physics 1710—warm-up quiz what is the first audible harmonic that has a frequency above 20 hz for...

Physics 1710Physics 1710—Warm-up Quiz—Warm-up QuizWhat is the first audible harmonic that has a frequency What is the first audible harmonic that has a frequency above 20 Hz for a cable that has a mass of 1.0 kg, is above 20 Hz for a cable that has a mass of 1.0 kg, is 10.0 long, and is supporting a 100.0 kg mass? 10.0 long, and is supporting a 100.0 kg mass?

A B C D E

9%

43%

4%6%

38%A.A. 11B.B. 2 2 C.C. 44D.D. 88E.E. The sound is never audible.The sound is never audible.

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Physics 1710Physics 1710Chapter 19 TemperatureChapter 19 Temperature

Solution:Solution:

μ = m/L = 1.0 kg/10 m = 0.10 kg/mμ = m/L = 1.0 kg/10 m = 0.10 kg/m

T = Mg = (100.0 kg) (9.8 N/kg) = 980 NT = Mg = (100.0 kg) (9.8 N/kg) = 980 N

ƒƒn n = n/(2L)= n/(2L)√[T/ √[T/ μ ] = n/(2* 10.0 m) μ ] = n/(2* 10.0 m) √[980./ 0.√[980./ 0.1 ] = n 1 ] = n (4.95 Hz)(4.95 Hz)

n = 20 Hz/ n = 20 Hz/ ƒƒ1 1 = 20/(4.95) = 4.0= 20/(4.95) = 4.0


11′ Lesson:′ Lesson:

• Temperature is a measure of the average kinetic Temperature is a measure of the average kinetic energy of a system of non-interacting particles (an energy of a system of non-interacting particles (an ideal gas).ideal gas).

• Thermal Equilibrium means that two bodies are at Thermal Equilibrium means that two bodies are at the same temperature.the same temperature.

• The “Zeroth Law of Thermodynamics” states that The “Zeroth Law of Thermodynamics” states that if system A and B are in thermal equilibrium with if system A and B are in thermal equilibrium with system C, then A and B are in thermal Equilibrium system C, then A and B are in thermal Equilibrium with each other.with each other.

• Kelvin is a unit of temperature where one degree K Kelvin is a unit of temperature where one degree K is 1/279.16 of the temperature of the triple point of is 1/279.16 of the temperature of the triple point of water (near freezing).water (near freezing).


11′ Lesson:′ Lesson:• A length body will expand in proportion to the A length body will expand in proportion to the change in temperature.change in temperature.

• The ideal gas law states that the product of The ideal gas law states that the product of the pressure and volume of a gas is the pressure and volume of a gas is proportional to the amount of the gas and the proportional to the amount of the gas and the absolute temperature.absolute temperature.


Boltzmann’s Dream:Boltzmann’s Dream:• A reductionist’s explanation of heat and A reductionist’s explanation of heat and temperature.temperature.

• Heat is the total internal energy of moving Heat is the total internal energy of moving atoms in a substance.atoms in a substance.

• Temperature is the (average) kinetic energy of Temperature is the (average) kinetic energy of the moving atoms.the moving atoms.

• Two systems with the same temperature are in Two systems with the same temperature are in Thermal Equilibrium.Thermal Equilibrium.


Boltzmann’s Dream:Boltzmann’s Dream:

vv11

vv22

vv33vv44

vv55GasGas

KEKEaverageaverage = 3/2kT = 3/2kTKEKEaverageaverage = = Σ ½ mΣ ½ mii v vi i 22 /N /N


Boltzmann’s Dream:Boltzmann’s Dream:

SolidSolid

KEKEaverageaverage = 3/2kT = 3/2kTKEKEaverageaverage = = Σ ½ mΣ ½ mii v vi i 22 /N /N


Zeroth (0 Zeroth (0 thth) Law of Thermodynamics) Law of Thermodynamics

If objects A and B are separately in If objects A and B are separately in thermal thermal equilibriumequilibrium with a third object C, then objects A with a third object C, then objects A

and B are in thermal equilibrium with each and B are in thermal equilibrium with each other.other.


TemperatureTemperature• Degrees of temperature Degrees of temperature

– Centigrade (Celsius, archaic) CCentigrade (Celsius, archaic) C– 0 C ~ ice point of water0 C ~ ice point of water– 100 C ~ boiling point of water100 C ~ boiling point of water

• MeasurementMeasurement– Gas thermometerGas thermometer– Linear expansionLinear expansion– Volume expansionVolume expansion– Phase changes (calibration points)Phase changes (calibration points)


Temperature ScalesTemperature Scales• Centigrade ( C) 0 C~ice; 100 C~steamCentigrade ( C) 0 C~ice; 100 C~steam• Fahrenheit (ripped off Roemer)Fahrenheit (ripped off Roemer)

00⁰F ~ lowest T that he could get (brine)⁰F ~ lowest T that he could get (brine)100⁰F ~ approximate body temperature100⁰F ~ approximate body temperature

(98.6 ⁰F normal)(98.6 ⁰F normal)

TTC C = (100/180) (T= (100/180) (TFF – 32 – 32 ⁰F⁰F))

TTF F = (180/100) T= (180/100) TC C + 32 + 32 ⁰F⁰F


Absolute TemperatureAbsolute Temperature• Kelvin (K) [N.B. not “degrees Kelvin”]Kelvin (K) [N.B. not “degrees Kelvin”]• T = TT = TCC +273.16 +273.16• At 0 K the total internal kinetic energy of a At 0 K the total internal kinetic energy of a system is at the absolute minimum.system is at the absolute minimum.


Linear ExpansionLinear Expansion• Change in T mean change in average kinetic Change in T mean change in average kinetic energyenergy

• More average kinetic energy means increase More average kinetic energy means increase in average displacement from equilibrium in average displacement from equilibrium positionposition

• Law of linear expansionLaw of linear expansion

∆∆L/L = L/L = αα ∆T ∆T

Fractional change in length is proportional to the Fractional change in length is proportional to the change in temperature.change in temperature.


PhasesPhases• Solid: atoms “locked” into positionSolid: atoms “locked” into position

– microstructure determines bulk propertiesmicrostructure determines bulk properties– distance between atoms determines distance between atoms determines densitydensity

• Liquid: atoms “dance” in groups and Liquid: atoms “dance” in groups and pairs, sliding past each other.pairs, sliding past each other.

• Gas: atoms far enough apart to Gas: atoms far enough apart to prevent “locking up” or pairing.prevent “locking up” or pairing.


Ideal Gas LawIdeal Gas Law• Idealizations: Idealizations:

no interaction between atomsno interaction between atomsno volume occupied by atomsno volume occupied by atoms

• Number of atoms n = m/M, Number of atoms n = m/M, m = mass; M = molar massm = mass; M = molar mass

• PV = n R TPV = n R TR = 8.315 J/ mol K R = 8.315 J/ mol K = 0.08214 L= 0.08214 L‧‧atm/mol Katm/mol K = 22.4 L= 22.4 L‧‧atm /273.16 mol Katm /273.16 mol K


Boltzmann’ ConstantBoltzmann’ Constant• k = R/Nk = R/NAA

• k = 1.38 x 10 k = 1.38 x 10 -23-23 J/K = 1 yJ/ 7.25 K J/K = 1 yJ/ 7.25 K

= 1 eV / 11,600 K= 1 eV / 11,600 K

PV = N kTPV = N kT


Summary:Summary:•Temperature is a measure of the average Temperature is a measure of the average kinetic energy of a system of particles.kinetic energy of a system of particles.

• Thermal Equilibrium means that two bodies Thermal Equilibrium means that two bodies are at the same temperature.are at the same temperature.

• The “Zeroth Law of Thermodynamics” states The “Zeroth Law of Thermodynamics” states that if system A and B are n thermal equilibrium that if system A and B are n thermal equilibrium with system C, then A and B are in thermal with system C, then A and B are in thermal Equilibrium with each other.Equilibrium with each other.


•Kelvin is a unit of temperature where Kelvin is a unit of temperature where one degree K is 1/279.16 of the one degree K is 1/279.16 of the temperature of the triple point of water temperature of the triple point of water (near freezing).(near freezing).

TTC C = (100/180) (T= (100/180) (TFF – 32 – 32 ⁰F⁰F))

TTF F = (180/100) T= (180/100) TC C + 32 + 32 ⁰F⁰F• ∆∆L/L = L/L = αα∆T∆T• PV = n R T = N kTPV = n R T = N kT

physics 1710—warm-up quiz what is the first audible harmonic that has a frequency above 20 hz for...

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