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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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