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ROCHESTER PHY 121 - Lecture 23 Notes - Temperature/Heat and the Ideal Gas Law

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Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121, April 15, 2008.Temperature/Heat and the Ideal Gas Law.http://www.brickinfo.org/BIA/technotes/t18.htmFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.April 15, 2008.• Course information• Topics to be discussed today:• Temperature (review).• The universal gas law.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.April 15, 2008.• Homework set # 9 is now available and is due on Saturdaymorning, April 19, at 8.30 am.• Midterm Exam # 3 will take place on Tuesday April 22between 8.00 am and 9.30 am in Hubbell. The material tobe covered is the material contained in Chapters 10, 11, 12,and 14.• There will be extra office hours on Sunday and Monday.Details will be announced via email.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterHomework set # 9.All about simple harmonic motion.In all cases:a = -ω2xFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterTemperature (a quick review).Measuring temperature.• In order to measure temperaturewe must:• Agree on a standard referencepoint to which we assign a certaintemperature.• Agree on a unit.• Agree on a standard thermometeragainst which all otherthermometers can be calibrated.• The unit of temperature will bethe Kelvin (K).• The standard reference point isthe triple point of water (T =273.16 K).http://www.fluke.fr/common/prod_pages/pages/hart/products/tpw.htmFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterTemperature (a quick review).Measuring temperature.• The standard thermometer is theconstant volume gasthermometer.• The bulb of the thermometer,which is filled with gas, is put inthermal contact with the systemto be studied.• The reservoir on the right is nowadjusted to change the mercurylevel so that the gas volumeremains unchanged.• The temperature of the body isdefined in terms of the pressure p: T = Cp = C(p0 + ρgh)hTReservoirFixedFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterTemperature (a quick review).Measuring temperature.• In general we can thus find thetemperature of the body bycomparing the measured pressurewith the triple-point pressure:T = T3 (p/p3) = 273.16 (p/p3)• The method described heredepends slightly on the amountand the type of gas in the bulb.However, this dependence isreduced when we use smaller andsmaller amounts of gas.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterTemperature (a quick review).Measuring temperature.• The Kelvin is not frequently used inour daily life.• More common temperature scales arethe Celsius scale:• 0° is defined as the freezing point ofwater.• 100° is defined as the boiling point ofwater.and the Fahrenheit scale:• 0° was defined as the temperature of amixture of water, ice, and ammoniumchloride.• 96° was as the temperature of theblood of Fahrenheit’s wife.• Note: initially Fahrenheit divided hisscale in 12 segments; later he dividedeach segment in 8 smaller segments.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThermodynamic variables.Pressure.• Pressure is an importantthermodynamic variable.• Pressure is defined as the forceper unit area.• The SI unit is pressure is thePascal: 1 Pa = 1 N/m2. Anothercommon unit is the atm(atmospheric pressure) which isthe pressure exerted by theatmosphere on us (1 atm =1.013!x!105 N/m2).• A pressure of 1 atm will push amercury column up by 76 cm.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThermodynamic variables.Pressure.• Many devices that measure pressure,actually measure the pressuredifference between the pressure ofinterest and the atmosphericpressure.• Atmospheric pressure changes withaltitude. The higher you go, the lessair is pressing on your head!Airplanes use the atmosphericpressure to measure altitude.• But keep into consideration that theatmospheric pressure at a fixedlocation and altitude is not constant!Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThermodynamic variables.Pressure.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThermal expansion.Linear expansion.• When the temperature of amaterial increases, its length willincrease:• The coefficient α is thecoefficient of linear expansion.Typical values are 0.5 x 10-6 K-1and 10 x 10-6 K-1 at roomtemperature.• Note: a solid will expand in everydirection!!!!!!L ="L!TFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThermal expansion.Linear expansion.• In everything we design we needto consider the effects of thermalexpansion:• Draw bridges must be able toopen in summer and winter.• Airplanes expand in flight due tofriction with the air! The width ofthe Concorde increases by a fewcm during its flight.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThermal expansion.Volume expansion.• When we deal with liquids weusually talk about volumeexpansion:• The coefficient β is the volumeexpansion coefficient.• The coefficient of volumeexpansion β is related to thecoefficient of linear expansion α.!V ="V !TFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterRelation between volume and linearexpansion.• Consider a volume V whose temperature is increased by ΔT:• We see that β = 3α.!V = L + !L( )W + !W( )H + !H( )" LWH == WH !L + LH !W + WL!H == V!LL+!HH+!WW#$%&'(= V 3)!T( )Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterVolume expansion.The water anomaly.• Water has a very different thermalbehavior from other liquids. Itexpands when it is cooled below4°C.• Its expansion continues even belowthe freezing point (frozen pipes).This is why ice cubes float!• The anomalous behavior of watereffects the way bodies of waterfreeze:• The body of water will cool downuntil it has a uniform temperature of4°C.• Ice will form on top (life continuesbelow).Frank L.


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ROCHESTER PHY 121 - Lecture 23 Notes - Temperature/Heat and the Ideal Gas Law

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