Heat and Temperature
So Far
l Temperature vs Heat
l Measuring temperature
l Temperature scales and absolute zero
l thermal expansion
l Heat capacity (absorption)
u Specific heat
l phase transitions
l Heat and Work
l 1st law of
thermodynamics
Coming
l
Ideal Gas Law
l
heat transfer
u conduction
u convection
u radiation
l
Kinetic Theory of Gases
l
Entropy …
today
Differential Expansion examples and demos
Thermostat
L L T α
∆ = ∆
First Law of Thermodynamics
l
Energy Conservation has three contributions
u W = work done (+) by system
u Q = thermal energy (+) added to system
u Eint = internal energy of system
system = gas
Heat energy added to the system less the work done by the system equals the increase in system's internal energy
dE
int= dQ − dW
review
Empirical Behavior of Ideal Gases in P, T, V
l 17 – 18th Centuries … Experiments giving empirical behavior of gases in terms of volume, pressure, temperature, and mass of gas
l Keep other quantities fixed … and …
pV = nRT
1 Boyle's Law Charles Law
Gay-Lussac Law
where = mass of gas V P
V T P T
V m m
∝
∝
∝
∝
l We put them
together and express as the Ideal Gas Law
l n=#of moles
Ideal Gas Law
(will discuss in detail next time)
l Units
u R = 8.31 J/(mol-K) = kNA
u k = 1.38 10-23 J/K (Boltzmann constant)
u N = 6.02 1023 (Avogadro’s number)
pV = nRT
= mass
molecu # moles
molecules
# molecules
lar o
. m
w le t
A
A
A
R
n
pV nRT nN T
N pV Nk
N N
T
=
= =
= =
=
equivalent
Problem 20-14 (not assigned)
Cyclic process starts at (a) with T=200K
u How many moles?
u Temperatures at (b) and (c)
u Net energy added to gas as heat
2 5 10 1 03
8 31 200 1 50
a a a
n p V
RT n
pV nRT
( . )( . ) ( . )( ) . moles
= = ×
=
=
7 5 3
200 1800
2 5 1
a b b
b a a
T T p V K
p V
( . )( )
( )
( . )( )
= = =
1 3
2
2 0 5000
5000 Q W
m Pa
J
area of triangle
( . )( )
= =
=
=
Heat Transfer
3 principal mechanisms
l
Conduction
u Heat transfer through material
u At microscopic level, thermal agitation of molecules causes adjacent molecules to also move more rapidly
l
Convection
u Occurs with fluids
u Has macroscopic cause: hotter fluid has
different (typically lower) density and moves up
l
Radiation
u NEW: completely different from those above
Conduction
l Heat flows from hot reservoir to cold thru sample of thickness L.
l Amount heat (Q) depends on temperatures of two reservoirs and properties of sample (L, A, and k)
l k = thermal conductivity property of sample type
l Pcond = heat per unit time conducted through sample
C cond H
T T
P Q kA
t L
≡ = −
Examples of Thermal Conductivity
l
Heat is not a fluid
l
Units for k : W/(m • K)
l
Large range of thermal conductivities
u See table 19-6 in text
u Metals typically 10 – 500 W/(m • K)
u Insulators (polyurethane, …, window glass) typically .01 – 1 W/(m • K)
u Gases Low, typically .02 - .2 W/(m • K)
2 1
cond
T T
P Q k A
t L
≡ = −
l
k is thermal conductivity
l Charactistic of specific material
Heat vs Solute Flow: Both are Diffusion
2 1
cond
T T
P Q kA
t L
≡ = −
2 1
C C
S A
t κ L −
=
l Heat flow equation represents
u diffusion of heat energy
l Looks similar to rule
governing rate of solute flow between two
concentrations
u diffusion of molecules
u Fick’s Law of Diffusion
u Diffusion constant(m2/s)
l Many instance of diffusion in nature
u eg. electric current in metals is carried by the same thing carrying heat
àelectrons
Multiple insulators
l Above for single conductor
l k in W/(m-K)
l Two insulators
l Same heat conduction in 1,2
l Solve for TX
l
Note important parameter is L/k
l
R value ≡ L/k
l
U.S. stores, R in
u ft2-oF-h/Btu
C / C
H H
cond Q T T T T
P kA A
t L L k
− −
≡ = =
( )
Do some algebra !!!
X X C
cond H
co C
nd H
kL
T T T T
k A k A
P L L
T T
P Q A
t
− −
= =
=
= −
∑
2 1
2 1
Convection
l
Complex phenomenon
u hotter fluid has
different (typically lower) density and moves to different level
u air in pix
l
Important and most familiar of heat
transfer mechanisms
Convection and Weather
l Water, with high specific heat,
maintains temperature longer
l Land gets hot faster, air rises inland and falls out on the water
l Breeze from the ocean
eagle rising on thermal
Stefan-Boltzmann Radiation
l All bodies radiate electromagnetic energy by virtue of the temperature of the body
l All bodies absorb electromagnetic energy by virtue of the temperature of the environment
l Energy radiated per unit time determined by universal law
u Measured in 19th cent: disagreed with calculations
u Completely correct form requires Quantum Mechanics
4 4
8 2 4
4 4
5 67 10
rad abs env
net env
P AT P AT
W m K
P A T T
σε σε
σ
σε
. /( )
( )
−
= =
= ×
= −
l ε is the emissivity of the body: 0 < ε < 1
l ε = 1 à black body … Note same ε for emit and absorb
Stefan-
Boltzmann
Law
Earth-Sun System
Sun radiates like a black body
(R=7×108m) with
surface temperature of about 5800K
l Earth (at R0 = 1.50 × 1011 m) intercepts tiny fraction of this energy, but enough (with small heat generated inside earth) to keep it at about 300K
l Energy hitting normally and
absorbed by Earth is called the Solar constant= S = 1350 W/m2
( )
( )
( )
A
o
A
A
A
dQ dQ
dt R dt
dQ W dt
dQ W
dt m
f
f S
dQ
1 2
incepted emitted
by Sun by Earth
26
1 incepted 11 2
by Earth
1 2
incepted by Earth
1
1
3.9 10
1.50 10 m 5570
fraction of Sun's energy hitting earth absorbed
π π
=
= ×
×
=
=
dt
1350 .245 5570 =
( ) ( )
4
18 2 8 3 4
26
6.09 10 (5.67 10 ) 5.8 10 3.9 10
dQ A T dt
m W σ
−
=
= × × ×
= ×
Earth Temperature
l If Earth re-emits all energy it absorbs
u estimate average Earth temperature
u Assume earth is uniform, uncomplicated black body at uniform temperature … clearly not really true
re
rays from Sun
( )
( )
e e
e
e
r r
dQ r S
dt
dQ r T
dt
S S
T
T T
2 2
2 absorbed
by Earth
2 4
emitted by Earth
4 4 4
2
4 8 2 4
4
4
1350 W/m
4 5.67 10 W/m -K 278 K 5 C:
π π
π
π σ
σ σ
−
=
=
= =
= × ×
=
If these are equal
Not too bad but … Limits in model …
Radiation Examples
l Familiar examples
l radiation and
wavelength (color)
u Reminders ……….
“false color” photo
l The color of light is consequence of its wavelength( λ)
l Visible light only in
restricted range around
Effect of emissivity
l Check out same amount of ice on
u sidewalk
u asphalt
4 4
net env
P = σε ( A T − T )
asphalt sidewalk
Radiation and wavelength
l Areas under curves ∝ total energy (Stefan Boltzmann Law)
l Also, peak wavelength found to depend on temperature
u λpeakT=constant
l Hot bodies
u radiate more energy
u radiate a larger fraction of energy at short wavelengths (away from red -> violet)
l Warm bodies
u Much of heat energy at longer wavelengths
u red, infrared and beyond
l Classical physics required EM radiation (wave) to have energy in equilibrium with body
l 19th century physics predicted that all bodies at finite temp (K) must radiate
culture
Important 19
thCentury Clue – Beginning of 20
thCentury physics
l Classical Physics predicted the
dependence of emitted radiation on wavelength (color)
u But it was wrong at short wavelengths (ie infinite flux there – prediction of integrated flux also infinite)
u Planck “fixed” the problem by
inventing model of atomic oscillators inside the matter of the body – that could not radiate the short
wavelengths
l Einstein resolved the problem by
postulating that the electromagnetic radiation intrinsically comes in fixed units dependent on frequency
u Called ‘quanta’ or ‘photons (γ)’
u Eγ = hf = hc/λ (h = Planck’s const.)
u Predicted the “photoelectric effect” … corroborated by experiment
Empirical dependence Classical prediction
l Note that classical theory predicts ∞ energy (integral)
l Quantum Mechanics predicts finite (and correct) total
Prad = σAT 4
culture
Greenhouse Effect
“blackbody” at 5800K
“blackbody” at 300K
IR wavelengths absorbed in CO2 and other gases (and re-emitted)
l Earth basks in
radiation from Sun
l Radiates with much lower temperature
l Complicated by
u Layers of atmosphere
u Nonuniform heating
culture
Heat and Temperature
Covered
l
specific heats
l
phase transitions
l
Heat and Work
l
1st law of thermodynamics
l
heat transfer
u conduction
u convection
u radiation
Coming Up
l
Kinetic Theory of Gases
today
