1. Engines Physics 313 Professor Lee Carkner Lecture 12

2. Exercise #11 Adiabatic  Adiabatic Work  W = - ∫ PdV, where P = KV -    W = - KV (-  +1) / (-  +1), but K = PV   W = -PV  V (-  +1) / (-  +1)  W = PV/(  -1) = -(P i V i – P f V f ) / (  -1)  Monatomic gas expansion (  = 5/3)  P i V i  = P f V f  or V f = (P i V i  /P f ) (3/5)   W = - [(5000)(1) – (4000)(1.14)] /(1.66667 – 1) =  Diatomic gas expansion (  = 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 (Q H ) into work (W) plus output heat (Q L )  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):  = (Q H -Q L ) / Q H   If Q L = 0 efficiency is 100%   < 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 Q L   Change in internal energy is zero

12. Otto Engine

13.  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 = C V  T (isochoric) TV  -1 = TV  -1 (adiabatic)

15. Efficiency and Temperature Q L = C V (T 4 -T 1 )  From adiabatic relations:  Result:  = 1 - (Q L /Q H ) = 1 - [(T 4 -T 1 )/(T 3 -T 2 )]   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  = 1 - (1/  )[(T 4 -T 1 )/(T 3 -T 2 )]  Can also write in terms of compression and expansion ratios:  = 1 - (1/  )[(1/r E )  - (1/r C )  / (1/r E )   (1/r C )   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

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

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

24. Stirling Cycle   Isochoric compression and expansion moving air to expansion piston   Isochoric compression and expansion moving air to compression piston

25. Engine Notes   Should be able to plot and compute key P,V and T 