History of the Standard Atmosphere
• With a little digging, you can discover that the Standard Atmosphere can be traced back to 1920 . The constant lapse rate of 6.5° per km in the troposphere was suggested by Prof. Toussaint, on the grounds that
– … what is needed is … merely a law that can be conveniently applied and which is sufficiently in concordance with the means adhered to. By this method, corrections due to temperature will be as small as possible in calculations of airplane performance, and will be easy to calculate. …
– The deviation is of some slight importance only at altitudes below 1,000 meters, which altitudes are of little interest in aerial navigation. The simplicity of the formula largely compensates this inconvenience.
• The above quotation is from the paper by Gregg (1920). The early motivations for this simplified model were evidently the calibration of aneroid altimeters for aircraft, and the construction of firing tables for long-range artillery, where air resistance is important.
• Unfortunately, it is precisely the inaccurate region below 1000 m that is most important for refraction near the horizon.
However, the Toussaint lapse rate, which Gregg calls “arbitrary”, is now embodied in so many altimeters that it cannot be altered: all revisions of the Standard Atmosphere have preserved it.
• Therefore, the Standard Atmosphere is really inappropriate for astronomical refraction calculations. A more realistic model would include the diurnal changes in the boundary layer; but these are still so poorly understood that no satisfactory basis seems to exist for realistic refraction tables near the horizon.
http://mintaka.sdsu.edu/GF/explain/thermal/std_atm.html
International Standard Atmosphere
• The ISA model divides the atmosphere into layers with linear temperature distributions .[2] The other values are computed from basic physical constants and relationships. Thus the standard consists of a table of values at various altitudes, plus some formulas by which those values were derived. For example, at sea level the standard gives a pressure of 1.013 bar and a temperature of 15°C, and an initial lapse rate of -
6.5 °C/km. Above 12km the tabulated temperature is essentially constant. The tabulation continues to
18km where the pressure has fallen to 0.075 bar and the temperature to -56.5 °C.[3][4]
* U.S. Extension to the ICAO Standard Atmosphere, U.S. Government Printing Office, Washington, D.C., 1958.
* U.S. Standard Atmosphere, 1962, U.S. Government Printing Office, Washington, D.C., 1962.
* U.S. Standard Atmosphere Supplements, 1966, U.S. Government Printing Office, Washington, D.C., 1966.
* U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976.
• Energy and its properties
– State functions or exact differentials
– Internal energy vs. enthalpy
• First law of thermodynamics
• Heat/work cycles
– Energy vs. heat/work?
– Adiabatic processes
– Reversible “P-V” work
• Homework problem Ch. 2, Prob. 2
Curry and Webster, Ch. 2 pp. 35-47
Van Ness, Ch. 2
• Difference b/w U and H
– U depends on v
– H depends on p
• Specific heats [a.k.a. heat capacity]
– c v
is constant v
– c p
is constant p
1

• Simplify to
• [Types of processes]
– Constant pressure
– Constant volume
• The First Law of Thermodynamics
• Consequences
Uniqueness of work values
Definition of energy
Conservation of energy
W rev
= − ∫ pdv
Q = 0 ⇒ Δ E = W
Q = 0, W = 0 ⇒ Δ E = 0 ⇒ E
2
= E
1
Impossibility of perpetual motion machine
(Relativity)
Q = 0, Δ E = 0 ⇒ W = 0
Δ E = mc
2
Reversible
Adiabatic
State function
See also 2nd law!
Proof follows..
€
• In addition to changes in internal energy, a system may change
– Potential energy for height change Δ z
– Kinetic energy for velocity change Δ v
– Nuclear energy for mass change Δ m
Δ E = Δ ( , V , T ) + mg Δ z +
1
2 m Δ v 2
− c 2
Δ m = Q + W if Δ E ≈ Δ ( , V , T ) , then Δ ( , V , T ) = Q + W
Van Ness, p. 13
• Expansion work W=-pdV or w=-pdv
– Lifting/rising
– Mixing
– Convergence
• Other kinds of work?
– Electrochemical (e.g. batteries)
2

• Work and heat are path-dependent transfers
– W work
– Q heat
• State functions are unique “states”
– U internal energy
– H enthalpy
– η (also S) entropy
– A Helmholtz free energy
• State functions are exact differentials
Carnot was an engineer in
Napoleon’s defeated army with an interest in engines.
• The efficiency with which work is accomplished in a reversible cyclic process depends only on the temperature of the reservoirs to which heat is transferred
T
1
THE CARNOT CYCLE
Q
1
STEP 1: Expand isothermally and reversibly at T
1
= = RT
1 ln A
P
STEP 2: Expand adiabatically and reversibly
W =
(
−
)
FLUID W
STEP 3: Compress isothermally and reversibly at T 2
=
Q
2
=
RT
2 ln Q
2
T
2
STEP 4: Compress adiabatically and reversibly
W =
(
− T
2
)
Efficiency:
η = 1 −
T
Cold
T
Hot
3

• Work is determined by pathway
1:Add Heat
(isothermally) 2:Adiabatic
3:Lose Heat
(isothermally) 4:Adiabatic
Nikolaus
Otto developed the Otto cycle in
1876.
Rudolf
Diesel developed the Diesel cycle in
1892.
Efficiency:
η = 1 −
T
B
T
A
−
T
C
− T
D
The Otto Cycle works by compressing a mixture of air and fuel in a piston and then igniting the mixture with a spark.
The Diesel Cycle works by compressing air and then adding fuel directly to the piston. The compressed air then combusts the mixture.
The compression ratio of the Diesel Cycle ranges from 14:1 to 25:1, while the Otto Cycle range is significantly lower, from 8:1 to 12:1.
Efficiency:
η =
1
−
1
γ


T
B
T
A
− T
C
−
T
D


γ =
5
3 for monatomic ideal gas
3:Lose Heat
(isothermally)
2:Adiabatic
4:Adiabatic
1:Add Heat
(isothermally)
€ c p
≡
 ∂ h

 ∂ T


 p dh
= dT
=
 ∂ h

 ∂ T


 v
Reversible mass is conserved
Ideal Gas
Adiabatic thick walls
Frictionless
Low P,
Low T
First Law
Internal Energy
Δ u = Q + W
Δ u = c v dT
Reversible, Adiabatic T
2
T
1
=

P
2

 P
1

R c

 p
W = − pdv p
1 v
1
T
1
Q = 0
= R = p
2 v
2
T
2
€
4

Reversible mass is conserved grain of sand
W rev
= − pdv
Frictionless
€
• Always at or infinitesimally close to equilibrium
• Infinitesimally small steps
• Infinite number of steps
• Each step can be reversed with infinitesimal force
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