20%

Thanks!

2. Aug 23, 2014

### Dear Sir

All Reversible Heat Engines have same efficiency when operating between the same two temperature reservoirs.

This is proved by showing that there is a contradiction, if they do not. We set the two heat engines to be compared operating between the same two heat reservoirs. Assume one is more efficient than the other. Run the less efficient one in reverse (as a refrigerator) using the fraction of the work from the more efficient engine that the less efficient engine would produce running forward. At that point there is zero net heat flow from the hot reservoir and the differential in work between the two engines is comes from the net heat removed from the cold heat reservoir. This contradicts the Carnot assumption. Thus to stay consistent:
Every reversible heat engine operating between the same two temperature reservoirs have identical efficiency. This means no matter how a reversible heat engine is constructed or what the working fluid is, its efficiency is the same as all other heat engines working from the same two temperatures.

3. Aug 23, 2014

### AbhiNature

I thought so. It is as improbable to create a lesser efficient reversible engine (compared to Carnot's) as to create a more efficient reversible engine.
Whenever second law is violated, maybe, it would be due to the lesser efficient engine.