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slide 1Physics 1401 - L 20 Frank Sciulli
To Comel Heat capacity
(absorption)uSpecific heat
l phase transitionsl Heat and Workl 1st law of
thermodynamicsl heat transfer
u conductionu convectionu radiation
l Kinetic Theory of Gases
Heat and Temperature
So Farl Temperature vs
Heatl Measuring
temperaturel Temperature
scales and absolute zero
l Thermal expansion
today
slide 2Physics 1401 - L 20 Frank Sciulli
Expansion with Temperature
Molecular explanation: u as temperature of solid increases, molecules move faster around
average locations further from each other (expansion)u High enough temp (kinetic energy), bonds holding atoms in lattice
break (liquid), but forces still hold atoms nearby (not fixed average location like solid) and more temp makes for greater separations (expansion)
u Raise temp even higher, bonds completely break --- gas ---more temp, more energy (expansion)
Solid Liquid Gas
review
slide 3Physics 1401 - L 20 Frank Sciulli
Absolute Zero Temperaturel Fixed amount of gas and
fixed volume of bulb l find empirically pressure
and temperature proportional to each other
T Cp=
l extrapolate to lower temperatures
l all gases intercept at T0=-273.15oC = absolute zero
review
slide 4Physics 1401 - L 20 Frank Sciulli
Temperature Scales and Expansion
;;
L L TA A TV V T
α
γ γ α
β β α
∆ = ∆
∆ ≡ ∆ =
∆ ≡ ∆ =
23
l Three temperature scales l Mass of any system stays
constant (until Relativitistic Quant Mech)
l Empirically as temperature increases, most materials increase their volume
l Coefficient of linear expansion, α (small)
review
slide 5Physics 1401 - L 20 Frank Sciulli
Dangers - Diff Expansion
l Pour boiling water into beaker - inside expands faster than outside
l train tracks laid too close together
slide 6Physics 1401 - L 20 Frank Sciulli
Expansion Issues
l Expansion of solids creates difficultiesl Note real-life solution on bridges, ...
slide 7Physics 1401 - L 20 Frank Sciulli
Special Case of Water
l Note ice density much smalleru ρice=.917 g/cm3 …… phase change
l Lakes and ponds in winter: ice floats, insulates water below; warmest water at bottomu Summer: water coolest at bottom
l Normal=lsystem of fixed mass increases its volume when temperature increaseslDensity normally decreases as T increaseslWater has peculiar property that density increasesbelow T=4oC lWater at the bottom of lakes is often at T=4oC even in winter
slide 8Physics 1401 - L 20 Frank Sciulli
Heat Capacityl System at top in equilibrium with
environmentl System at bottom at lower
temperature. Heat energy, Q, will flow into system and temperature will rise
l For fixed ∆T, amount of heat, Q depends on system type and mass
Q C TQ cm T
≡ ∆
≡ ∆
C = heat capacity
c=specific heat
Note convention: heat added heat removed
><
00
slide 9Physics 1401 - L 20 Frank Sciulli
Specific Heats l Measure of how much heat
energy it takes to raise unit mass one degree temperature
l Examples in table 19-3l Note units and examples: water
and copper or iron (more typical)u cw=1 cal/g-oC = 1 Btu/lb-oFu cw=4190 J/kg-Ku cCu=386 J/kg-Ku cFe=460 J/kg-K
l Molar specific heat multiplies by the number of kg in a mole = .001 × molecular wtu Note similar values-elements in tableu 1 mole has 6.02 1023molecules (see
later)
Q cm T≡ ∆
Again, notice that water is different!!
slide 10Physics 1401 - L 20 Frank Sciulli
Heat changing temperatureSample prob 19-4
l Beaker: Cb Til Water: mw Ti cwl Copper: mc Tc ccl Drop copper in waterl What is final temp, Tf?l Intuitively, Ti < Tf < Tc
( )( )( ) ( )
( )
w w w if
ib b f
c c c cf
w cb
c c c w w ibf
c c w wb
Q c m T TQ C T TQ c m T TQ Q Q
c mT C c m TTc m C c m
= −
= −
= − <
+ + =
+ +=
+ +
00
Cu
Q C TQ cm T
≡ ∆
≡ ∆
Tf
slide 11Physics 1401 - L 20 Frank Sciulli
Changing phases … heat required
l To go from more ordered state to less ordered state requires adding energy
l This added energy supplies the necessary potential energy of the bonding (or breaksthe atomic bonds holding atoms together)
Solid Liquid Gas
slide 12Physics 1401 - L 20 Frank Sciulli
Heat of transformationl Materials can exist in different
“states” or phases. Typicallyu Solid → liguid at T=melting pointu Liquid → gas at T=boiling pointu Example water
l Go from most ordered (solid) to least ordered (gas) as heat added
l Certain amount of heat required to change the stateu Heat of fusion, LF….solid to liquidu Heat of vaporization, LV……liq to gas
l See table 19-4 in text for examplesu Most notable: WATER
oLF= 333 kJ/kgoLv=2256 kJ/kg
can be or F V
Q mLL L L
=
Gallium 30C
slide 13Physics 1401 - L 20 Frank Sciulli
State or Phase Changes
Solid Liquid Gas
Motions of
Molecules
l If forces holding together a solid are more tightly bound, might expectu Melting temp higheru Expansion rate with
temperature slowerl Correlation should exist!
Correlation exists for
most metals
slide 14Physics 1401 - L 20 Frank Sciulli
Heat changing the phase of water
l Water molecules vs ice molecules (avg locations)
l Behavior of 1 kg water vs temp
fusion vaporization
80 kcal333 kJ
539 kcal2256 kJ
00
100T (oC)
slide 15Physics 1401 - L 20 Frank Sciulli
Problem 46 (not assigned)An insulated Thermos contains
130 cm3 of hot coffee, at a temperature of 80.0°C. You put in a 12.0 g ice cube at its melting point to cool the coffee.
By how many degrees has your coffee cooled once the ice has melted? Treat the coffee as though it were pure water and neglect energy transfers with the environment.
Ice
slide 16Physics 1401 - L 20 Frank Sciulli
Back to Gases: Heat Doing Work … Work depends on how gas expands
dW F ds pA dsdW p dV
r r=
=
• =
l Note that heat (Q ) supplied to gas has a portion (W ) doing work
l Work is area under p-V curvel direction of process (sign W)
determines whether work done byor on the system
System of gas above: i→fu insulated from outside world except
reservoiru reservoir supplies heat at rate
determined by knobu as piston on top rises, gas expands
(& vice versa)u Can vary pressure and volume (with
temperature and weights)
slide 17Physics 1401 - L 20 Frank Sciulli
First Law of Thermodynamics restricts the possibilities
l First Law of Thermodynamics = Energy Conservation
l Energy Conservation has three contributionsu W = work done (+) by systemu Q = thermal energy (+) added to
systemu Eint = internal energy of system u Eint is a consequence of the system
state (eg,could be function of P,V,T,…)
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 dWi n t = −
slide 18Physics 1401 - L 20 Frank Sciulli
Example processes – see table 19-5
l Adiabatic Q=0l Constant volume W=0l cyclical ∆Eint=0l free expansion Q=W=0
dE dQ dWint = −
slide 19Physics 1401 - L 20 Frank Sciulli
Sample Prob 19-5 work it through
int
kJ/kg
( )f
i
f fV
ifV
Q L m L
W pdV p V V
E Q W
= =
= = −
∆ = −
∫
2256
. . .
. in
Q kJ MJW J MJE Q W
MJ
= =
= × =
∆ = −
=
5
2256 2 261 69 10 0 17
2 09
l 1 kg boiling water at 1 atmosphere (1.01 105 Pa)
l vol of water (10-3 m3) changes to steam (1.671 m3)
l What changes & how much?
slide 20Physics 1401 - L 20 Frank Sciulli
Processes and Cycles
l In the above processes, work is done, and the gas state might also change u if Eint is different at i than at f
l Cycles are processes that return the gas to the starting point, have the gas end up in the same state as initially.u Note that, even though the gas is in the same state,
net work can be done in the cycleu Some of the heat energy is converted to work
slide 21Physics 1401 - L 20 Frank Sciulli
Problem 49 (not assigned)A sample of gas expands
from 1.0 m3 to 4.0 m3 while its pressure decreases from 40 Pa to 10 Pa.
How much work is done by the gas if its pressure changes with volume via each of the three paths shown in the p-V diagram in figure ?
A
B
C
W JouleW JoulesW Joules
=
=
=
120
75
30
slide 22Physics 1401 - L 20 Frank Sciulli
Problem 51 (not assigned)Gas within a closed
chamber undergoes the cycle shown in the p-V diagram of Fig. 19-36 .
Calculate the net energy added to the system as heat during one complete cycle.
Work do
ne by
system
(positi
ve)
Work done on system(negative)
No
work
don
e
Q=-30 Joules (system lost heat)
slide 23Physics 1401 - L 20 Frank Sciulli
Processes – return later
1. Adiabatic Q=02. Constant volume W=03. cyclical ∆Eint=04. free expansion Q=W=0
intdE dQ dW dQ pdV= − = −
l In chapters 20 and 21, we will discuss these more fully
l Also use processes to understand “ideal” and real gases
l And to understand “entropy”
slide 24Physics 1401 - L 20 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 25Physics 1401 - L 20 Frank Sciulli
Heat and Temperature So Far
l 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
thermodynamicsl heat transfer
To Comel heat transfer
u conductionu convectionu Radiation
u Processes and Cyclesl Kinetic Theory of
Gasesu Where gas properties
come fromu …
u Entropy …
![Ch 5: ARIMA model · 1.1 Non-Stationary Data [ToC] Dow Jones Index From Aug. 28 to Dec. 18, 1972 l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l](https://img.pdfslide.net/doc/110x75/5ee0213ead6a402d666b5f8b/ch-5-arima-model-11-non-stationary-data-toc-dow-jones-index-from-aug-28-to.jpg)
