Lecture 23Thermodynamics: A macroscopic description of matterModern Definition of Kelvin ScaleTransferring energy to a solid (ice)Temperature scalesSome interesting factsIdeal gas: Macroscopic descriptionBoltzmann’s constantThe Ideal Gas LawExampleExample problem: Air bubble risingSlide 15Buoyancy and the Ideal Gas LawBuoyancy and the Ideal Gas LawPV diagrams: Important processesWork and Energy Transfer (Ch. 16)Work and Energy Transfer (Ch. 17)1st Law of ThermodynamicsSlide 221st Law: Work & HeatSlide 241st Law: Work (“Area” under the curve)RecapPhysics 207: Lecture 23, Pg 1Lecture 23Goals:Goals:•Chapter 16Chapter 16 Use the ideal-gas law. Use pV diagrams for ideal-gas processes.•Chapter 17Chapter 17 Employ energy conservation in terms of 1st law of TD Understand the concept of heat. Relate heat to temperature change Apply heat and energy transfer processes in real situations Recognize adiabatic processes.•AssignmentAssignment HW9, Due Wednesday, Apr. 15th HW10, Due Wednesday, Apr. 22nd (9 AM)Physics 207: Lecture 23, Pg 2Thermodynamics: A macroscopic description of matterRecall “3” Phases of matter: Solid, liquid & gas All 3 phases exist at different p,T conditions Triple point of water: p = 0.06 atm T = 0.01°CTriple point of CO2: p = 5 atm T = -56°CPhysics 207: Lecture 23, Pg 3Modern Definition of Kelvin ScaleWater’s triple point on the Kelvin scale is 273.16 KOne degrees Kelvin is defined to be 1/273.16 of the temperature at the triple point of waterTriple pointAccurate water phase diagramPhysics 207: Lecture 23, Pg 4Transferring energy to a solid (ice)1. Temperature increase or2. State ChangeIf a gas, then V, p and T are interrelated….equation of statePhysics 207: Lecture 23, Pg 7Temperature scalesThree main scales212Farenheit100Celcius32 0 273.15373.15KelvinWater boilsWater freezes0-273.15-459.67Absolute ZeroFTTCFo3259 FTTFCo3295K 15.273TTCK 15.273CTTPhysics 207: Lecture 23, Pg 8Some interesting factsIn 1724, Gabriel Fahrenheit made thermometers using mercury. The zero point of his scale is attained by mixing equal parts of water, ice, and salt. A second point was obtained when pure water froze (originally set at 30oF), and a third (set at 96°F) “when placing the thermometer in the mouth of a healthy man”. On that scale, water boiled at 212. Later, Fahrenheit moved the freezing point of water to 32 (so that the scale had 180 increments).In 1745, Carolus Linnaeus of Upsula, Sweden, described a scale in which the freezing point of water was zero, and the boiling point 100, making it a centigrade (one hundred steps) scale. Anders Celsius (1701-1744) used the reverse scale in which 100 represented the freezing point and zero the boiling point of water, still, of course, with 100 degrees between the two defining points.T (K)1081071061051041031001010.1Hydrogen bombSun’s interiorSolar coronaSun’s surfaceCopper meltsWater freezesLiquid nitrogenLiquid hydrogenLiquid heliumLowest T~ 10-9KPhysics 207: Lecture 23, Pg 9Ideal gas: Macroscopic descriptionConsider a gas in a container of volume V, at pressure P, and at temperature TEquation of state Links these quantities Generally very complicated: but not for ideal gasPV = nRTR is called the universal gas constantIn SI units, R =8.315 J / mol·Kn = m/M : number of molesEquation of state for an ideal gas Collection of atoms/molecules moving randomly No long-range forces Their size (volume) is negligible Density is low Temperature is well above the condensation pointPhysics 207: Lecture 23, Pg 10Boltzmann’s constantIn terms of the total number of particles NP, V, and T are the thermodynamics variablesPV = nRT = (N/NA ) RTkB is called the Boltzmann’s constantkB = R/NA = 1.38 X 10-23 J/K PV = N kB TNumber 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 m=mass M=mass of one molePhysics 207: Lecture 23, Pg 11What is the volume of 1 mol of gas at STP ?T = 0 °C = 273 Kp = 1 atm = 1.01 x 105 PanRTpV 4.22m0224.0Pa1001.1K 273Kmol/J31.835PnRTVThe Ideal Gas LawPhysics 207: Lecture 23, Pg 12ExampleA spray can containing a propellant gas at twice atmospheric pressure (202 kPa) and having a volume of 125.00 cm3 is at 27oC. It is then tossed into an open fire. When the temperature of the gas in the can reaches 327oC, what is the pressure inside the can? Assume any change in the volume of the can is negligible.Steps1. Convert to Kelvin (From 300 K to 600 K)2. Use P/T = nR/V = constant P1/T1 = P2/T23. Solve for final pressure P2 = P1 T2/T1http://www.thehumorarchives.com/joke/WD40_StupidityPhysics 207: Lecture 23, Pg 13Example problem: Air bubble risingA diver produces an air bubble underwater, where the absolute pressure is p1 = 3.5 atm. The bubble rises to the surface, where the pressure is p2 = 1.0 atm. The water temperatures at the bottom and the surface are, respectively, T1 = 4°C, T2 = 23°CWhat is the ratio of the volume of the bubble as it reaches the surface,V2, to its volume at the bottom, V1? (Ans.V2/V1 = 3.74)Is it safe for the diver to ascend while holding his breath? No! Air in the lungs would expand, and the lung could rupture.Physics 207: Lecture 23, Pg 15Example problem: Air bubble risingA diver produces an air bubble underwater, where the absolute pressure is p1 = 3.5 atm. The bubble rises to the surface, where the pressure is p2 = 1 atm. The water temperatures at the bottom and the surface are, respectively, T1 = 4°C, T2 = 23°CWhat is the ratio of the volume of the bubble as it reaches the surface,V2, to its volume at the bottom, V1? (Ans.V2/V1 = 3.74)pV=nRT pV/T = const so p1V1/T1 = p2V2/T2 V2/V1 = p1T2/ (T1 p2) = 3.5 296 / (277 1)If thermal transfer is efficient. [More than likely the expansion will be “adiabatic” and, for a diatomic gas, PV = const. where = 7/5, see Ch. 17 & 18]Physics 207: Lecture 23, Pg 16Buoyancy and the Ideal Gas LawA typical 5 passenger hot air balloon has approximately 700 kg of total mass and the balloon itself can be thought as spherical with a radius of 10.0 m. If the balloon is launched on a day with conditions of 1.0 atm and 273 K, how hot would you have to heat the air inside (assuming the density of the surrounding air is 1.2 kg/m3 and the air behaves and as an
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