Phase Transitions Physics 313 Professor Lee Carkner Lecture 22.
Engines Physics 313 Professor Lee Carkner Lecture 12.
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Transcript of Engines Physics 313 Professor Lee Carkner Lecture 12.
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Engines
Physics 313Professor Lee
CarknerLecture 12
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Exercise #11 Adiabatic Adiabatic Work
W = - ∫ PdV, where P = KV-
W = - KV(-+1) / (-+1), but K = PV
W = -PVV(-+1) / (-+1) W = PV/(-1) = -(PiVi – PfVf) / (-1)
Monatomic gas expansion ( = 5/3) PiVi
= PfVf or Vf = (PiVi
/Pf) (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) =
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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
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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
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Waste Heat
The efficiency can be written (using the
first law): = (QH -QL) / QH
If QL = 0 efficiency is 100%
< 1
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Ideal and Real Efficiency
Our values for efficiency are ideal
Real engines have all of these problems
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Papin’s Device - 1690
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Newcomen’s Engine - 1705
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Watt’s Engine - 1770
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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
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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
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Otto Engine
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Otto Engine Intake stroke -- Compression stroke --
Combustion -- Power stroke -- Exhaust -- Exhaust stroke -- Isobaric compression
Intake and exhaust are identical and cancel
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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 = CVT (isochoric)TV-1 = TV-1 (adiabatic)
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Efficiency and Temperature
QL = CV(T4-T1)
From adiabatic relations:
Result: = 1 - (QL/QH) = 1 - [(T4-T1)/(T3-T2)]
This is the ideal efficiency
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Diesel Engine
Constant pressure maintained by adjusting the rate of fuel input
Can compute in similar way, but with different expression for input heat
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Diesel Engine Efficiency
= 1 - (1/)[(T4-T1)/(T3-T2)]
Can also write in terms of compression and expansion ratios:
= 1 - (1/)[(1/rE) - (1/rC) / (1/rE)(1/rC)
Real efficiency ~ 30-35 %
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Steam Engine
External high T reservoir (furnace)
vaporizes water which expands doing work
The idealized process is called the Rankine cycle
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Rankine Cycle
Adiabatic compression (via pump) Adiabatic expansion (doing work)
Real efficiency ~ 30-40 %
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Stirling Engine Working substance is air instead of water
Expansion piston in contact with high T reservoir
Real efficiency ~ 35-45%
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Stirling Cycle
Isochoric compression and expansion moving air to expansion piston
Isochoric compression and expansion moving air to compression piston
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Engine Notes
Should be able to plot and compute key P,V and T