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Transcript of Physics 1501: Lecture 35, Pg 1 Physics 1501: Lecture 35 Today’s Agenda l Announcements çHomework...
Physics 1501: Lecture 35, Pg 1
Physics 1501: Lecture 35Physics 1501: Lecture 35TodayToday’’s Agendas Agenda
AnnouncementsHomework #11 (Dec. 2) and #12 (Dec. 9): 2 lowest dropped
Honors’ students: see me after the class !
Today’s topicsChap.16: Temperature and Heat
» Latent HeatHeat transfer processes
» Conduction, convection, radiation
» ApplicationChap. 17: ideal gas
» Kinetic theory
Physics 1501: Lecture 35, Pg 2
Temperature scalesTemperature scales Three main scales
212
Farenheit
100
Celcius
32 0 273.15
373.15
Kelvin
Water boils
Water freezes
0-273.15-459.67Absolute Zero
Physics 1501: Lecture 35, Pg 3
Thermal expansionThermal expansion
In most liquids or solids, when temperature risesmolecules have more kinetic energy
» they are moving faster, on the averageconsequently, things tend to expand
amount of expansion L depends on…change in temperature Toriginal length L0
coefficient of thermal expansion
» L0 + L = L0 + L0 T
L = L0 T (linear expansion)
V = L0 T (volume expansion)
L0 L
V
V + V
Physics 1501: Lecture 35, Pg 4
Special system: WaterSpecial system: Water
Most liquids increase in volume with increasing T water is specialdensity increases from
0 to 4 oC !ice is less dense than
liquid water at 4 oC: hence it floats
water at the bottom of a pond is the denser, i.e. at 4 oC
Water has its maximum density at 4 degrees.
(kg/m3)
T (oC)
Reason: chemical bonds of H20 (see your chemistry courses !)
Physics 1501: Lecture 35, Pg 5
HeatHeat
Solids, liquids or gases have internal energyKinetic energy from random motion of molecules
translation, rotation, vibration
At equilibrium, it is related to temperature Heat: transfer of energy from one object to another as a
result of their different temperatures Thermal contact: energy can flow between objects
T1T2
U1U2
>
Physics 1501: Lecture 35, Pg 6
HeatHeat Heat: Q = C T
Q = amount of heat that must be supplied to raise the temperature by an amount T .
[Q] = Joules or calories. 1 cal = energy to raise 1 g of water
from 14.5 to 15.5 oC James Prescott Joule found mechanical equivalent of heat.
C : Heat capacity
1 cal = 4.186 J
1 kcal = 1 Cal = 4186 J
Q = c m T c: specific heat (heat capacity per units of mass) amount of heat to raise T of 1 kg by 1oC [c] = J/(kg oC)
Sign convention: +Q : heat gained- Q : heat lost
Physics 1501: Lecture 35, Pg 7
Latent HeatLatent Heat
L = Q / m Heat per unit mass
[L] = J/kg Q = m L
+ if heat needed (boiling)- if heat given (freezing)
Lf : Latent heat of fusionsolid liquid
Lv : Latent heat of vaporizationliquid gas
Latent heat: amount of energy needed to add or to remove from a substance to change the state of that substance. Phase change: T remains constant but internal energy changes heat does not result in change in T (latent = “hidden”) e.g. : solid liquid or liquid gas
heat goes to breaking chemical bonds
Lf (J/kg) Lv (J/kg)
water 33.5 x 104 22.6 x 105
Physics 1501: Lecture 35, Pg 8
Latent Heats of Fusion and VaporizationLatent Heats of Fusion and Vaporization
Energy added (J)
T (oC)
120
100
80
60
40
20
0
-20
-40Water
Water+
Ice
Water + Steam Steam
62.7 396 815 3080
Physics 1501: Lecture 35, Pg 9
Energy in Thermal ProcessesEnergy in Thermal Processes
Solids, liquids or gases have internal energyKinetic energy from random motion of molecules
translation, rotation, vibration
At equilibrium, it is related to temperature Heat: transfer of energy from one object to another as a
result of their different temperatures Thermal contact: energy can flow between objects
T1T2
U1U2
>
Physics 1501: Lecture 35, Pg 10
Energy transfer mechanismsEnergy transfer mechanisms
Thermal conduction (or conduction):Energy transferred by direct contact.E.g.: energy enters the water through
the bottom of the pan by thermal conduction.
Important: home insulation, etc.
Rate of energy transferthrough a slab of area A and
thickness x, with opposite faces at different temperatures, Tc and Th
k : thermal conductivity
x
Th Tc A
Energy flow
=Q/t = k A (Th - Tc ) / x
Physics 1501: Lecture 35, Pg 11
Thermal ConductivitiesThermal Conductivities
Aluminum 238 Air 0.0234 Asbestos 0.25
Copper 397 Helium 0.138 Concrete 1.3
Gold 314 Hydrogen 0.172 Glass 0.84
Iron 79.5 Nitrogen 0.0234 Ice 1.6
Lead 34.7 Oxygen 0.0238 Water 0.60
Silver 427 Rubber 0.2 Wood 0.10
J/s m 0C J/s m 0C J/s m 0C
Physics 1501: Lecture 35, Pg 12
Energy transfer mechanismsEnergy transfer mechanisms Convection:
Energy is transferred by flow of substance E.g. : heating a room (air convection) E.g. : warming of North Altantic by warm waters
from the equatorial regions Natural convection: from differences in density Forced convection: from pump of fan
Radiation: Energy is transferred by photons E.g. : infrared lamps Stephan’s law
= 5.710-8 W/m2 K4 , T is in Kelvin, and A is the surface area e is a constant called the emissivity
= Q/t = Ae T4 : Power
Physics 1501: Lecture 35, Pg 13
Resisting Energy TransferResisting Energy Transfer
The Thermos bottle, also called a Dewar flask is designed to minimize energy transfer by conduction, convection, and radiation. The standard flask is a double-walled Pyrex glass with silvered walls and the space between the walls is evacuated.
VacuumVacuum
SilveredSilveredsurfacessurfaces
Hot orHot orcoldcoldliquidliquid
Physics 1501: Lecture 35, Pg 14
Chap.17: Ideal gas and kinetic theoryChap.17: Ideal gas and kinetic theory Consider a gas in a container of volume V, at pressure P,
and at temperature T Equation of state
Links these quantitiesGenerally very complicated: but not for ideal gas
PV = nRT R is called the universal gas constant
In SI units, R =8.315 J / mol·K n = m/M : number of moles
Equation of state for an ideal gasCollection of atoms/molecules moving randomlyNo long-range forcesTheir size (volume) is negligible
Physics 1501: Lecture 35, Pg 15
BoltzmannBoltzmann’’s constants constant
In terms of the total number of particles N
P, V, and T are the thermodynamics variables
PV = nRT = (N/NA ) RT
kB is called the Boltzmann’s constant
kB = R/NA = 1.38 X 10-23 J/K
PV = N kB T
Number of moles: n = m/M
One mole contains NA=6.022 X 1023 particles : Avogadro’s number = number of carbon atoms in 12 g of carbon-12
m=mass M=mass of one mole
Physics 1501: Lecture 35, Pg 16
Note on massesNote on massesTo facilitate comparison of the mass of one atom with another, a
mass scale know as the atomic mass scale has been established.
The unit is called the atomic mass unit (symbol u). The reference element is chosen to be the most abundant isotope of carbon, which is called carbon-12.
The atomic mass is given in atomicmass units. For example, a Li atom has a mass of 6.941u.
Physics 1501: Lecture 35, Pg 17
What is the volume of 1 mol of gas at STP ?T = 0 oC = 273 Kp = 1 atm = 1.01 x 105 Pa
The Ideal Gas LawThe Ideal Gas Law
Physics 1501: Lecture 35, Pg 18
ExampleExample Beer Bubbles on the Rise
Watch the bubbles rise in a glass of beer. If you look carefully, you’ll see them grow in size as they move upward, often doubling in volume by the time they reach the surface. Why does the bubble grow as it ascends?
Physics 1501: Lecture 35, Pg 19
Kinetic Theory of an Ideal GasKinetic Theory of an Ideal Gas
Assumptions for ideal gas:Number of molecules N is largeThey obey Newton’s laws (but move
randomly as a whole)Short-range interactions during elastic
collisionsElastic collisions with wallsPure substance: identical molecules
Microscopic model for a gas Goal: relate T and P to motion of
the molecules
Physics 1501: Lecture 35, Pg 20
Distribution of Molecular Speeds The particles are in constant, random motion, colliding with
each other and with the walls of the container. Each collision changes the particle’s speed. As a result, the atoms and molecules have different speeds.
Physics 1501: Lecture 35, Pg 21
Kinetic TheoryKinetic Theory The average force exerted by one wall
Time between successive collisions on the wall
Action-reaction gives
Physics 1501: Lecture 35, Pg 22
For N molecules, the average force is:
root-mean-squarespeed
volume
PressurePressure
Physics 1501: Lecture 35, Pg 24
Does a Single Particle Have a Temperature?
Each particle in a gas has kinetic energy. On the previous page, we have established the relationship between the average kinetic energy per particle and the temperature of an ideal gas.
Is it valid, then, to conclude that a single particle has a temperature?
Concept of temperatureConcept of temperature
Physics 1501: Lecture 35, Pg 25
Air is primarily a mixture of nitrogen N2 molecules (molecular mass 28.0u) and oxygen O2 molecules (molecular mass 32.0u). Assume that each behaves as an ideal gas and determine
the rms speeds of the nitrogen and oxygen molecules when the temperature of the air is 293K.
For nitrogen
Example: Example: Speed of Molecules in Air
Physics 1501: Lecture 35, Pg 26
Internal energy of a monoatomic ideal gasInternal energy of a monoatomic ideal gas The kinetic energy per atom is
Total internal energy of the gas with N atoms
Physics 1501: Lecture 35, Pg 27
Kinetic Theory of an Ideal Gas: summaryKinetic Theory of an Ideal Gas: summary
Assumptions for ideal gas:Number of molecules N is largeThey obey Newton’s laws (but move
randomly as a whole)Short-range interactions during elastic
collisionsElastic collisions with wallsPure substance: identical molecules
Temperature is a direct measure of average kinetic energy of a molecule
Microscopic model for a gas Goal: relate T and P to motion of the
molecules
Physics 1501: Lecture 35, Pg 28
Theorem of equipartition of energy
Each degree of freedom contributes kBT/2 to the energy of a system (e.g., translation, rotation, or vibration)
Kinetic Theory of an Ideal Gas: summaryKinetic Theory of an Ideal Gas: summary
Total translational kinetic energy of a system of N molecules
Internal energy of monoatomic gas: U = Kideal = Ktot trans
Root-mean-square speed:
Physics 1501: Lecture 35, Pg 29
Consider a fixed volume of ideal gas. When N or T is doubled the pressure increases by a factor of 2.
11) If T is doubled, what happens to the rate at which ) If T is doubled, what happens to the rate at which a single a single moleculemolecule in the gas has a wall bounce? in the gas has a wall bounce?
b) x2a) x1.4 c) x4
22) If N is doubled, what happens to the rate at which ) If N is doubled, what happens to the rate at which a single a single moleculemolecule in the gas has a wall bounce? in the gas has a wall bounce?
b) x1.4a) x1 c) x2
Lecture 35: Lecture 35: ACT 1ACT 1
Physics 1501: Lecture 35, Pg 30
DiffusionDiffusion The process in which molecules move from a region
of higher concentration to one of lower concentration is called diffusion.Ink droplet in water
Physics 1501: Lecture 35, Pg 31
Why is diffusion a slow process ?Why is diffusion a slow process ? A gas molecule has a translational rms speed of hundreds of
meters per second at room temperature. At such speed, a molecule could travel across an ordinary room in just a fraction of a second. Yet, it often takes several seconds, and sometimes minutes, for the fragrance of a perfume to reach the other side of the room. Why does it take so long?Many collisions !
Physics 1501: Lecture 35, Pg 32
Comparing heat and molecule diffusionComparing heat and molecule diffusion Both ends are maintained at constant concentration/temperature
Physics 1501: Lecture 35, Pg 33
concentration gradientbetween ends
diffusion constant
SI Units for the Diffusion Constant: m2/s
FickFick’’s law of diffusions law of diffusion For heat conduction between two side at constant T
L
Th Tc A
Energy flow
conductivity temperature gradientbetween ends
The mass m of solute that diffuses in a time t through a solvent contained in a channel of length L and cross sectional area A is