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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
Engines

Physics 313

Professor Lee Carkner

Lecture 12

exercise 11 adiabatic
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) =
heat and work
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
efficiency
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
waste heat
Waste Heat
  • The efficiency can be written (using the first law):

h = (QH -QL) / QH

  • If QL = 0 efficiency is 100%

h < 1

ideal and real efficiency
Ideal and Real Efficiency
  • Our values for efficiency are ideal
  • Real engines have all of these problems
engines1
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
parts of the cycle
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
otto engine1
Otto Engine
  • Intake stroke --
  • Compression stroke --
  • Combustion --
  • Power stroke --
  • Exhaust --
  • Exhaust stroke -- Isobaric compression
      • Intake and exhaust are identical and cancel
between processes
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)

efficiency and temperature
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
diesel engine
Diesel Engine
    • Constant pressure maintained by adjusting the rate of fuel input
  • Can compute in similar way, but with different expression for input heat
diesel engine efficiency
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 %
steam engine
Steam Engine
  • External high T reservoir (furnace) vaporizes water which expands doing work
  • The idealized process is called the Rankine cycle
rankine cycle
Rankine Cycle
  • Adiabatic compression (via pump)
  • Adiabatic expansion (doing work)
  • Real efficiency ~ 30-40 %
stirling engine
Stirling Engine
  • Working substance is air instead of water
  • Expansion piston in contact with high T reservoir
  • Real efficiency ~ 35-45%
stirling cycle
Stirling Cycle
  • Isochoric compression and expansion moving air to expansion piston
  • Isochoric compression and expansion moving air to compression piston
engine notes
Engine Notes
  • Should be able to plot and compute key P,V and T
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