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Engines
Physics 313Professor Lee
CarknerLecture 12
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) =
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): = (QH -QL) / QH
If QL = 0 efficiency is 100%
< 1
Ideal and Real Efficiency
Our values for efficiency are ideal
Real engines have all of these problems
Papin’s Device - 1690
Newcomen’s Engine - 1705
Watt’s Engine - 1770
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
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 = CVT (isochoric)TV-1 = TV-1 (adiabatic)
Efficiency and Temperature
QL = CV(T4-T1)
From adiabatic relations:
Result: = 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
= 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 %
Steam Engine
External high T reservoir (furnace)
vaporizes water which expands doing work
The idealized process is called the Rankine cycle
Rankine Cycle
Adiabatic compression (via pump) Adiabatic expansion (doing work)
Real efficiency ~ 30-40 %
Stirling Engine Working substance is air instead of water
Expansion piston in contact with high T reservoir
Real efficiency ~ 35-45%
Stirling Cycle
Isochoric compression and expansion moving air to expansion piston
Isochoric compression and expansion moving air to compression piston
Engine Notes
Should be able to plot and compute key P,V and T
Recommended