Physics 13: Temperature and Kinetic Theory

1. Physics 13: Temperature and Kinetic Theory Christopher Chui Physics 13: Temperature and Kinetic Theory - Christopher Chui

2. Atomic Theory of Matter • Dalton (1800s): law of definite proportions • Atomic mass: assign C=12.0000 u • 1 u = 1.66 x 10-27 kg • Molecular mass = sum of all atomic masses in 1 molecule of compound • Brown (1927): atoms are constantly in motion • Molecular motion stops at unreachable 0o K • Diameter of a typical atom ~ 10-10 m Physics 13: Temperature and Kinetic Theory - Christopher Chui

3. Temperature and Thermometers • Temperature is a measure of hot/cold • Thermometers are instruments to measure temperature • In science, both Celsius and Kelvin are used • Fahrenheit scale is used in daily lives • Water freezes at 0o C or 32o F or 273o K at 1 atm • Water boils at 100o C or 212o F or 373o K at 1 atm • 2 simple formulas: C = 5/9[ F-32]; F = 9/5 [C] + 32 • Constant-volume gas thermometer is chosen as the standard thermometer Physics 13: Temperature and Kinetic Theory - Christopher Chui

4. 0th Law of Thermo & Expansion • If 2 systems are in thermal equilibrium with a 3rd system, then they are in thermal equilibrium with each other • Linear expansion: DL = aL0DT; L = L0 (1 + a DT) • Coefficient of vol expansion ~ 3 x coeff of linear exp • Volume expansion: DV = bV0DT • Water is unusual: it expands when cooled from 4o C to 0o C. For this reason, life exists under ice Physics 13: Temperature and Kinetic Theory - Christopher Chui

5. Thermal Stresses & Gas Laws • Large stress exists for expansion • DL= 1/E F/A L0 aL0DT= 1/E F/A L0F= aEADT • Boyle’s law (1600s): the volume of a gas is inversely proportional to the pressure applied to it when the temperature is kept constant  V prop 1/P • PV = constant when T is kept constant • Absolute zero = -273.15o C = 0o K; K = C + 273.15 • Charles’ law: the volume of a given amount of gas is directly proportional to the absolute temperature when the pressure is kept constant  V prop T • Gay-Lussac’s law: at constant volume, the pressure of a gas is directly proportional to the absolute temperature  P prop T • Ideal gas law: PV prop T or PV prop mT; PV = nRT Physics 13: Temperature and Kinetic Theory - Christopher Chui

6. STP and Avogadro’s Number • STP (standard temp and pressure) = 273K and 1 atm • Under conditions 1 and 2: P1V1/T1 = P2V2/T2 • 1 mole of gas at STP has volume = 22.4 L • Always give T in K, and P as absolute, not gauge, P • Equal volumes of gas at the same pressure and temperature contain equal numbers of molecules • Avogadro’s number ~ 6.02 x 1023 • Ideal gas law: PV = NkT in terms of no. of molecules • Boltzmann’s constant, k = R/NA = 1.38 x 10-23 J/K Physics 13: Temperature and Kinetic Theory - Christopher Chui

7. Kinetic Theory of Molecules • 1. Large number of molecules, N, each of mass m, move in random directions with a variety of speeds • 2. Molecules are far apart from one another • 3. Molecules are assumed to obey the laws of classical mechanics and assumed to interact when they collide • 4. Collisions with another molecule or the wall of the vessel are assumed to be perfectly elastic • All gas laws can be explained using the kinetic theory of gases Physics 13: Temperature and Kinetic Theory - Christopher Chui

8. Kinetic Energy of Gases-1 • Pressure in a gas = 1/3 NmV2 / V • Average KE = ½ mv2 = 3/2 kT • The average translational kinetic energy of molecules in a gas in directly proportional to the absolute temperature • Root-mean-square (rms) velocity= sq v2=sq(3kT/m) • Maxwell distribution of speeds ~ skewed normal • Activation energy, EA, is the min energy required for a chemical reaction to occur • For real gases, there is a critical temperature at which liquid and gas coexist at the same time • On a P vs T graph (phase diagram), a triple point exists at which solid, liquid, and gas coexist together Physics 13: Temperature and Kinetic Theory - Christopher Chui

9. Kinetic Energy of Gases-2 • Kinetic theory predicts that evaporation is a cooling process. Fast moving molecules evaporate. Some molecules strike the liquid surface and condense • The pressure of the vapor when it is saturated is the saturated vapor pressure • Vapor pressures occur at all temperature above 0 K • When temperature is raised above the vapor pressure, boiling occurs. At boiling, saturated vapor pressure = external pressure • The total pressure is the sum of all partial pressures of each gas present Physics 13: Temperature and Kinetic Theory - Christopher Chui

10. Kinetic Energy of Gases-3 • Partial pressure is the pressure each gas would exert if it were to occupy the whole volume • Relative humidity is the ratio of the partial pressure to the saturated vapor pressure at a given temp. • Relative humidity = [partial pressure of H2O / saturated pressure of H2O ] 100% • Proper humidity is maintained in museums to protect artwork. A humidity of 40-50% is optimum for comfort • If the partial pressure of water > the saturated vapor pressure, the air is supersaturated • When air containing water is cooled, a temperature is reached where the partial pressure=sat vapor pressuredew point Physics 13: Temperature and Kinetic Theory - Christopher Chui

11. Diffusion • Random movement of foreign molecules throughout a liquid or gas is called diffusion • The diffusing substance moves from a region where its concentration is high to one where its concentration is low • Concentration gradient = (C1 – C2)/Dx • Fick’s law: rate of diffusion, J = DA(C1 – C2)/Dx • D is the diffusion constant • Diffusion occurs in plants and animals for nutrients and gases Physics 13: Temperature and Kinetic Theory - Christopher Chui