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Chapter 13

Chapter 13. Temperature and Kinetic Theory. Topics in this Chapter. Atomic Theory of Matter Temperature and Thermometers Thermal Equilibrium and the Zeroth Law of Thermodynamics Thermal Expansion. The Gas Laws and Absolute Temperature The Ideal Gas Law

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Chapter 13

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  1. Chapter 13 Temperature and Kinetic Theory

  2. Topics in this Chapter • Atomic Theory of Matter • Temperature and Thermometers • Thermal Equilibrium and the Zeroth Law of Thermodynamics • Thermal Expansion • The Gas Laws and Absolute Temperature • The Ideal Gas Law • Ideal Gas Law in Terms of Molecules: Avogadro’s Number • Kinetic Theory and the Molecular Interpretation of Temperature

  3. Atomic Theory of Matter • The atomic theory of matter states that matter has a limited number of subdivisions in which the smallest indivisible piece is called an atom. • Modern evidence for atomic theory comes from the law of definite proportions and Brownian movement.

  4. Atomic Theory of Matter • Atomic and molecular masses are measured in unified atomic mass units (u). • This unit is defined so that the carbon-12 atom has a mass of exactly 12.0000 u. • Expressed in kilograms: • 1 u = 1.6605 x 10-27 kg • Remember: The molecular mass of a compound is the sum of atomic masses of the atoms making up the molecules of that compound.

  5. Atomic Theory of Matter • On a microscopic scale, the arrangements of molecules in solids (a), liquids (b), and gases (c) are quite different.

  6. Temperature and Thermometers • Temperature is a measure of how hot or cold something is. • The more physicsy definition: Temperature is the average kinetic energy of molecules. • Many properties of matter change with temperature. • Most materials expand when heated. • The color radiated by objects can change at high temperatures. • The electrical resistance of matter changes with temperature. (Ch.18)

  7. Temperature and Thermometers • Thermometers are instruments designed to measure temperature. • Their operation depends on some property of matter that changes with temperature: • Δ volume of a liquid • Δ length of a solid • Δ pressure of a gas held at a constant volume • Δ electric resistance of a conductor • Most thermometers rely on the expansion of a material with an increase in temperature. • For example the liquid-in-glass type and the bimetallic strip:

  8. Temperature Scales • In order to measure temperature quantitatively, a scale must be defined. • The most common scale is the Celsius scale, also called the centigrade scale. • We use the Fahrenheit scale in the United States. • The most important scale in science is the Kelvin scale, also called the absolute scale. • One way a temperature scale can be defined is to assign arbitrary values to two readily reproducible temperatures. • For both Celsius and Fahrenheit, these two fixed points are the freezing point (0°C, 32°F) and boiling point of water (100°C, 212 °F). • The Kelvin scale is based on absolute zero. It has the same intervals as Celsius, but it’s zero point is 0 K, the lowest theoretical possible temperature.

  9. Temperature Scales You may need to convert between the different scales in problems. In case you have forgotten them, the formulas are as follows: Fahrenheit to Celsius: Celsius to Fahrenheit: Celsius to Kelvin:

  10. Totally Obvious, Fifth Grade Stuff Oops, I mean: Thermal Equilibrium and the Zeroth Law of Thermodynamics Thermal Equilibrium The Zeroth Law of Thermodynamics • When two objects at different temperatures are placed in thermal contact, the two objects will reach the same temperature, or thermal equilibrium. • When two objects are in thermal equilibrium, no energy flows from one to the other, and their temperatures don't change. • If two substances are in thermal equilibrium with a third system, then the two substances are in thermal equilibrium with each other. • Kind of like: • If A=C and B=C, then A=B.

  11. Thermal Expansion • Most substances expand when heated and contract when cooled. • The expansion is due to an increased separation between molecules as they gain more energy from an increased in temperature. • Exactly how much expansion or contraction depends on the material of the object. • We will discuss how to calculate thermal expansion: • Linear Expansion (1D) • Volume Expansion (3D)

  12. Where: • Δl= change in length of the object (m) • α= coefficient of linear expansion (°C)-1 • Use the table on page 358. • Use a (+) for expansion. • Use a (–) for contraction. • l0= original length (m) • ΔT = change in temperature (°C) Linear Expansion Calculating Thermal Expansion • *Not for gases or liquids – no fixed shape.

  13. Where: • ΔV= change in area of the object (m2) • β= coefficient of volume expansion (°C)-1 • β ≈ 3α, usually (for isotropic solids) • Use the table on page 358. • Use a (+) for expansion. • Use a (–) for contraction. • V0= original area (m2) • ΔT = change in temperature (°C) Volume Expansion Calculating Thermal Expansion

  14. Thermal Expansion • Can you think of any substances that do not follow this trend (expand when heated and contract when cooled)? • WATER! • Water is weird. As it is heated from 0°C, it decreases in volume until the temperature reaches 4°C (about 40°F), then it behaves normally. • Without this strange property of water, life on this planet as we know it would not be possible.

  15. The Gas Laws • The volume of a gas depends on the pressure and temperature of the gas. Therefore, it is not always useful to use the equation for volume expansion for gases. • Therefore, it is valuable to determine a relationship between the mass, volume, pressure, and temperature of a gas – this relation is called an equation of state. • We will review: • Boyle’s Law • Charles’s Law • Gay-Lussac’s Law • The Ideal Gas Law

  16. Boyle’s Law • Stated by Robert Boyle (1627-1691) • “The volume of a gas is inversely proportional to the absolute pressure applied to it when the temperature is kept constant.”

  17. Charles’s Law • Stated by Jacques Charles (1746-1823) • “The volume of a given amount of gas is directly proportional to the absolute temperature when the pressure is kept constant.”

  18. Gay-Lussac’s Law • Stated by Joseph Gay-Lussac (1778-1850) • “At a constant volume, the absolute pressure of a gas is directly proportional to the absolute temperature.”

  19. The Ideal Gas Law • The ideal gas law is a combination of Boyle’s, Charles’s, and Gay-Lussac’s laws. • The ideal gas law also includes the mass of the substance and a proportionality constant. • The proportionality constant turns out to be the same for all gases if, instead of the mass, we use the number of moles. • Mole is the unit for amount of a substance. • One mole (mol) is defined as the number of grams of a substance numerically equal to the molecular mass of the substance. • Ex. The number of moles in 132 g of CO2 = 30. mol

  20. The Ideal Gas Law PV = nRT Where: • P = absolute pressure • V = volume • n= number of moles • R= universal gas constant • T = temperature (in K) • Values for R in various units: • 8.314 J/(mol·K) • 0.0821 (L·atm)/(mol·K) • 1.99 calories/(mol·K) • Standard temperature and pressure (STP): • T = 273 K • P = • 1 atm • 1.013 x 105 N/m2 • 101.3 kPa • FYI - The volume of 1 mol of an ideal gas at STP is 22.4 L.

  21. Ideal Gas Law in Terms of Avogadro’s Number • Since the gas constant is universal, the number of molecules in one mole is the same for all gases. • This number is called Avogadro’s number: (molecules/mol) • The number of molecules in a gas is the number of moles times Avogadro’s number:

  22. Ideal Gas Law in Terms of Avogadro’s Number • Therefore we can write the ideal gas law as: • PV = NkT • kis called Boltzmann’s constant:

  23. Kinetic Theory and the Molecular Interpretation of Temperature • The analysis of matter in terms of atoms in continuous random motion is called the kinetic theory. • Assumptions of kinetic theory: • large number of molecules, moving in random directions with a variety of speeds • molecules are far apart, on average • molecules obey laws of classical mechanics and interact only when colliding • collisions are perfectly elastic

  24. The Results of Kinetic Theory that are Important to Us: • The relationship between the internal energy of a gas and its temperature is: • This equation allows us to find the temperature of a gas given its internal energy, or vice versa. • The root-mean-square (rms) speed of gas molecules is: Where: • M = molar mass • μ = mass of molecule

  25. Chapter 13 - Practice Problemsp. 380-381 • Atomic Theory • #1 + 2 • Temp. and Thermometers • #3 • Thermal Expansion • #7, 11, 13, • Gas Laws • #26 + 27 • Ideal Gas Law • #29, 32, 33 • Ideal Gas Law in terms of Avogadro’s Number • #41, 42 • Molecular Interpretation of Temperature • #46, 47, 50

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