Engines

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# Engines - PowerPoint PPT Presentation

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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Presentation Transcript
Engines

Physics 313

Professor Lee Carkner

Lecture 12

• 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
• 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
• 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
• 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
• Our values for efficiency are ideal
• Real engines have all of these problems
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
• 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 Engine
• Intake stroke --
• Compression stroke --
• Combustion --
• Power stroke --
• Exhaust --
• Exhaust stroke -- Isobaric compression
• Intake and exhaust are identical and cancel
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)

Efficiency and Temperature

QL = CV(T4-T1)

• Result:

h = 1 - (QL/QH) = 1 - [(T4-T1)/(T3-T2)]

• This is the ideal efficiency
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

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