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Understanding Heat Engines and Efficiency in Physics

Explore the concepts of adiabatic work, heat conversion, engine efficiency, and types of engines like Otto, Diesel, Steam, and Stirling. Learn about real vs. ideal efficiency and their application in various engine cycles.

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Understanding Heat Engines and Efficiency in Physics

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  1. Engines Physics 313 Professor Lee Carkner Lecture 12

  2. Exercise #11 Adiabatic • Adiabatic Work • W = - ∫ PdV, where P = KV-g • W = - KV(-g+1) / (-g+1), but K = PVg • W = -PVgV(-g+1) / (-g+1) • W = PV/(g-1) = -(PiVi – PfVf) / (g-1) • Monatomic gas expansion (g = 5/3) • PiVig = PfVfg or Vf = (PiVig /Pf) (3/5) • W = - [(5000)(1) – (4000)(1.14)] /(1.66667 – 1) = • Diatomic gas expansion (g = 7/5) • W = - [(5000)(1) – (4000)(1.17)] / (1.4 – 1) =

  3. Heat and Work • It is easy to convert work into heat • 100 % efficient • It is harder to convert heat into work • Need a series of processes called a cycle to extract work from heat • A machine that converts heat into work with a series of processes is called an engine

  4. Efficiency • Engines convert heat (QH) into work (W) plus output heat (QL) • The ratio of output work to input heat is called efficiency • All Q and W are absolute values

  5. Waste Heat • The efficiency can be written (using the first law): h = (QH -QL) / QH • If QL = 0 efficiency is 100% h < 1

  6. Ideal and Real Efficiency • Our values for efficiency are ideal • Real engines have all of these problems

  7. Papin’s Device - 1690

  8. Newcomen’s Engine - 1705

  9. Watt’s Engine - 1770

  10. Engines • An (idealized) engine consists of a gas (the working substance) in a cylinder that drives a piston • Types of engines: • External combustion • Internal combustion

  11. Parts of the Cycle • Cycle can be broken down into specific parts • In general: • One involves compression • One involves the output of heat QL • Change in internal energy is zero

  12. Otto Engine

  13. Otto Engine • Intake stroke -- • Compression stroke -- • Combustion -- • Power stroke -- • Exhaust -- • Exhaust stroke -- Isobaric compression • Intake and exhaust are identical and cancel

  14. Between Processes • Can specify 4 points, each with its own T, V and P: • 1: • 2: Before heat gain (after compression) • 2: • 4: Before heat loss (after expression) • Can relate P,V and T using our equations for the various processes Q = CVDT (isochoric) TVg-1 = TVg-1 (adiabatic)

  15. Efficiency and Temperature QL = CV(T4-T1) • From adiabatic relations: • Result: h = 1 - (QL/QH) = 1 - [(T4-T1)/(T3-T2)] • This is the ideal efficiency

  16. Diesel Engine • Constant pressure maintained by adjusting the rate of fuel input • Can compute in similar way, but with different expression for input heat

  17. Diesel Engine Efficiency h = 1 - (1/g)[(T4-T1)/(T3-T2)] • Can also write in terms of compression and expansion ratios: h = 1 - (1/g)[(1/rE)g - (1/rC)g / (1/rE)- (1/rC)] • Real efficiency ~ 30-35 %

  18. Steam Engine • External high T reservoir (furnace) vaporizes water which expands doing work • The idealized process is called the Rankine cycle

  19. Rankine Cycle • Adiabatic compression (via pump) • Adiabatic expansion (doing work) • Real efficiency ~ 30-40 %

  20. Stirling Engine • Working substance is air instead of water • Expansion piston in contact with high T reservoir • Real efficiency ~ 35-45%

  21. Stirling Cycle • Isochoric compression and expansion moving air to expansion piston • Isochoric compression and expansion moving air to compression piston

  22. Engine Notes • Should be able to plot and compute key P,V and T

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