Physics 1710—Warm-up Quiz What is the first audible harmonic that has a frequency above 20 Hz for a cable that has a mass of 1.0 kg, is 10.0 long, and is supporting a kg mass? A.1 B.2 C.4 D.8 E.The sound is never audible.

Physics 1710 Chapter 19 Temperature Solution: μ = m/L = 1.0 kg/10 m = 0.10 kg/m μ = m/L = 1.0 kg/10 m = 0.10 kg/m T = Mg = (100.0 kg) (9.8 N/kg) = 980 N T = Mg = (100.0 kg) (9.8 N/kg) = 980 N ƒ n = n/(2L)√[T/ μ ] = n/(2* 10.0 m) √[980./ 0.1 ] = n (4.95 Hz) ƒ n = n/(2L)√[T/ μ ] = n/(2* 10.0 m) √[980./ 0.1 ] = n (4.95 Hz) n = 20 Hz/ ƒ 1 = 20/(4.95) = 4.0 n = 20 Hz/ ƒ 1 = 20/(4.95) = 4.0

Physics 1710 Chapter 19 Temperature 1′ Lesson: Temperature is a measure of the average kinetic energy of a system of non-interacting particles (an ideal gas). Temperature is a measure of the average kinetic energy of a system of non-interacting particles (an ideal gas). Thermal Equilibrium means that two bodies are at the same temperature. Thermal Equilibrium means that two bodies are at the same temperature. The “Zeroth Law of Thermodynamics” states that if system A and B are in thermal equilibrium with system C, then A and B are in thermal Equilibrium with each other. The “Zeroth Law of Thermodynamics” states that if system A and B are in thermal equilibrium with system C, then A and B are in thermal Equilibrium with each other. Kelvin is a unit of temperature where one degree K is 1/ of the temperature of the triple point of water (near freezing). Kelvin is a unit of temperature where one degree K is 1/ of the temperature of the triple point of water (near freezing).

Physics 1710 Chapter 19 Temperature 1′ Lesson: A length body will expand in proportion to the change in temperature. A length body will expand in proportion to the change in temperature. The ideal gas law states that the product of the pressure and volume of a gas is proportional to the amount of the gas and the absolute temperature. The ideal gas law states that the product of the pressure and volume of a gas is proportional to the amount of the gas and the absolute temperature.

Physics 1710 Chapter 19 Temperature Boltzmann’s Dream: A reductionist’s explanation of heat and temperature. A reductionist’s explanation of heat and temperature. Heat is the total internal energy of moving atoms in a substance. Heat is the total internal energy of moving atoms in a substance. Temperature is the (average) kinetic energy of the moving atoms. Temperature is the (average) kinetic energy of the moving atoms. Two systems with the same temperature are in Thermal Equilibrium. Two systems with the same temperature are in Thermal Equilibrium.

Physics 1710 Chapter 19 Temperature Boltzmann’s Dream: v1v1v1v1 v2v2v2v2 v3v3v3v3 v4v4v4v4 v5v5v5v5 Gas KE average = 3/2kT KE average = Σ ½ m i v i 2 /N

Physics 1710 Chapter 19 Temperature Boltzmann’s Dream: Solid KE average = 3/2kT KE average = Σ ½ m i v i 2 /N

Physics 1710 Chapter 19 Temperature Zeroth (0 th ) Law of Thermodynamics If objects A and B are separately in thermal equilibrium with a third object C, then objects A and B are in thermal equilibrium with each other.

Physics 1710 Chapter 19 Temperature Temperature Degrees of temperature Degrees of temperature – Centigrade (Celsius, archaic) C – 0 C ~ ice point of water – 100 C ~ boiling point of water Measurement Measurement – Gas thermometer – Linear expansion – Volume expansion – Phase changes (calibration points)

Physics 1710 Chapter 19 Temperature Temperature Scales Centigrade ( C) 0 C~ice; 100 C~steam Centigrade ( C) 0 C~ice; 100 C~steam Fahrenheit (ripped off Roemer) Fahrenheit (ripped off Roemer) 0⁰F ~ lowest T that he could get (brine) 100⁰F ~ approximate body temperature (98.6 ⁰F normal) T C = (100/180) (T F – 32 ⁰F) T F = (180/100) T C + 32 ⁰F

Physics 1710 Chapter 19 Temperature Absolute Temperature Kelvin (K) [N.B. not “degrees Kelvin”] Kelvin (K) [N.B. not “degrees Kelvin”] T = T C T = T C At 0 K the total internal kinetic energy of a system is at the absolute minimum. At 0 K the total internal kinetic energy of a system is at the absolute minimum.

Physics 1710 Chapter 19 Temperature Linear Expansion Change in T mean change in average kinetic energy Change in T mean change in average kinetic energy More average kinetic energy means increase in average displacement from equilibrium position More average kinetic energy means increase in average displacement from equilibrium position Law of linear expansion Law of linear expansion ∆L/L = α ∆T Fractional change in length is proportional to the change in temperature. Fractional change in length is proportional to the change in temperature.

Physics 1710 Chapter 19 Temperature Phases Solid: atoms “locked” into position Solid: atoms “locked” into position – microstructure determines bulk properties – distance between atoms determines density Liquid: atoms “dance” in groups and pairs, sliding past each other. Liquid: atoms “dance” in groups and pairs, sliding past each other. Gas: atoms far enough apart to prevent “locking up” or pairing. Gas: atoms far enough apart to prevent “locking up” or pairing.

Physics 1710 Chapter 19 Temperature Ideal Gas Law Idealizations: Idealizations: no interaction between atoms no volume occupied by atoms Number of atoms n = m/M, Number of atoms n = m/M, m = mass; M = molar mass PV = n R T PV = n R T R = J/ mol K = L‧atm/mol K = L‧atm/mol K = 22.4 L‧atm / mol K = 22.4 L‧atm / mol K

Physics 1710 Chapter 19 Temperature Boltzmann’ Constant k = R/N A k = R/N A k = 1.38 x J/K = 1 yJ/ 7.25 K k = 1.38 x J/K = 1 yJ/ 7.25 K = 1 eV / 11,600 K = 1 eV / 11,600 K PV = N kT

Physics 1710 Chapter 19 Temperature Summary: Temperature is a measure of the average kinetic energy of a system of particles.Temperature is a measure of the average kinetic energy of a system of particles. Thermal Equilibrium means that two bodies are at the same temperature. Thermal Equilibrium means that two bodies are at the same temperature. The “Zeroth Law of Thermodynamics” states that if system A and B are n thermal equilibrium with system C, then A and B are in thermal Equilibrium with each other. The “Zeroth Law of Thermodynamics” states that if system A and B are n thermal equilibrium with system C, then A and B are in thermal Equilibrium with each other.

Physics 1710 Chapter 19 Temperature Kelvin is a unit of temperature where one degree K is 1/ of the temperature of the triple point of water (near freezing).Kelvin is a unit of temperature where one degree K is 1/ of the temperature of the triple point of water (near freezing). T C = (100/180) (T F – 32 ⁰F) T F = (180/100) T C + 32 ⁰F ∆L/L = α∆T ∆L/L = α∆T PV = n R T = N kT PV = n R T = N kT