Image 1 Caption: A schematic diagram of a heat engine: heat energy in from hot bath, heat energy rejected to cold bath---there must always be some---and work done---which is the whole point. A heat engine by definition works in a thermodynamic cycle (AKA engine cycle) in which the operations repeat in order.

Features:

1. A heat engine run in reverse is a refrigerator. To see this schematically, just reverse the arrows in the schematic diagram.

2. To expand on a key preamble point, heat engines and refrigerators operate in a thermodynamic cycle (AKA engine cycle). Their internal state always runs through same sequence of states. Thus, there must be processes that return them to the state where they begin in order to carry out their function.

3. Heat engine efficiency definition:

         W    (Q_H-Q_L)       Q_L
    ε = --- = --------- = 1 - --- 
        Q_H      Q_H          Q_H 
   
            T_L
      ≤ 1 - --- = ε_Carnot engine ≤ 1 ,
            T_H 

   where temperatures T_H and T_L are on Kelvin temperature scale and even the Carnot engine CANNOT be 1, unless T_L = 0 K (i.e., absolute zero T = 0 K) which is impossible in practice.

4. The ideal Carnot engine is the most efficient possible heat engine in principle as dictated by 2nd law of thermodynamics. It CANNOT be beat.

5. Actually, the ideal Carnot engine CANNOT be built, but less-than-ideal Carnot engines can be built. So why do we actually NOT use them---except for certain experimental uses?

   Heat engine efficiency as defined above is only one heat engine desideratum. Another is power: i.e., energy per unit time. The ideal Carnot engine actually has zero power: it runs infinitely slowly. Less-than-ideal Carnot engines have very, very low power, and so have only the aforementioned experimental uses.

   

6. Now the ε_Carnot engine is just an upper limit on practical heat engine efficiency. Nevertheless, making T_H as large as practically possible is a usually a good strategy in improving the heat engine efficiency of any heat engine. Note T_L is usually set by the ambient medium (e.g, the air) and usually CANNOT be changed practically.

   But there are practical limits on T_H. You do NOT want your heat engine to melt or meltdown as can happen in nuclear-fission nuclear power plants---which are just heat engines where nuclear fission provides the hot bath.

7. Image 2 Caption: "Sadi Carnot (1796--1832) in 1813 at age of 17 in the traditional uniform of a student of the Ecole Polytechnique, Paris, France." (Slightly edited.) Sadi Carnot was the discoverer of the eponymous Carnot engine. See also St. Andrews: MacTutor: Sadi Carnot (1796--1832). By the by, Sadi Carnot was the son of Lazare Carnot (1753--1823), one of the leaders of the French Revolution.

8. Yours truly CANNOT digress further here on heat engines, but for a digression, see the extended version of this figure (Thermodynamics file: heat_engine_schematic_4.html).

Images:

1. Credit/Permission: © Antonio Gonzalez Fernandez (AKA User:Gonfer), 2009 / Creative Commons CC BY-SA 3.0.
   Image link: Wikimedia Commons: File:Heat engine.png.
   
2. Credit/Permission: Louis-Leopold Boilly (1761--1845), 1813 (uploaded to Wikimedia Commons by User:Maksim, 2006) / Public domain.
   Image link: Wikimedia Commons: File:Sadi Carnot.jpeg.
   
3. Credit/Permission: Sadi Carnot (1796--1832), 1824, User:Libb Thims, 2008, (uploaded to Wikipedia by User:Balph Eubank (AKA User:Burpelson AFB), 2010) / Public domain.
   Image link: Wikipedia: File:Carnot engine (hot body - working body - cold body).jpg.