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Ppa6 lecture ch_13

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  • 1. Chapter 13Temperature and Kinetic Theory
  • 2. 13-2 Temperature and ThermometersTemperature is a measure of how hot or coldsomething is.Most materials expand when heated.
  • 3. 13-2 Temperature and ThermometersThermometers are instruments designed tomeasure temperature. In order to do this, they takeadvantage of some property of matter thatchanges with temperature. Early thermometers:
  • 4. 13-2 Temperature and ThermometersCommon thermometers used today include theliquid-in-glass type and the bimetallic strip.
  • 5. 13-2 Temperature and Thermometers Temperature is generally measured using either the Fahrenheit or the Celsius scale. The freezing point of water is 0°C, or 32°F; the boiling point of water is 100°C, or 212°F.
  • 6. 13-4 Thermal Expansion Linear expansion occurs when an object is heated. (13-1b)Here, α is the coefficient of linearexpansion.
  • 7. 13-4 Thermal ExpansionVolume expansion is similar, except that it isrelevant for liquids and gases as well as solids: (13-2) Here, β is the coefficient of volume expansion. For uniform solids,
  • 8. 13-4 Thermal Expansion
  • 9. 13-4 Thermal ExpansionWater behaves differently from most other solids – itsminimum volume occurs when its temperature is 4°C. As itcools further, it expands, as anyone who has left a bottle inthe freezer to cool and then forgets about it can testify.
  • 10. 13-7 The Ideal Gas LawWe can combine the three relations justderived into a single relation:What about the amount of gas present? Ifthe temperature and pressure are constant,the volume is proportional to the amount ofgas:
  • 11. 13-7 The Ideal Gas LawA mole (mol) is defined as the number of gramsof a substance that is numerically equal to themolecular mass of the substance:1 mol H2 has a mass of 2 g1 mol Ne has a mass of 20 g1 mol CO2 has a mass of 44 gThe number of moles in a certain mass ofmaterial:
  • 12. 13-7 The Ideal Gas LawWe can now write the ideal gas law: (13-3)where n is the number of moles andR is the universal gas constant.
  • 13. 13-8 Problem Solving with the Ideal Gas LawUseful facts and definitions:• Standard temperature and pressure (STP) • Volume of 1 mol of an ideal gas is 22.4 L • If the amount of gas does not change: • Always measure T in kelvins • P must be the absolute pressure
  • 14. 13-10 Kinetic Theory and the Molecular Interpretation of TemperatureRewriting, (13-7)so (13-8)The average translational kinetic energy ofthe molecules in an ideal gas is directlyproportional to the temperature of the gas.
  • 15. 13-10 Kinetic Theory and the Molecular Interpretation of TemperatureWe can invert this to find the average speed ofmolecules in a gas as a function oftemperature: (13-9)
  • 16. 13-11 Distribution of Molecular Speeds These two graphs show the distribution of speeds of molecules in a gas, as derived by Maxwell. The most probable speed, vP, is not quite the same as the rms speed. As expected, the curves shift to the right with temperature.