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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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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) =

• 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

• 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

• The efficiency can be written (using the first law):

h = (QH -QL) / QH

• If QL = 0 efficiency is 100%

h < 1

• Our values for efficiency are ideal

• Real engines have all of these problems

• An (idealized) engine consists of a gas (the working substance) in a cylinder that drives a piston

• Types of engines:

• External combustion

• Internal combustion

• 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

• Intake stroke --

• Compression stroke --

• Combustion --

• Power stroke --

• Exhaust --

• Exhaust stroke -- Isobaric compression

• Intake and exhaust are identical and cancel

• 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)

QL = CV(T4-T1)

• Result:

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

• This is the ideal efficiency

• Constant pressure maintained by adjusting the rate of fuel input

• Can compute in similar way, but with different expression for input heat

• 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 %

• External high T reservoir (furnace) vaporizes water which expands doing work

• The idealized process is called the Rankine cycle

• Real efficiency ~ 30-40 %

• Working substance is air instead of water

• Expansion piston in contact with high T reservoir

• Real efficiency ~ 35-45%

• Isochoric compression and expansion moving air to expansion piston

• Isochoric compression and expansion moving air to compression piston

• Should be able to plot and compute key P,V and T