Intro Physics II
Administrivia
Intro Physics II Physics 11b
! !
Web quizzes start Monday Regular office hours this week !
Phases Thermal Expansion First Law
!
!
Bonus office hours this week (no section) !
!
!
!
Goals for today
Temperature
!
!
!
Scale defined using triple point of water and absolute 0 Use ideal gas thermometer to label temperature of everything else Remember, we went through the whole song and dance so that ! We have an unambiguous way to assign a temperature to any object !
!
!
p T = 273.16 lim p3 → 0 p 3
!
!
!
M 2 P (v ) = 4π v e 2 RT
Describes probability of different molecular speeds in the gas
2
− Mv 2 RT
2
v
∫
may not equal !Average KE is given by ! !
!
=< ½ Not ½ m2
½
m
Result ! !
=3/2 RT m/M = 3/2 kBT ! kB=Rm/M=R/NA
!
Specific Heat
Heat, work, and energy Expansions
Equations of State !
3/2
2
4 − C ve v P (v )dv 4π 2π =∫ = ∫ 1 P ( v )dv 2
mv2>=
Thermal properties of matter
Equation of state
!Average value of v may not equal vmax
Long tail to right skews average high
!
!
Some comments on distribution
!2
1st Law
! 3 2
Sublimation Critical temperature Water
!
Meaning: it’s physics
Maxwell Distribution
!
Equations of State Phases !
Theoretically tractable with only Newton’s Laws No subject to our intuition’s ! Fallibility ! Circularity ! Imprecision
!
!
Closed Friday at noon Try to turn in HW to mailbox of your section TF
8 k BT π m
Lab times posted on website (will do sectioning next week)
What We Learned Last Time !
Hint for Young’s Modulus on website (under “Assignments”) Use for mean frequency problem
Should be completing course sectioning on website !
!
TF’s taking OH during regular section times ! See website for locations (under “Sections”)
HW #1 this week due at 4 PM !
!
ADF Tue, Wed @ 1 See web for TF office hours
C
v 2
Relates macroscopic variables of a system to one another ! Pressure, volume, temperature
Ideal gas
!
2
v C 4 − 2
∫
ve
!
dv
!This is a hard but doable integral (do for homework) !
!
dv
Do need answer today 2
v
=3
RT
From ME learned that 2 ! ½ m=(3/2)k T B !
(1/3)m=kBT
Know ρ=n/V Here n is number, in molecules If we wish to count in moles ! N mole=n/nA; nA=Avogadro’s number ! R=n k A B
P=mρ/3
!
!
! !
P=ρ m/3 = (n/V)(kBT)
!
PV = nkBT=(n/nA)(nA*kB) T =nmoleRT
!
1
Problem-Working Notes Temperature Scales
!
Obviously, labels T are Kelvin ! Absolute 0 is 0 ! Kelvin is linear 273.16 (p/p ) 3 Celsius system offset from Kelvin ! Scale is the same
!
!
!
!
! !
!
Not 273.16! 0 of Celsius system: freezing point of water at 1 atm Diff’t from triple point temperature!
! !
!
!
Fahrenheit almost too silly to discuss ! TF=TC*1.8+32
!
!Imagine gas trapped in box with semi-permeable membrane !Molecule can penetrate membrane & escape if (and only if) it has high kinetic energy !Over time, does the temperature inside the box
!Molar and molecular masses
kB is J/K R is J / (K . mole)
I.e. a change of 1 degree Celsius !Pattern equals a change of 1 K
TC=TK-273.15
Evaporative Cooling
When solving a thermo problem
recognition
If problem has R running around, then to get the units right, it must be the molar mass If kB, the molecular mass !
Go up? Go down? Remain the same?
! !
kB=Rm/M=R/NA
!
!
Convert ALL temps to Kelvin first!
!
Evaporative Cooling
Real Gases: Clausius Volume
!Over time, does the temperature inside the box !
! !
!In a real gas, the full volume is not available for motion
Go up?
Go down
!Find total “unavailable volume” due to non-zero atomic size
Remain the same?
Note the “r”’s and “2r”’s in the picture; unavailable volume surrounding a molecule is actually (4/3)π(2r)3
!
As with lopping off the top test scores, the average KE comes down !
!
Know that in ideal gas ! =(3/2)k T B
Molcules will re-arrange to achieve Maxwell distribution of the lower temperature
KEescape
“Evaporative cooling”
Real Gases: Van der Waals Interactions !Each molecule pulls a little on every other one !
Very weak “van der Waals” force
KE
Vclausius=V-nmoleb b depends on molecular radius ! Differs from gas to gas
!
KEescape
!
KE
!
Inside the earth, pull is equal in all directions ! Only outside surface is there a net effect Force is product of masses
!
Similarly for vdW force
Force felt by molecules at edge of gas headed for container ! Pulled back inwards ! Force product of !
!
Density of inner gas molecules (~earth) Density of surface molecules (~mass of object)
Divide by nmole
P(
V − b ) = RT nmole
!Both densities are simply equal to “the density” n/V
Force is proportional to (n/V)2 Constant of proportionality depends on details of force law and distribution of molecules ! Easier to measure than to calculate!
!
!
P (V − nmole b ) = nmole RT
Van der Waals
Recall gravity
!
PV = nmole RT
Subtract unavailable volume per mole
!
!
r
!
!
!
2r
Atomic sizes not necessarily negligible
!
! !
Differs from gas to gas
Reduce pressure by a(n/V)2
The real gas equation of state
!
P=
RT a 2 − b ) (V / ) (V /
a 2 (V / n − b ) = RT P + (V / ) Add vdW term, multiply by Clausius
2
Real Gases: Equation of State !Clausius term generally serves to increase pressure !
!As you know, the same molecular substance can have a variety of intermolecular configurations
P
Reduced available volume for molecules -> increased # of collisions with walls
!
T1 T2 T3 T4
Increases intermolecule attractions, clumping the molecules inside away from walls
!
V,P,T
!
P-V plot is useful for understanding
!
Lines show points of constant temperature Moving right to left = pressing on gas
!
V
Phases: P-V plots
!
!
!
P vs T even more common
!
!
!
!
!
Liquid
Liquidvapor region
Vapor
T1 T2 T3 T4 V
Liquid-solid transition 218 ! Slope is wrong way! ! Expands upon freezing Liquid contracts from 0 to 4 C
!Again, freezing temp illdefined ! !
! !
Note
Solid
Melting Freezing
Liquid Evaporating Condensing
Gas
5 Subliming
Vapor
!
Freezing temperature not well defined! ! Depends on pressure
-56.6
T(C)
31
Quiz
!Water has very unusual P (atm) properties
!
!
73
Critical point ! End of liquid-gas phase transition Triple point ! All three phases coexist Freezing, evaporation transitions Sublimation transition
!
Gas above critical temperature Vapor is gas which could, if pressed on, become a liquid
Phases: Water !
E.g. CO2
Features
!
Gas and vapor !
P (atm)
Often called “the phase plot”
Normal substance shown to right
Gas
!
!
V
Phases: P-T plots
!If a line is horizontal, it is leaving the gas phase and entering the liquid phase P
Suddenly “shrinks” without need of additional pressure application T3: highest temperature which passes through such a region= Critical temperature Tc At all temperatures below this ! There is a horizontal section ! You can form a liquid At all above ! You can never get into liquid state, no matter how hard you press!
T1 T2 T3 T4
!Configuration depends on the macroscopic variables of the system
!
!
P
Gas (simplest) Liquid ! Molecules essentially in contact but able to move about Solid ! Molecules in regular arrays
!
!Van der Waals term generally serves to reduce pressure !
Phases: P-V plots
1
Depends on temperature 0.006 Triple point is a single point
Melting
!Today, Mars has a surface temperature of –60C and pressure of 0.0056 atmosphere !The Martian atmosphere has very fast thermal reactions
Liquid
Freezing
!
Evaporating Condensing
!Suppose Mars were warmer once, but at the same atmospheric pressure
Solid
Subliming
0.01
Vapor
100 374
High and low pressure areas, caused by solar heating, can differ by 20%
!
T
!
Would oceans have formed? Could it have rained?
Alien Cheez DoodlesTM?
3
Quiz
Goals for today
P (atm)
!Mars has a surface temperature of –60C and pressure of 0.0056 atmosphere 218 !The Martian atmosphere has very fast thermal reactions !
High and low pressure areas, caused by solar heating, can differ by 20%
!
!
Melting
1
!
Liquid
!
Condensing
0.01
!
!
Total energy of all molecules in an object This energy could be ! Kinetic: ideal gas ! Rotational or vibrations: diatomic gas ! Potential: crystalline solids
!Internal energy depends on size of object !
! !
!
!
!
100 374
Sublimation Critical temperature Water
Thermal properties of matter
! !
Heat, work, and energy
Specific Heat Calorimetry
Specific Heat
1st Law of Thermodynamics !
!
!
Mathematical statement
∆U = Q − W
More generally, it is proportional to the average internal energy
!
Physical statement !
A transfer of internal energy which results from a temperature differential The heat is positive if heat flows into the object
!
!
We call work (W)
More molecules -> more internal energy
Expansion Bond Lengths
Expansion Bond Lengths
!
!
!
!
We call heat (Q)
1st Law
!
!
Heat, work, and energy
!
!
!
Thermal properties of matter
!For ideal gas, temperature is related to average kinetic energy
Phases !
!
!
Goals for today !
1st Law
T
Heat, Work, Energy
Sublimation Critical temperature Water
!
!
Vapor
Would oceans have formed? ! No. At this pressure, water sublimates Could it have rained? ! Yes. At only 10% higher pressure, such as in a storm front, liquid water can exist
!“Intuitively know” that heat is related both to energy and temperature !Define internal energy (U)
!
Evaporating
Freezing
Solid
!Suppose Mars were warmer once, but at the same atmospheric 0.006 pressure !
Phases
!
A transfer of energy which does not result from a temperature differential The work is positive when work is done by the object
Heat is a form of energy It therefore obeys conservation of energy It can be converted into work, or vice versa In the absence of work, heat changes the internal energy of a system
Real Materials !Success of my research project depends on construction of detector to accuracy better than 10 µm !Fancy optical surveyor and mechanical placement system !Biggest issue: stability of clean room temperature system !1C change in temperature led to 25 µm changes on our survey table! !
ADF in the bunny suit
Aluminum base
4
Bond Lengths
“Dear Liza, A Hole”
!Intermolecular potential energy from 11a Epot ! Potential looks like
−
!If you have an aluminum bucket with a hole, and fill the bucket with boiling water
Repulsive B/r2
A B + r rn
Inner-shell repulsion
Coulomb-like attraction ! Take n=2 for this case
!
r1 r2
rsep
!
Recall
!
! !
rsep oscillates between extremes KE=0 at extremes, maximum in middle
E2 E1
T2
T1
Rising temp -> raised U -> raised Etot Midpoint of oscillation grows with temperature -> average separation increases expansion
Does the bucket expand into the hole? Or the hole expand into the bucket?
! !
Attractive –A/r
Real Materials: Linear Expansion
“Dear Liza, A Hole”
!Now we take a blowtorch to our crème brulee
Each bond length increases
It remains a crème brulee, but its temperature changes ! Is now in equilibrium with the rising phoenix set of objects
L0
The ramekin diameter gets larger! !As we heat it up through Mr. Sun, it continues to get larger !Find extra length of diameter proportional to change in temperature !
Circumference increases, so hole diameter increases
!
!
Slope=α
Brulee length (diameter)
!
Atomic bond lengths in the solid are growing! ! Material dependent ∆L=L0α∆T
L
L(T ) = L0 + L0α∆T
T
α called “linear coefficient of thermal expansion” !
Volume Expansion
Some materials
!We could also take the blowtorch to our tropical drink*! !
!
It would eventually spill over the top Most useful to measure volume expansion
Linear coefficients
!
! !
V0
Measure V(T) as with ship !Again, change in volume proportional to
!
Slope=β
! !
!
! !
!
V
These things are important for ! ! !
!
!
T
∆V=V0β∆T
β called “volume coefficient of thermal expansion” !
!
If you stare at Table 17-1 for a while, you might notice a relationship between α and β. Can you explain it?
V (T ) V
V β∆T
* Disclaimer: this is a nonalcoholic tropical drink.
Taking a blowtorch to an alcoholic drink would be very dangerous
!
Volume coefficients ! ! ! ! !
Gasoline: 950 x 10-6 /oC Mercury: 180 x 10-6 /oC Ethanol: 1100 x 10-6 /oC Water: 210 x 10-6 /oC Air: 3400 x 10-6 /oC
!
Original volume Change in temperature
Also due to atomic bond lengths
Lead: 29 x 10-6 /oC Aluminum : 25 x 10-6 /oC Copper : 17 x 10-6 /oC Steel : 12 x 10-6 /oC Glass : 3 x 10-6 /oC Quartz : 0.4 x 10-6 /oC
! !
Building bridges Building highways Construction techniques ! Rivets cooled by dry ice, then inserted for tight fit Stringing power cables Keeping buildings standing in winter
!Shrinkage of gasoline in winter pulls in water vapor -> ice -> plugged fuel lines !
Keep your gas tank full in winter!
5
Or building a Silicon Vertex Detector
Some materials Linear coefficients
Volume coefficients
!
! ! ! ! ! !
!
Lead: 29 x 10-6 /oC Aluminum : 25 x 10-6 /oC Copper : 17 x 10-6 /oC Steel : 12 x 10-6 /oC Glass : 3 x 10-6 /oC Quartz : 0.4 x 10-6 /oC
! ! ! ! !
These things are important for
!
! ! !
! !
Goals for today !
! !
!
!
!
!
Heat, work, and energy
!
Thermal properties of matter !
!
Expansion Bond Lengths
!
The change in temperature depends on
!
! !
The amount of heat energy The mass of the material being heated The actual material itself
!
∆T =
Q
c is a constant that depends on the material !
Called “heat capacity” If c is large, a lot of heat can be stored with little change in temperature
Units of heat capacity ! !
The more mass, the more energy it takes to raise the temperature (reasonable)
!
!Alcohol & mercury thermometers
Is it a constant for all materials? Can we calculate it? What does it depend on?
Plumbing
!
!
Keep your gas tank full in winter!
Specific Heat
Specific Heat !
!
!Suppose you add a certain amount of heat energy to a substance !By how much does the temperature change?
Sublimation Critical temperature Water
1st Law !
!Shrinkage of gasoline in winter pulls in water vapor -> ice -> plugged fuel lines
Building bridges Building highways Construction techniques ! Rivets cooled by dry ice, then inserted for tight fit Stringing power cables Keeping buildings standing in winter
Specific Heat
Phases !
Gasoline: 950 x 10-6 /oC Mercury: 180 x 10-6 /oC Ethanol: 1100 x 10-6 /oC Water: 210 x 10-6 /oC Air: 3400 x 10-6 /oC
!
J / (kg oC) or kcal / (kg oC) Also, remember ! Cal=kcal ! 1 cal = 4.186 J
If you want to cool or heat up something with a fluid, should you use a fluid with high or low heat capacity? !
!
Use a High heat capacity !
If it’s too low ! Small amount of energy could heat up fluid inordinately ! Fluid could BOIL ! This is bad for heat capacity!
!Cooling system for research detector needs to take away about 5 kW of power with 40 mL/s with a chiller of maximum input temperature of 60 C !Initial temperature is 30 C !
!
∆T =
Q
This “runaway” can happen in your brake fluid if it is contaminated
Try water ! ∆T=5kJ/(0.040*4186)=29.8C ! OK! Ethanol ! ∆T=5kJ/(0.040*2400)=52C ! 82C is above boiling point of Ethanol (78)! ! In vapor form, c is reduced to 2000 ! ∆T=5kJ/(0.040*2000)=62.5
6
Plumbing
Goals for today !
Phases !
Reservoir Pump
! !
!
1st Law
!
Thermal properties of matter
!
! !
Chiller !
Summary P=
Van der Waals
pV = nRT (P +
Thermal properties of materials !
L' L(1
∆T )
Q ∆T = mc
Expansion Bond Lengths
Specific Heat
a V n
2
= Q −W
!Always remember conservation of energy! !Heat is a form of energy so CoE is valid !Heat delivered / time is a power (energy / time) !E.g. the coffeemaker
Solution
!
)(V − bn) = RT
V ' V (1 β∆T )
Phases !1st Law ∆U !Specific Heat !
Heat, work, and energy
Calorimetry
RT !Equations of state ! Ideal gas V −b ! Clausius EOS n !
Sublimation Critical temperature Water
! ! Liquid Solid
! Gas Vapor
750 W of heating power Boil 750 mL of water which starts at 8C Pot: 360 g of Al
How long do I have to wait? !
! ! !
!
! !
!
! ! !
Need water + aluminum at 100C ∆T=92 Specific heat of aluminum ! C=900 J/kgC Specific heat of water ! C=4186 J/kgC Beware Joules / Calories! Total energy to aluminum ! Q=mc∆T=0.36*92*900=29808J Total energy to water ! Q=mc∆T=0.75*92*900=62100 J Total energy required:91908J Power: 750 W Time = Energy / power = 122 s
7
Intro Physics II Physics 11b
! !
Web quizzes start Monday Regular office hours this week !
Phases Thermal Expansion First Law
!
!
Bonus office hours this week (no section) !
!
!
!
Goals for today
Temperature
!
!
!
Scale defined using triple point of water and absolute 0 Use ideal gas thermometer to label temperature of everything else Remember, we went through the whole song and dance so that ! We have an unambiguous way to assign a temperature to any object !
!
!
p T = 273.16 lim p3 → 0 p 3
!
!
!
M 2 P (v ) = 4π v e 2 RT
Describes probability of different molecular speeds in the gas
2
− Mv 2 RT
2
v
∫
may not equal !Average KE is given by ! !
!
=< ½ Not ½ m2
½
m
Result ! !
=3/2 RT m/M = 3/2 kBT ! kB=Rm/M=R/NA
!
Specific Heat
Heat, work, and energy Expansions
Equations of State !
3/2
2
4 − C ve v P (v )dv 4π 2π =∫ = ∫ 1 P ( v )dv 2
mv2>=
Thermal properties of matter
Equation of state
!Average value of v may not equal vmax
Long tail to right skews average high
!
!
Some comments on distribution
!2
1st Law
! 3 2
Sublimation Critical temperature Water
!
Meaning: it’s physics
Maxwell Distribution
!
Equations of State Phases !
Theoretically tractable with only Newton’s Laws No subject to our intuition’s ! Fallibility ! Circularity ! Imprecision
!
!
Closed Friday at noon Try to turn in HW to mailbox of your section TF
8 k BT π m
Lab times posted on website (will do sectioning next week)
What We Learned Last Time !
Hint for Young’s Modulus on website (under “Assignments”) Use for mean frequency problem
Should be completing course sectioning on website !
!
TF’s taking OH during regular section times ! See website for locations (under “Sections”)
HW #1 this week due at 4 PM !
!
ADF Tue, Wed @ 1 See web for TF office hours
C
v 2
Relates macroscopic variables of a system to one another ! Pressure, volume, temperature
Ideal gas
!
2
v C 4 − 2
∫
ve
!
dv
!This is a hard but doable integral (do for homework) !
!
dv
Do need answer today 2
v
=3
RT
From ME learned that 2 ! ½ m=(3/2)k T B !
(1/3)m=kBT
Know ρ=n/V Here n is number, in molecules If we wish to count in moles ! N mole=n/nA; nA=Avogadro’s number ! R=n k A B
P=mρ/3
!
!
! !
P=ρ m/3 = (n/V)(kBT)
!
PV = nkBT=(n/nA)(nA*kB) T =nmoleRT
!
1
Problem-Working Notes Temperature Scales
!
Obviously, labels T are Kelvin ! Absolute 0 is 0 ! Kelvin is linear 273.16 (p/p ) 3 Celsius system offset from Kelvin ! Scale is the same
!
!
!
!
! !
!
Not 273.16! 0 of Celsius system: freezing point of water at 1 atm Diff’t from triple point temperature!
! !
!
!
Fahrenheit almost too silly to discuss ! TF=TC*1.8+32
!
!Imagine gas trapped in box with semi-permeable membrane !Molecule can penetrate membrane & escape if (and only if) it has high kinetic energy !Over time, does the temperature inside the box
!Molar and molecular masses
kB is J/K R is J / (K . mole)
I.e. a change of 1 degree Celsius !Pattern equals a change of 1 K
TC=TK-273.15
Evaporative Cooling
When solving a thermo problem
recognition
If problem has R running around, then to get the units right, it must be the molar mass If kB, the molecular mass !
Go up? Go down? Remain the same?
! !
kB=Rm/M=R/NA
!
!
Convert ALL temps to Kelvin first!
!
Evaporative Cooling
Real Gases: Clausius Volume
!Over time, does the temperature inside the box !
! !
!In a real gas, the full volume is not available for motion
Go up?
Go down
!Find total “unavailable volume” due to non-zero atomic size
Remain the same?
Note the “r”’s and “2r”’s in the picture; unavailable volume surrounding a molecule is actually (4/3)π(2r)3
!
As with lopping off the top test scores, the average KE comes down !
!
Know that in ideal gas ! =(3/2)k T B
Molcules will re-arrange to achieve Maxwell distribution of the lower temperature
KEescape
“Evaporative cooling”
Real Gases: Van der Waals Interactions !Each molecule pulls a little on every other one !
Very weak “van der Waals” force
KE
Vclausius=V-nmoleb b depends on molecular radius ! Differs from gas to gas
!
KEescape
!
KE
!
Inside the earth, pull is equal in all directions ! Only outside surface is there a net effect Force is product of masses
!
Similarly for vdW force
Force felt by molecules at edge of gas headed for container ! Pulled back inwards ! Force product of !
!
Density of inner gas molecules (~earth) Density of surface molecules (~mass of object)
Divide by nmole
P(
V − b ) = RT nmole
!Both densities are simply equal to “the density” n/V
Force is proportional to (n/V)2 Constant of proportionality depends on details of force law and distribution of molecules ! Easier to measure than to calculate!
!
!
P (V − nmole b ) = nmole RT
Van der Waals
Recall gravity
!
PV = nmole RT
Subtract unavailable volume per mole
!
!
r
!
!
!
2r
Atomic sizes not necessarily negligible
!
! !
Differs from gas to gas
Reduce pressure by a(n/V)2
The real gas equation of state
!
P=
RT a 2 − b ) (V / ) (V /
a 2 (V / n − b ) = RT P + (V / ) Add vdW term, multiply by Clausius
2
Real Gases: Equation of State !Clausius term generally serves to increase pressure !
!As you know, the same molecular substance can have a variety of intermolecular configurations
P
Reduced available volume for molecules -> increased # of collisions with walls
!
T1 T2 T3 T4
Increases intermolecule attractions, clumping the molecules inside away from walls
!
V,P,T
!
P-V plot is useful for understanding
!
Lines show points of constant temperature Moving right to left = pressing on gas
!
V
Phases: P-V plots
!
!
!
P vs T even more common
!
!
!
!
!
Liquid
Liquidvapor region
Vapor
T1 T2 T3 T4 V
Liquid-solid transition 218 ! Slope is wrong way! ! Expands upon freezing Liquid contracts from 0 to 4 C
!Again, freezing temp illdefined ! !
! !
Note
Solid
Melting Freezing
Liquid Evaporating Condensing
Gas
5 Subliming
Vapor
!
Freezing temperature not well defined! ! Depends on pressure
-56.6
T(C)
31
Quiz
!Water has very unusual P (atm) properties
!
!
73
Critical point ! End of liquid-gas phase transition Triple point ! All three phases coexist Freezing, evaporation transitions Sublimation transition
!
Gas above critical temperature Vapor is gas which could, if pressed on, become a liquid
Phases: Water !
E.g. CO2
Features
!
Gas and vapor !
P (atm)
Often called “the phase plot”
Normal substance shown to right
Gas
!
!
V
Phases: P-T plots
!If a line is horizontal, it is leaving the gas phase and entering the liquid phase P
Suddenly “shrinks” without need of additional pressure application T3: highest temperature which passes through such a region= Critical temperature Tc At all temperatures below this ! There is a horizontal section ! You can form a liquid At all above ! You can never get into liquid state, no matter how hard you press!
T1 T2 T3 T4
!Configuration depends on the macroscopic variables of the system
!
!
P
Gas (simplest) Liquid ! Molecules essentially in contact but able to move about Solid ! Molecules in regular arrays
!
!Van der Waals term generally serves to reduce pressure !
Phases: P-V plots
1
Depends on temperature 0.006 Triple point is a single point
Melting
!Today, Mars has a surface temperature of –60C and pressure of 0.0056 atmosphere !The Martian atmosphere has very fast thermal reactions
Liquid
Freezing
!
Evaporating Condensing
!Suppose Mars were warmer once, but at the same atmospheric pressure
Solid
Subliming
0.01
Vapor
100 374
High and low pressure areas, caused by solar heating, can differ by 20%
!
T
!
Would oceans have formed? Could it have rained?
Alien Cheez DoodlesTM?
3
Quiz
Goals for today
P (atm)
!Mars has a surface temperature of –60C and pressure of 0.0056 atmosphere 218 !The Martian atmosphere has very fast thermal reactions !
High and low pressure areas, caused by solar heating, can differ by 20%
!
!
Melting
1
!
Liquid
!
Condensing
0.01
!
!
Total energy of all molecules in an object This energy could be ! Kinetic: ideal gas ! Rotational or vibrations: diatomic gas ! Potential: crystalline solids
!Internal energy depends on size of object !
! !
!
!
!
100 374
Sublimation Critical temperature Water
Thermal properties of matter
! !
Heat, work, and energy
Specific Heat Calorimetry
Specific Heat
1st Law of Thermodynamics !
!
!
Mathematical statement
∆U = Q − W
More generally, it is proportional to the average internal energy
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Physical statement !
A transfer of internal energy which results from a temperature differential The heat is positive if heat flows into the object
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We call work (W)
More molecules -> more internal energy
Expansion Bond Lengths
Expansion Bond Lengths
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We call heat (Q)
1st Law
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Heat, work, and energy
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Thermal properties of matter
!For ideal gas, temperature is related to average kinetic energy
Phases !
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Goals for today !
1st Law
T
Heat, Work, Energy
Sublimation Critical temperature Water
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Vapor
Would oceans have formed? ! No. At this pressure, water sublimates Could it have rained? ! Yes. At only 10% higher pressure, such as in a storm front, liquid water can exist
!“Intuitively know” that heat is related both to energy and temperature !Define internal energy (U)
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Evaporating
Freezing
Solid
!Suppose Mars were warmer once, but at the same atmospheric 0.006 pressure !
Phases
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A transfer of energy which does not result from a temperature differential The work is positive when work is done by the object
Heat is a form of energy It therefore obeys conservation of energy It can be converted into work, or vice versa In the absence of work, heat changes the internal energy of a system
Real Materials !Success of my research project depends on construction of detector to accuracy better than 10 µm !Fancy optical surveyor and mechanical placement system !Biggest issue: stability of clean room temperature system !1C change in temperature led to 25 µm changes on our survey table! !
ADF in the bunny suit
Aluminum base
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Bond Lengths
“Dear Liza, A Hole”
!Intermolecular potential energy from 11a Epot ! Potential looks like
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!If you have an aluminum bucket with a hole, and fill the bucket with boiling water
Repulsive B/r2
A B + r rn
Inner-shell repulsion
Coulomb-like attraction ! Take n=2 for this case
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r1 r2
rsep
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Recall
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rsep oscillates between extremes KE=0 at extremes, maximum in middle
E2 E1
T2
T1
Rising temp -> raised U -> raised Etot Midpoint of oscillation grows with temperature -> average separation increases expansion
Does the bucket expand into the hole? Or the hole expand into the bucket?
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Attractive –A/r
Real Materials: Linear Expansion
“Dear Liza, A Hole”
!Now we take a blowtorch to our crème brulee
Each bond length increases
It remains a crème brulee, but its temperature changes ! Is now in equilibrium with the rising phoenix set of objects
L0
The ramekin diameter gets larger! !As we heat it up through Mr. Sun, it continues to get larger !Find extra length of diameter proportional to change in temperature !
Circumference increases, so hole diameter increases
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Slope=α
Brulee length (diameter)
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Atomic bond lengths in the solid are growing! ! Material dependent ∆L=L0α∆T
L
L(T ) = L0 + L0α∆T
T
α called “linear coefficient of thermal expansion” !
Volume Expansion
Some materials
!We could also take the blowtorch to our tropical drink*! !
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It would eventually spill over the top Most useful to measure volume expansion
Linear coefficients
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V0
Measure V(T) as with ship !Again, change in volume proportional to
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Slope=β
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V
These things are important for ! ! !
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T
∆V=V0β∆T
β called “volume coefficient of thermal expansion” !
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If you stare at Table 17-1 for a while, you might notice a relationship between α and β. Can you explain it?
V (T ) V
V β∆T
* Disclaimer: this is a nonalcoholic tropical drink.
Taking a blowtorch to an alcoholic drink would be very dangerous
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Volume coefficients ! ! ! ! !
Gasoline: 950 x 10-6 /oC Mercury: 180 x 10-6 /oC Ethanol: 1100 x 10-6 /oC Water: 210 x 10-6 /oC Air: 3400 x 10-6 /oC
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Original volume Change in temperature
Also due to atomic bond lengths
Lead: 29 x 10-6 /oC Aluminum : 25 x 10-6 /oC Copper : 17 x 10-6 /oC Steel : 12 x 10-6 /oC Glass : 3 x 10-6 /oC Quartz : 0.4 x 10-6 /oC
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Building bridges Building highways Construction techniques ! Rivets cooled by dry ice, then inserted for tight fit Stringing power cables Keeping buildings standing in winter
!Shrinkage of gasoline in winter pulls in water vapor -> ice -> plugged fuel lines !
Keep your gas tank full in winter!
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Or building a Silicon Vertex Detector
Some materials Linear coefficients
Volume coefficients
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Lead: 29 x 10-6 /oC Aluminum : 25 x 10-6 /oC Copper : 17 x 10-6 /oC Steel : 12 x 10-6 /oC Glass : 3 x 10-6 /oC Quartz : 0.4 x 10-6 /oC
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These things are important for
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Goals for today !
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Heat, work, and energy
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Thermal properties of matter !
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Expansion Bond Lengths
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The change in temperature depends on
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The amount of heat energy The mass of the material being heated The actual material itself
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∆T =
Q
c is a constant that depends on the material !
Called “heat capacity” If c is large, a lot of heat can be stored with little change in temperature
Units of heat capacity ! !
The more mass, the more energy it takes to raise the temperature (reasonable)
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!Alcohol & mercury thermometers
Is it a constant for all materials? Can we calculate it? What does it depend on?
Plumbing
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Keep your gas tank full in winter!
Specific Heat
Specific Heat !
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!Suppose you add a certain amount of heat energy to a substance !By how much does the temperature change?
Sublimation Critical temperature Water
1st Law !
!Shrinkage of gasoline in winter pulls in water vapor -> ice -> plugged fuel lines
Building bridges Building highways Construction techniques ! Rivets cooled by dry ice, then inserted for tight fit Stringing power cables Keeping buildings standing in winter
Specific Heat
Phases !
Gasoline: 950 x 10-6 /oC Mercury: 180 x 10-6 /oC Ethanol: 1100 x 10-6 /oC Water: 210 x 10-6 /oC Air: 3400 x 10-6 /oC
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J / (kg oC) or kcal / (kg oC) Also, remember ! Cal=kcal ! 1 cal = 4.186 J
If you want to cool or heat up something with a fluid, should you use a fluid with high or low heat capacity? !
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Use a High heat capacity !
If it’s too low ! Small amount of energy could heat up fluid inordinately ! Fluid could BOIL ! This is bad for heat capacity!
!Cooling system for research detector needs to take away about 5 kW of power with 40 mL/s with a chiller of maximum input temperature of 60 C !Initial temperature is 30 C !
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∆T =
Q
This “runaway” can happen in your brake fluid if it is contaminated
Try water ! ∆T=5kJ/(0.040*4186)=29.8C ! OK! Ethanol ! ∆T=5kJ/(0.040*2400)=52C ! 82C is above boiling point of Ethanol (78)! ! In vapor form, c is reduced to 2000 ! ∆T=5kJ/(0.040*2000)=62.5
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Plumbing
Goals for today !
Phases !
Reservoir Pump
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1st Law
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Thermal properties of matter
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Chiller !
Summary P=
Van der Waals
pV = nRT (P +
Thermal properties of materials !
L' L(1
∆T )
Q ∆T = mc
Expansion Bond Lengths
Specific Heat
a V n
2
= Q −W
!Always remember conservation of energy! !Heat is a form of energy so CoE is valid !Heat delivered / time is a power (energy / time) !E.g. the coffeemaker
Solution
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)(V − bn) = RT
V ' V (1 β∆T )
Phases !1st Law ∆U !Specific Heat !
Heat, work, and energy
Calorimetry
RT !Equations of state ! Ideal gas V −b ! Clausius EOS n !
Sublimation Critical temperature Water
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! Gas Vapor
750 W of heating power Boil 750 mL of water which starts at 8C Pot: 360 g of Al
How long do I have to wait? !
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Need water + aluminum at 100C ∆T=92 Specific heat of aluminum ! C=900 J/kgC Specific heat of water ! C=4186 J/kgC Beware Joules / Calories! Total energy to aluminum ! Q=mc∆T=0.36*92*900=29808J Total energy to water ! Q=mc∆T=0.75*92*900=62100 J Total energy required:91908J Power: 750 W Time = Energy / power = 122 s
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