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Engines

Engines. Physics 313 Professor Lee Carkner Lecture 12. Exercise #11 Adiabatic. Adiabatic Work W = - ∫ PdV, where P = KV - g W = - KV (- g +1) / (- g +1), but K = PV g W = -PV g V (- g +1) / (- g +1) W = PV/( g -1) = -(P i V i – P f V f ) / ( g -1) Monatomic gas expansion ( g = 5/3)

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Engines

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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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