Physics Chapter 13: Temperature and Kinetic Theory

Chapter 13: Temperature and Kinetic Theory

• This chapter covers the atomic theory of matter, temperature, and thermometers.
• It also discusses thermal equilibrium, the zeroth law of thermodynamics, thermal expansion, gas laws, absolute temperature and the ideal gas law.
• Additional topics include problem-solving with ideal gas laws, the kinetic theory and molecular interpretation of temperature, distribution of molecular speeds, real gases and changes of phase, vapor pressure and humidity, and diffusion.

13-1 Atomic Theory of Matter

• Atomic and molecular masses are measured in unified atomic mass units (u).
• One unified atomic mass unit (u) is equal to 1.6605 x 10⁻²⁷ kg.
• Carbon-12 has a mass of exactly 12.0000 u.
• Brownian motion is the jittery motion of tiny flecks in water, caused by collisions with individual water molecules.
• Molecules in solids, liquids, and gases have different microscopic arrangements.

13-2 Temperature and Thermometers

• Temperature measures how hot or cold something is.
• Most materials expand when heated.
• Thermometers use properties of matter that change with temperature to measure temperature.
• Common thermometers include liquid-in-glass and bimetallic strip types.
• Temperature is typically measured using the Fahrenheit or Celsius scale.
• The freezing point of water is 0°C or 32°F; the boiling point is 100°C or 212°F.

13-3 Thermal Equilibrium and the Zeroth Law of Thermodynamics

• Two objects in thermal contact eventually reach the same temperature (thermal equilibrium).
• The zeroth law states that if two objects are each in thermal equilibrium with a third object, then they are in thermal equilibrium with each other.
• Linear expansion happens when an object is heated.

13-4 Thermal Expansion

• The coefficient of linear expansion (represented by 'a') describes how much a solid expands when heated.
• Volume expansion (represented by 'β') is similar to linear expansion, but applies to liquids and gases as well as solids.
• For uniform solids, β is roughly equal to 3α.
• Water's expansion behavior is different from other substances; it has a minimum volume at 4°C.
• Thermal stress occurs when a material is fixed at its ends and cannot expand freely when the temperature changes.

13-5 The Gas Laws and Absolute Temperature

• The relationship between volume, pressure, temperature, and mass of a gas is described by an equation of state.
• Boyle's Law: The volume of a gas is inversely proportional to its pressure when temperature is constant.
• Gas volume is linearly proportional to temperature when pressure is constant.
• Extrapolating this relationship, the volume becomes zero at -273.15°C, known as absolute zero.
• Absolute (Kelvin) temperature scale starts at 0 K at absolute zero, similar to Celsius, but with different numerical values for freezing and boiling points of water. (273.15K & 373.15 K respectively).

13-6 The Ideal Gas Law

• Combining the gas laws gives the ideal gas law: PV = nRT.
• A mole (mol) is the mass of a substance (grams) equivalent to its molecular mass.
• For example, 1 mole of H₂ = 2 grams.
• The ideal gas law includes the number of moles (n) and the universal gas constant (R).

13-7 Problem Solving with the Ideal Gas Law

• Standard temperature and pressure (STP) is defined as T=273K and P=1.00atm (101.3kPa).
• The volume of 1 mole of an ideal gas at STP is about 22.4 L.
• Temperature must be measured in Kelvin when using the Ideal Gas Law.

13-8 Ideal Gas Law in Terms of Molecules: Avogadro's Number

• The universal gas constant allows for the same number of molecules to be found in 1 mole of any gas (Avogadro’s number).
• Avogadro's number is approximately 6.02 x 10²³.
• The number of molecules (N) in a gas is the number of moles (n) times Avogadro's number.

13-9 Kinetic Theory and the Molecular Interpretation of Temperature

• Kinetic theory assumptions include that gases have many molecules moving randomly at various speeds, molecules are far apart, molecules interact only when colliding, and collisions are perfectly elastic.
• The pressure of a gas is related to the average kinetic energy of its molecules and the temperature of the gas is related to the average translational kinetic energy of gas molecules.
• The average speed of molecules is related to the temperature and the molar mass of the gas.

13-10 Distribution of Molecular Speeds

• Maxwell derived graphs showing the distribution of speeds for molecules in a gas; the most probable speed isn't the same as the root-mean-square speed.
• As expected, the curves shift further along the speed axis towards higher speeds as the temperature increases.

13-11 Real Gases and Changes of Phase

• Gas behavior deviates from ideality at lower temperatures. (Further from ideal as temperature decreases)
• At lower temperatures, gases can transition to a liquid phase if pressure is high enough.
• The critical point is the highest temperature at which a gas can be liquefied.
• A phase diagram shows all three phases of matter and phase transitions like melting, freezing, boiling, condensation, and sublimation.
• The triple point shows the unique temperature and pressure at which all three phases can coexist. (Phase diagrams for water and carbon dioxide are discussed).

13-12 Vapor Pressure and Humidity

• Evaporation is the process by which the fastest molecules escape from a liquid surface. (cooling process)
• Condensation is the opposite process of evaporation.
• When evaporation and condensation are at equilibrium, the vapor is saturated, and its pressure is called the saturated vapor pressure.
• Saturated vapor pressure increases with temperature.
• Liquid boils when its saturated vapor pressure equals the external pressure.
• Partial pressure and relative humidity are defined in relation to mixtures of gases.
• Humidity describes how close or far a mixture of gases is from saturation relative to water vapor.

13-13 Diffusion

• Diffusion is the process of a substance spreading out until its concentration is uniform.
• Diffusion occurs from a high concentration region towards a region of lower concentration.
• The rate of diffusion is directly proportional to the diffusion constant (D)