Overview of lectures in this series

1.  Introduction and Motors (Oct. 3) 2.  Motors and Generators (Oct. 10) 3.  Distribution and use of Electricity (Oct. 17) 4.  The Wind (Oct. 24) 5.  Thermodynamics (Oct. 31) 6.   Heat Engines and Transportation (Nov. 7) 7.  Nuclear Generation (Nov. 14) 8.  Solar Power – Thermal and Electric (Nov. 21) 9.  Fuel Cells (Dec. 5) 10.  Summary, Consumption and the future (Dec. 12)

http://kicp.uchicago.edu/~switzer/

C O M P T O N L E C T U R E 6 : N O V E M B E R 7 , 2 0 0 9 E R I C S W I T Z E R

Heat Engines and Transportation

“The study of these engines is of the greatest interest, their importance is enormous, their use is continually increasing, and they seem destined to produce a great revolution in the civilized world.” – S. Carnot 1824 Réflexions sur la puissance motrice du feu

Resources

 Mere Thermodynamics D. Lemons  DOE/EERE (Oak Ridge): Transportation Energy

Data Book (Ed. 28)  American Physical Society: Energy = Future:

Think Efficiency

Why care?

  Steam engines   Gas/Diesel engines   Magnetohydrodynamic

generators   Thermoelectrics,

Thermionics   Solar thermal   Refrigerators, AC, etc.   Perhaps the greatest

reward: the drinking bird   …

Image: wikipedia

Adding heat increases the number of accessible states

  E=0 1   E=1 3   E=2 6   E=3 10   E=4 15   E=5 21   E=6 28   E=7 36   E=8 45   E=9 55   E=10 66   E=11 78   E=12 91   E=13 105   E=14 120   E=15 136 and so on…

How much does the entropy increase for some added heat?

S = kBln(number of states)

How much does the entropy change for some amount of heat ΔQ added?: ΔS = ΔQ/T

Heat flows across a gradient spontaneously: entropy increases

  Hot room (298 K), cold ice (273 K)

  Thermal gradient drives a heat flow

  Thermal energy ΔQ spread in the cooler system

  Heat flow continues until the temperatures match (entropy is maximized.)

Image: wikipedia

Hot Cold

Entropy increasing

Entropy decreasing

Entropy is (globally) increasing.

Heat flows across a gradient spontaneously: entropy increases

Image: wikipedia

Hot Cold

ΔSice = ΔQ/(273 K)

ΔSroom = - ΔQ/(298 K)

ΔStot= ΔSroom +ΔSice= ΔQ*[1/273 – 1/298] > 0

Entropy of the water/ice increases more than the entropy of the room.

Thus, a net entropy increase. ΔS = ΔQ/T

The second law of thermodynamics (entropy statement)

The entropy of a system increases in spontaneous processes.

Joule’s experiment– making entropy

Energy is conserved – entropy is not.

Entropy “increase” is entropy production

Image: wikipedia

Flowing heat increases entropy

Carnot efficiency

ΔS = ΔQ/T

Carnot efficiency

How efficient?

  Want hottest possible source and coldest sink   Waste heat: Earth’s ambient temperature ~300 K   Unwanted emissions containing NOx compounds can

form at temperature ~1770 K   840 K is a standard materials limit for stainless steel   600 K might be typical in a nuclear reactor, so

efficiency = 1-300/600 = 50%; 30% might be attained.

The second law of thermodynamics (Kelvin form)

A cyclic engine can not convert thermal energy into mechanical energy unless the device uses two temperatures and discards heat to the cold side.

Increasing entropy implies an upper bound on the efficiency.

Reminder: why you need two temperatures

Losses in “real engines”

Combining heat engines

  Engines often work over a limited temperature range.

  So… combine two of them!

  Efficiency: η = ηA+ηB-ηAηB

  Example: 40% top cycle and 30% bottom cycle is 60% combined cycle

  Still can not beat Carnot!   See notes for more

details.

Topp

ing

Bot

tom

ing

In the news: the combined cycle

  Mitsubishi Heavy Industries M701G2 outputs 334 MW at 39.5 percent efficiency, TH=1,500oC (2,732 oF), TC=587 oC (1,089 oF).

  Using the exhaust in the second cycle, on achieves ~60% efficiency!

  More exotic: MHD and steam.

Images: wikipedia, data “Efficiency by the Numbers” by L. Langston (AMSE)

4-stroke engine

Ready to start!

Image: Wikipedia

4-stroke engine

Intake stroke.

Image: Wikipedia

4-stroke engine

Compression stroke.

Image: Wikipedia

4-stroke engine

Ignition!

Image: Wikipedia

4-stroke engine

Power stroke.

Image: Wikipedia

4-stroke engine

Exhaust stroke.

Image: Wikipedia

Also possible: A six stroke engine that uses steam for an additional power stroke.

The compression ratio and Carnot

Where are the “hot side” and “cold side” of this engine?

Image: Wikipedia

For diatomic molecules: 3 dimensions and 2 rotation so γ=7/5=1.4 once you add fuel γ=1.3

Typical compression ratio ~ 9:1, γ=1.3 Implies 50% maximum efficiency! Maximize r, maximize γ – octane and lean air-fuel mixes.

My other car is a sphere

Image: wikipedia (sphere added)

Fuel densities

American Physical Society: efficiency report

Power balance in a spherical car

Gasoline embodies 114000 BTU/gal

For a 5’ diameter sphere (here, CdA ~8 ft2) going 55 mph, drag is 6.5 kW. Suppose that 50% of the embodied energy in the gasoline is converted into motion, then one needs 13 kW. ~50% is the (Carnot) limit for an Otto engine with a compression ratio of 9:1 and adiabatic index 1.3. Such a vehicle would then get 138 mpg (at constant velocity).

A real car’s energy loss

American Physical Society: efficiency report (image from fueleconomy.gov)

O.3% into motion of humans A. Lovins

Power balance in a spherical car

We were off-target – let’s use 12% instead.

The sphere would then get 33 mpg (at constant velocity). Pretty reasonable!

A real car has similar CdA, but this can span from 2 ft2 (for the Aptera) to 26 ft2 (for the Hummer).

Into the real world

The Garden of Earthly Delights – Hieronymus Bosch

Image: Museo del Prado via Wikipedia

Net energy flows

32% eff.

25%

eff.

Fertilizers!

Units

  1 BTU = British thermal unit, the heat to raise the temperature of 1 pound of water by 1 degree Fahrenheit. 1 Quad = 1 quadrillion BTU = 1015 Btu.

  1 BTU is also equal to 1054 joules   1 Joule = lifting an apple one meter   Rule of thumb 1: 1/3 of heat energy reaches

consumers as electrical energy.   Rule of thumb 2: 1/3 of CO2 is emitted in

transportation.

Energy scales

25 bbl/year per capita, ~300 million

How far do we travel?

  80 % cars, 10% air, 10% other

  27% vehicle miles-traveled commuting (avg. 12 miles)

  76.3% commute alone, 5.2% public transit, 3% walk or bike

  0.7 fuel stations per 1000 vehicles

  Households: 10% 0 cars, 34% 1 car, 38% 2 cars

  Gas tax in US: 17%   Japan, Europe: 30%-70%

American Physical Society: efficiency report, DOE/EERE at ORNL: Transportation energy data book Ed. 28

Cars these days…

Maximum attainable efficiency? Compare: 40-47 mpg in E.U. and Japan

Infl. adj. oil barrel: 1979 $106 (max) 1985 $50 1986 $25 1998 $15 2004 $35

American Physical Society: efficiency report

Comparison of transportation modes

1970 Btu per pass-mile

2472

4868

10,115

DOE/EERE at ORNL: Transportation energy data book Ed. 28

A reminder to ride the bus

A more complete picture

“By reducing vehicle miles traveled, public transportation reduces energy use in the transportation sector and emissions. The total energy saved, less the energy used by public transportation and adding fuel savings from reduced congestion, is equivalent to 4.2 billion gallons of gasoline.” –The Broader Connection between Public Transportation, Energy Conservation and Greenhouse Gas Reduction

ICF International

The catch-up game

  In the US, 845 vehicles per 1000 people (2007)

  India in 2007 is like the US in 1913 (12 vehicles per 1000)

  China: 1916 (30 per 1000)   Middle east: 1921 (101 per

1000)   Central/South America: 1923

(128 per 1000)   Eastern Europe: 1948 (271

per 1000)   Western Europe, Canada, the

Pacific: 1972 (541-609 per 1000)

The model-T in 1910.

Image: wikipedia

DOE/EERE at ORNL: Transportation energy data book Ed. 28

Imported Oil

Compare Japan: 87% Middle East (Barclays, “Burning Violins”)

Source: EIA

Import=66%

Summary

  Thermodynamics fundamentally limits how efficiently heat can be converted into work.

  Carnot efficiency = 1 – TC/TH   Fuel economy in the spherical car approximation is

fairly reasonable.   Annually in the US, transportation heat engines

consume 26 Quadrillion BTUs of primary energy from Petroleum; 13% directed into motion.

  100 Quads total annually – almost all in heat engines.

A world with no gradients

On Angelus Novus: “…the angel of history. His face is turned towards the past. Where we perceive a chain of events, he sees one single catastrophe which keeps piling wreckage upon wreckage.” – Walter Benjamin

Dürer: Melencolia Klee: Angelus Novus

Images: wikipedia in public domain