heat and temperature - nevis laboratories · heat and temperature so far l temperature vs heat ......
TRANSCRIPT
slide 1Physics 1401 - L 21 Frank Sciulli
Heat and Temperature
So Farl Temperature vs Heatl Measuring temperaturel Temperature scales and
absolute zerol thermal expansionl Heat capacity
(absorption)u Specific heat
l phase transitionsl Heat and Workl 1st law of
thermodynamics
Comingl Ideal Gas Lawl heat transfer
u conductionu convectionu radiation
l Kinetic Theory of Gases
l Entropy …
today
slide 2Physics 1401 - L 21 Frank Sciulli
Differential Expansion examples and demos
Thermostat
L L Tα∆ = ∆
slide 3Physics 1401 - L 21 Frank Sciulli
First Law of Thermodynamics
l Energy Conservation has three contributionsuW = work done (+) by systemuQ = thermal energy (+) added
to systemu 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 dQ dWint = −
review
slide 4Physics 1401 - L 21 Frank Sciulli
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
VP
V TP TV m m
∝
∝∝
∝l We put them together and express as the Ideal Gas Lawl n=#of molesl R= gas constant
slide 5Physics 1401 - L 21 Frank Sciulli
Ideal Gas Law (will discuss in detail next time)
l Unitsu R = 8.31 J/(mol-K) = kNAu k = 1.38 10-23 J/K (Boltzmann constant)u NA= 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 TN
pV Nk
N N
T
=
= =
= =
=
equiva
lent
slide 6Physics 1401 - L 21 Frank Sciulli
Problem 20-14 (not assigned)Cyclic process starts at (a)
with T=200KuHow many moles?u Temperatures at (b) and (c)uNet energy added to gas as
heat
32 5 10 1 08 31 200
1 50
a a
a
p VnRT
n
pV nRT( . )( . )
( . )( ). moles
×= =
=
=
7 5 3200 18002 5 1
b bab
a a
p VT T KpV
( . )( )( )( . )( )
= = =
312 2 0 50005000
Q Wm PaJ
area of triangle( . )( )
= =
==
slide 7Physics 1401 - L 21 Frank Sciulli
Heat Transfer 3 principal mechanisms
l ConductionuHeat transfer through materialuAt microscopic level, thermal agitation of
molecules causes adjacent molecules to also move more rapidly
l ConvectionuOccurs with fluidsuHas macroscopic cause: hotter fluid has
different (typically lower) density and moves up l RadiationuNEW: completely different from those above
slide 8Physics 1401 - L 21 Frank Sciulli
Conductionl 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
CHcond
T TQP kAt L
−≡ =
slide 9Physics 1401 - L 21 Frank Sciulli
Examples of Thermal Conductivity
l Heat is not a fluidl Units for k : W/(m • K)l Large range of thermal conductivitiesu See table 19-6 in textuMetals 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 1cond
T TQP kAt L
−≡ =
l k is thermal conductivityl Charactistic of specific material
slide 10Physics 1401 - L 21 Frank Sciulli
Heat vs Solute Flow: Both are Diffusion
2 1cond
T TQP kAt L
−≡ =
2 1C CS At L
κ−
=
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 moleculesu Fick’s Law of Diffusionu Diffusion constant(m2/s)
l Many instance of diffusion in natureu eg. electric current in
metals is carried by the same thing carrying heat
àelectrons
slide 11Physics 1401 - L 21 Frank Sciulli
Multiple insulators
l Above for single conductorl k in W/(m-K)l Two insulatorsl Same heat conduction in 1,2l Solve for TX
l Note important parameter is L/k
l R value ≡ L/kl U.S. stores, R inu ft2-oF-h/Btu
/C CH H
condQ T T T TP kA At L L k
− −≡ = =
( )
Do some algebra !!!
X X CHcond
coC
ndH
Lk
T T T Tk A kAPL L
T TQP At
− −= =
==−
∑
2 12 1
slide 12Physics 1401 - L 21 Frank Sciulli
Convection
l Complex phenomenonu 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
slide 13Physics 1401 - L 21 Frank Sciulli
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
slide 14Physics 1401 - L 21 Frank Sciulli
Stefan-Boltzmann Radiationl 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 lawu Measured in 19th cent: disagreed with calculationsu Completely correct form requires Quantum Mechanics
4 4
8 2 4
4 4
5 67 10envrad abs
net env
P AT P ATW 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-BoltzmannLaw
slide 15Physics 1401 - L 21 Frank Sciulli
Earth-Sun SystemSun 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
( )( )
( )
Ao
A
A
A
dQ dQdt R dt
WdQdt
dQ Wdt m
f
SfdQ
12incepted emitted
by Sunby Earth
261
211inceptedby Earth
12incepted
by Earth
1
1
3.9 10
1.50 10 m
5570
fraction of Sun's energy hitting earth absorbed
π
π
=
× = ×
=
=
dt inceptedby Earth
1350 .2455570
=
( ) ( )
4
418 2 8 3
26
6.09 10 (5.67 10 ) 5.8 10
3.9 10
dQ A Tdt
m
W
σ
−
=
= × × ×
= ×
slide 16Physics 1401 - L 21 Frank Sciulli
Earth Temperaturel If Earth re-emits all energy it absorbs
u estimate average Earth temperatureu Assume earth is uniform, uncomplicated black body at
uniform temperature … clearly not really true
re
rays from Sun ( )
( )
e
e
e
e
rr
dQ r Sdt
dQ r Tdt
S ST
T
T
2
2
2absorbedby Earth
2 4emittedby Earth
44 4
24
8 2 4
4
41350 W/m
4 5.67 10 W/m -K278 K 5 C∼
ππ
π
π σ
σ σ
−
=
=
= =
=× ×
=
If these are equal
Not too bad but …Limits in model …
slide 17Physics 1401 - L 21 Frank Sciulli
Radiation Examples
l Familiar examplesl radiation and
wavelength (color)u Reminders ………………….
“false color” photol The color of light is consequence of its wavelength( λ)
l Visible light only in restricted range around λ~500 nm
slide 18Physics 1401 - L 21 Frank Sciulli
Effect of emissivity
l Check out same amount of ice onu sidewalku asphalt
4 4net envP A T Tσε ( )= −
asphaltsidewalk
slide 19Physics 1401 - L 21 Frank Sciulli
Radiation and wavelength
l Areas under curves ∝ total energy (Stefan Boltzmann Law)
l Also, peak wavelength found to depend on temperatureu λpeakT=constant
l Hot bodies u radiate more energyu radiate a larger fraction of
energy at short wavelengths (away from red -> violet)
l Warm bodiesu 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
slide 20Physics 1401 - L 21 Frank Sciulli
Important 19th Century Clue –Beginning of 20th Century 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 frequencyu 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
radP ATσ= 4
culture
slide 21Physics 1401 - L 21 Frank Sciulli
Greenhouse Effect“blackbody” at 5800K
“blackbody” at 300K
IR wavelengths absorbed in CO2and other gases (and re-emitted)
l Earth basks in radiation from Sun
l Radiates with much lower temperature
l Complicated byu Layers of atmosphereu Nonuniform heating u …
culture
slide 22Physics 1401 - L 21 Frank Sciulli
Heat and Temperature
Coveredl specific heatsl phase transitionsl Heat and Workl 1st law of thermodynamicsl heat transfer
u conductionu convectionu radiation
Coming Upl Kinetic Theory of Gases
today