Boşluktan Taneciklere Yolculuk

Boşluktan Taneciklere
Yolculuk
Veysi Erkcan Özcan
22 Haziran 2015
Hedef
Madde ve boşluğun, uzay ve zamanın antik
felsefecilerden 21. yüzyıla uzanan tarihçesi.
Maddenin kütlesinin evreni saran alanlarla ilişkisi.
Kuantum fiziği ve özel göreliliğe giriş.
Böylesi soruların yanıtlanmasında çağımızda
kullanılan yöntemlerin tanıtılması, örneğin
CERN’deki Büyük Hadron Çarpıştırıcısı ve benzeri
hızlandırıcıların teknolojisi.
Higgs bozonu ve diğer temel parçacıklar için
çıkılan define avı.
2
Nasıl Öğrenmeli?
Okuma tavsiyesi: “Two Approaches to
Learning Physics”, David Hammer, Physics
Teacher, Aralık 1989.
5 sayfa, 10 dakikalık bir okuma (maalesef
İngilizce).
“I look at all those formulas...”
“I am trying to imagine…”
Elinizi kirletmeden olmaz!
3
Particle Phys.
Nuclear Phys.
Cosmology
Astronomy
Condensed Matter P.
Geophysics
Chemistry-Biology
Mechanics
Astrophysics
Zm
Fizik = Doğayı Anlama
Ym
Insan gozu en ufak neyi gorebilir? Baska yer belirtecleri olmadan hangi uzakliklari tahmin edebilir? 10^-4’den 10^4
metreye.
Legolas’in gozleri.
Bizim gozumuz arastirdigimiz olcegin cok azini aliyor. Diger tum duyularimiz da. O zaman arastirdigimizda ortaya
cikanlar bize tuhaf gelebilir.
Ama ne kadar ilginctir ki, insan dillerinin ifade etmekte yetersiz kalabildigi kavramlari cozumleyecek ve tum bu
skaladaki olgulari anlatabilecek matematik diye bir dil icat edebiliyoruz. Insan beyninin bu cesit bir becerisi olmasi
ilginc degil mi? => Wigner.
17 denklem: 7-8’i calculus uzerine. Bunu ogrenmeden olmaz.
Guzel denklem ne demek? (1) Zor olmali, zanaat. (2) Sade, estetik olmali.
Euler özdeşliği, 5 ana sabiti birbirine bagliyor.
e sayisi nedir? bilesik faizi tartisalim. 12 ay yuzde 10 mu daha iyi, yoksa iki kere 6 ay yuzde 5 mi?
1.05’in karesi mi buyuktur, 1.10 mu? Iki tarafi da 100x100 ile carpalim. 105x105 mi buyuktur, yoksa
110x100 mu? Elimizde belli uzunlukta cit olsun, o citlerle tarlamizi belirleyeceksek, hangi cesit dikdortgen en
cok alani verir? Cevabin kare cikmasi neden? Seklin “ozel” olmasi bize ne verir? a*(210-a) nerede max olur?
Parabol cizebiliriz. (1+x)^2 = 1+2x+x^2
Sonsuz kisa vadede sonsuz bilesik faiz yaparsak ne kadar kazaniriz? e^0.10 = 1.10517
(Limit ve convergence’a geri gelmek olabilir?)
5
graph buyemYazFizik {
node [style="setlinewidth(0)"];
sr [label="ozelGörelilik"]; gr [label="genelGorelilik"]; gravity [label=yercekimi];
higgs; mass [label="kütle"]; field [label=alan]; sb [label="simetriKirilmasi"];
qft [label="kuantumAlani"];
light [label=isik]; wave [label=dalga]; EM [label="elektromanyetizmaMaxwell"];
mechanics [label=mekanik]; optics [label=optik];
diffraction [label=kirinim]; MM [label=MichelsonMorley];
fma [label="F=ma"]; inertia [label=eylemsizlik];
higgs -- mass;
qft -- field;
higgs -- sb;
higgs -- qft;
Einstein -- sr;
gravity -- mass;
field -- Faraday;
Faraday -- EM;
EM -- light;
light -- optics;
light -- wave;
EM -- wave;
wave -- mechanics;
wave -- diffraction;
optics -- MM;
diffraction -- MM;
mass -- inertia;
inertia -- Galileo;
Galileo -- Kepler;
Kepler -- Newton;
Newton -- mechanics;
Kepler -- epicycle;
fma -- inertia;
Newton -- gravity;
gravity -- gr;
gr -- sr;
Newton -- fma;
Einstein -- light;
}
6
Dünyayı değiştiren 17
denklem
7
Dünyayı değiştiren 17
denklem
⑇
✓
✓⑇
⑇
✓
✓
✓
✓
101 102 201 202
7
Nasıl?
“Kuramınızın ne kadar da güzel
olduğu, sizin ne kadar da zeki
olduğunuz falan farketmez. Eğer
deney ile uyuşmuyorsa, yanlıştır.”
- Richard Feynman (1965 Nobel F.)
“Matematiğin fen bilimlerindeki
inanılmaz verimi/başarısı” - Eugene
Wigner (1963 Nobel F.)
“…, denklemlerinizin güzellik
barındırması, onların deneye
uyumlu olmasından daha
önemlidir…”
- Paul Dirac (1933 Nobel F.)
Ölçüm (gözlem, deney) + matematik model (kuram).
8
Gerçek Güzellik!
Bunun için biraz
sabır gerekiyor.
9
Pisagor Fayans Kaplama
10
Pisagor Fayans Kaplama
10
1845
Mechanical Equivalent of Heat
Mechanical
equivalent of heat
11
Von Mayer
independently got
the same result.
Phase Diagram
•
•
•
•
Tube data: height = 580mm, diameter = 105mm, m(CO2) = 2kg
Volume = πr2h = 5.0 L
n = 2kg / (12+16+16 g/mol) = 45 mol
If C02 were only in gas form, the pressure in the can at room
temperature would be:
• P = nRT/V = 22.1 MPa = 218 atm
• From the phase diagram, we see that at that pressure & room
temperature, it is not possible to have C02 only in gas form.
• Actually, the vapor pressure at 25°C is about 63atm.
12
Consider a CO2 filled
fire-extinguisher tube.
CO2 is mostly in liquid
form initially. When it is
activated with the
opening of the tube, it
starts boiling and
maintains an essentially
constant gas pressure
significantly above
1atm. This goes on until
almost all of the liquid
CO2 turns into gas.
Joseph Black
Discovers and names “latent
heat”
Talks about “heat capacity” and
points out that different
substances have different
“specific heat”s.
Also: One of the “discovers” of
carbon dioxide.
13
1750s
(≤1762)
Mpemba Effect
In 2013, Royal Society of
Chemistry held a
competition.
Nikola Bregović’s
explanation:
1969 Phys. Educ. 4 172
Convection and
supercooling were the
reasons of the effect.
14
Heat Capacity Ratio
molar specific heat under
constant pressure
molar specific heat when
volume is kept constant
For monoatomic ideal gases it is
about: 1+2/3 = 5/3
For diatomic ideal gases around room
temperature it is about: 1+2/5 = 7/5
f = number of degrees of freedom (ie.
number of parameters to characterise
the status of a given molecule)
15
Monatomic Gas In a Box
px =
N = number of molecules
2mvx
2mvx
px / t =
=
2L/vx
< fx >=
mvx2 /L
P = Fonwall /L2 = N m < vx2 > /L3
< vx2 >=< vy2 >=< vz2 >=< v 2 > /3
P L3 = N < mv 2 > /3
PV =
PV =
16
2
1
N < mv 2 >
3
2
2
N < KE >= N kB T
3
Monatomic Gas In a Box
px =
N = number of molecules
2mvx
2mvx
px / t =
=
2L/vx
< fx >=
mvx2 /L
P = Fonwall /L2 = N m < vx2 > /L3
< vx2 >=< vy2 >=< vz2 >=< v 2 > /3
P L3 = N < mv 2 > /3
PV =
PV =
CV dT = dQ
CV = d(NA < KE >)/dT =
< KE >=
3
R
2
16
2
1
N < mv 2 >
3
2
2
N < KE >= N kB T
3
3
kB T
2
Temperature is really
the name of the
average kinetic energy
of the molecules!
Equipartition Theorem
In 3D, we found the average kinetic energy of a monatomic
2
2
2
molecule as 3kBT/2. The factor 3 came from vx , vy and vz .
If we were in a 2D universe, we would find the average kinetic
energy as 2kBT/2, so the cV would be R.
For a diatomic gas in 3D space,
energy of the gas molecules
would not just be the
tranlational KE. It would also
be rotational (2 degrees of
freedom) and vibrational (2
additional degrees of freedom).
So cV becomes (3+2+2)R/2 =
7R/2. γ=9/7
17
Equipartition = equal division
of energy amongst different
degrees of freedom
Heat Engine / Heat Pump
First law of thermodynamics, ie. conservation of energy: QH=W+QC
efficiency of heat engine: ε=W/QH
coefficient of performance of a heat pump: COP=Qrequired/W
Heater: COP=QH/W (mathematically equal to 1/ε)
Refrigator or air-conditioner: COP=QC/W
18
A Simple “Hypothetical” Engine
(c) Calculate
the efficiency
of the engine.
19
Efficiency of Human “Engine”
Report from the “Physics at the
British Association”, published in
Nature, September 29, 1898!
“…the law of conservation of
energy is found to be true…”
“ratio of mechanical work by a
man to the total energy supplied
to him, …, is usually about 7%,
and may be as high as 10%…”
“higher than perfect heatengine”
For more information (like the
energy content of feces, the
calories of food stuffs, and how
the apparatus works), see “The
Elements of the Science of
Nutrition”.
20
Atwater-Rosa Respiration Calorimeter
“The apparatus represented technical perfection, as was
evidenced by the fact that when a measured amount of
heat was generated by an electric current within the box it
was determined as 100.01 per cent, of the actual value. This
test of accuracy is called an electric check. Also, when a
known quantity of alcohol was oxidized, the carbon dioxid
recovered amounted to 99.8 per cent, and the heat to 99.9
per cent, of the theoretic value.” - From The Elements of the
Science of Nutrition, 3rd edition (1917), by Graham Lusk.
Read more: https://archive.org/stream/
elementsscience02luskgoog#page/n63/mode/2up
Figure from: http://chestofbooks.com/health/
nutrition/Science/Principle-Of-The-AtwaterRosa-Benedict-Respiration-Calorimeters.html
21
Carnot
1824
Carnot’s theorem: for heat engines between two
heat reservoirs, the efficiency: ε ≤ 1 − TC/TH.
Max eff. when reversible engine <=> Carnot cycle.
22
Carnot Cycle
PV=constant
reversible adiabatic
PVγ=constant
PVγ=constant
reversible adiabatic
PV=constant
This is an idealised cycle, it would
take infinite time to complete.
23
Clausius
1850-1865
Common form of 2nd law of thermodynamics: “Heat can never pass
from a colder to a warmer body without some other change,
connected therewith, occurring at the same time.”
Definition of “change in entropy” as a thermodynamic quantity. ΔS
over a full reversible cycle is zero.
24
Reversible Engine
Consider a reversible heat engine (ex. Carnot cycle)
Note: Idealization, no real heat engine is
completely reversible.
We can run it backwards as a heat pump.
If two copies are running together in “opposite
directions”, zero net flow of energy.
Imagine a hypothetical heat engine with higher
efficiency connected to our reversible engine.
ε=W/Qh > εr=W/QhC
QhC > Qh
Given the conservation of energy, this means we
are extracting energy from the cold reservoir and
heating up the hot reservoir. ==> Not allowed! ==>
No engine can have higher efficiency than Carnot’s.
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