The Carnot Cycle in Thermodynamics

Explore the principles of the Carnot cycle, efficiency of a Carnot engine, and the significance of isotherms and adiabats in thermodynamics. Gain insights into the working of such engines and their efficiency calculations through a series of informative visual representations.

• Thermodynamics
• Carnot Cycle
• Efficiency
• Isotherms
• Adiabats

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1. v = 10:1:100; t = 100; r = 8.314; gamma = 1.67; p = r*t./v; k = (10^(gamma-1)).*r*t; pa = k./v.^gamma; plot(v,pa,v,p) 90 80 70 60 50 p Isotherm, pV = constant = NkBT 40 30 20 10 Adiabat, pV = constant 0 10 20 30 40 50 60 70 80 90 100 V

2. v = 10:1:100; th = 100; tl = 50; r = 8.314; gamma = 1.67; p1 = r*th./v; k1 = (30^(gamma-1)).*r*th; pa1 = k1./v.^gamma; p2 = r*tl./v; k2 = (30^(gamma-1)).*r*tl; pa2 = k2./v.^gamma; plot(v,p1,v,pa1,v,p2,v,pa2) Carnot cycle

3. Carnot cycle

4. Carnot cycle pA, VA, TA Isotherm 1 Th p Qh pB, VB, TB Adiabat 2 Adiabat 1 pD, VD, TD Isotherm 2 pC, VC, TC V

5. Carnot cycle pA, VA, TA Isotherm 1 Th p Qh pB, VB, TB Adiabat 2 Adiabat 1 pD, VD, TD Isotherm 2 pC, VC, TC V

6. Carnot cycle pA, VA, TA Isotherm 1 Tl p Qh pB, VB, TB Adiabat 2 Adiabat 1 pD, VD, TD Ql Isotherm 2 pC, VC, TC V

7. Carnot cycle pA, VA, TA Isotherm 1 Tl p Qh pB, VB, TB Adiabat 2 Adiabat 1 pD, VD, TD Ql Isotherm 2 pC, VC, TC V

8. Why such a strange engine? Will discuss in class

9. Efficiency of a Carnot engine ??,??,?? Isotherm 1 ??= ??= ? p ??,??,?? Adiabat 2 Adiabat 1 ??,??,?? ??,??,?? Isotherm 2 ??= ??= ?? V

10. Efficiency of a Carnot engine ??,??,? Isotherm 1 ? = ?? ln?? p ?? Adiabat 2 ??,??,? ? = 0 ???? ? 1= ? ?? ? 1 Adiabat 1 ? = 0 ? ?? ? 1= ???? ? 1 ??,??,?? ??,??,?? Isotherm 2 ??= ???ln?? ?? V

11. Efficiency of a Carnot engine ? = ?? ln?? (1) From isotherm 1 ?? ? 1= ???? ? 1 (2) From adiabat 1 ? ?? ??= ???ln?? (3) From isotherm 2 ?? ? 1= ? ?? ? 1 ???? (4) From adiabat 2 From the first law of thermodynamics: ? = ? + ? For the complete Carnot cycle ? = 0 since ? is a state variable

12. Efficiency of a Carnot engine ? = ?? ln?? (1) From isotherm 1 ?? ? 1= ???? ? 1 (2) From adiabat 1 ? ?? ??= ???ln?? (3) From isotherm 2 ?? ? 1= ? ?? ? 1 ???? (4) From adiabat 2 From the first law of thermodynamics: ? = ? + ? For the complete Carnot cycle ? = 0 since ? is a state variable ? = ? ?is the work done on the engine (system), let ? be the work done by the engine ? = ? = ? From (1) and (3): ? = ? + ??= ?? ln?? ??+ ???ln?? ??

13. Efficiency of a Carnot engine ? = ?? ln?? (1) From isotherm 1 ?? ? 1= ???? ? 1 (2) From adiabat 1 ? ?? ??= ???ln?? (3) From isotherm 2 ?? ? 1= ? ?? ? 1 ???? (4) From adiabat 2 From (1) and (3): ? = ? + ??= ?? ln?? ??+ ???ln?? ??= ? Efficiency is defined as:Output Input Output is the work done by the engine i.e. ? and input is the heat absorbed by the engine i.e. ? ? ? ? = ? + ?? = 1 + ?? ? efficiency = ?

14. Efficiency of a Carnot engine ? = ?? ln?? (1) From isotherm 1 ?? ? 1= ???? ? 1 (2) From adiabat 1 ? ?? ??= ???ln?? (3) From isotherm 2 ?? ? 1= ? ?? ? 1 ???? (4) From adiabat 2 = ? + ?? ? ? ? = 1 + ?? ? efficiency = ? ???ln?? ln?? = 1 ?? ?? ?? (from (1) and (3)) ? = 1 + ?? ln?? ln?? ? ?? ?? ? 1 ? 1 ?? =?? ?? =?? (2) ? ?? ?? ? ?? ?? and (4) = = ?? ?? ?? ?? ?? ??

15. Efficiency of a Carnot engine ? = 1 ?? ?

16. Laws of thermodynamics 0. There is a game 1.You can never win 2. You cannot break even, either 3. You cannot quit the game

17. Carnot engine: Schematic representation ? ? = ? ? = ? + ??= ? ?? Carnot ??= ?? = ?? ??

18. Carnot engine: Schematic representation ? ? ? = ? ?? Carnot ?? ??

19. Carnot engine is reversible ? ? ? = ? ?? Carnot ?? ??

20. Carnot engine is reversible (refrigerator) ? ? ? = ? ?? Carnot ?? ??

21. Carnots theorem reversible Of all heat engines working between two given temperatures, none is more efficient than a Carnot engine

22. Carnot engine is reversible (refrigerator) ? ? ? ?? ? = ? ? = ? ?? R Carnot ?? ?? ?? Adjust the cycles so that ? = ?

23. Carnot engine is reversible (refrigerator) ? ? ? ?? ? = ? ??= ? R Carnot ?? ?? ??

24. Carnot engine is reversible (refrigerator) ? ? ? If ? > ? then: ? ? >? ?? ? ? = ? ??= ? R Carnot < ? ? ? > 0 ? ?? Also: ? ??= ? ?? ?? = ?? ?? > 0 ? ? ??

25. Is this possible? ? ? ? ? ? = ?? ?? > 0 ? ? ?? ? = ? ??= ? R Carnot ??? ??> ?? ? > ? ?? ?? ?? ?? ??

26. The Second Law of Thermodynamics Clausius statement: It is impossible to construct a device that operates in a cycle and whose sole effect is to transfer heat from a cooler body to a hotter body. ? ?

27. Carnots theorem reversible Of all heat engines working between two given temperatures, none is more efficient than a Carnot engine ????< ???? ????< ????

28. For reversible engines ? ? ? ?? ? = ? ??= ? R Carnot ?? ?? ?? ? ? ??? ? ? ? = ?

29. Carnots theorem Of all heat engines working between two given temperatures, none is more efficient than a Carnot engine All reversible engines working between two temperatures have the same efficiency as ?Carnot

30. The Second Law of Thermodynamics Clausius statement: It is impossible to construct a device that operates in a cycle and whose sole effect is to transfer heat from a cooler body to a hotter body. Kelvin-Planck statement: It is impossible to construct a device that operates in a cycle and produces no other effect than the performance of work and the exchange of heat from a single reservoir.

31. Carnot refrigerator and Kelvin violator ? ? ? ? ??= ? = ??> 0 = ? ?? ? ? ? = ? Kelvin violator Carnot ?? ??

32. Carnot engine and Claussius violator ? ? ?? ? = ? ?? Claussius violator Carnot ?? ?? ??