Chapters 16, 17 Temperature, Heat, and the Thermal Behavior of Matter

1. Chapters 16, 17 Temperature, Heat, and the Thermal Behavior of Matter

2. William Thomson (Lord Kelvin)(1824 - 1907) • Temperature • Thermodynamics – branch of physics studying thermal energy of systems • Temperature (T), a scalar – measure of the thermal (internal) energy of a system • SI unit: K (Kelvin) • Kelvin scale has a lower limit (absolute • zero) and has no upper limit

3. Kelvin scale • Kelvin scale is defined by the temperature of the triple point of pure water • Triple point – set of pressure and temperature values at which solid, liquid, and gas phases can coexist • International convention: • T of the triple point of water is

4. The zeroth law of thermodynamics • If two (or more) bodies in contact don’t change their internal energy with time, they are in thermal equilibrium • 0th law of thermodynamics: if bodies are in thermal equilibrium, their temperatures are equal

5. Measuring temperature • Temperature measurement principle: if bodies A and B are each in thermal equilibrium with a third body C, then A and B are in thermal equilibrium with each other (and their temperatures are equal) • The standard temperature for the Kelvin scale is measured by the constant-volume gas thermometer

6. Constant-volume gas thermometer

7. Anders Cornelius Celsius (1701 - 1744) Gabriel Daniel Fahrenheit (1686 - 1736) • Celsius and Fahrenheit scales • Celsius scale: • Fahrenheit scale:

8. Temperature and heat • Heat (Q): energy transferred between a system and its environment because of a temperature difference that exists between them • SI Unit: Joule • Alternative unit: calorie (cal):

9. Q Q • Absorption of heat • Specific heat (c): heat capacity per unit mass • Common states (phases) of matter: solid, liquid, gas • Latenet heat (L): the amount of energy per unit mass transferred during a phase change (boiling, condensation, melting, freezing, etc.)

10. Q Q Absorption of heat

11. Absorption of heat

12. Absorption of heat

13. Chapter 17 Problem 25 How much energy does it take to melt a 65-g ice cube?

14. Thermal conductivity • Heat transfer mechanisms • Thermal conduction • Conduction rate: • Thermal resistance: • Conduction through a composite rod:

15. Absorption of heat

16. Emissivity Josef Stefan (1835-1893) • Heat transfer mechanisms • Thermal radiation • Radiation rate: • Stefan-Boltzmann constant: • Absorption rate:

17. Heat transfer mechanisms • Convection

18. Heat transfer mechanisms

19. Chapter 16 Problem 35 An oven loses energy at the rate of 14 W per °C temperature difference between its interior and the 20°C temperature of the kitchen. What average power must be supplied to maintain the oven at 180°C?

20. Amedeo Avogadro (1776 -1856) • Avogadro’s number • Mole – amount of substance containing a number of atoms (molecules) equal to the number of atoms in a 12 g sample of 12C • This number is known as Avogadro’s number (NA): • NA = 6.02 x 1023 mol -1 • The number of moles in a sample • N – total number of atoms (molecules) • m – total mass of a sample, m0 – mass of a single atom (molecule); M – molar mass

21. Ludwig Eduard Boltzmann (1844-1906) • Ideal gases • Ideal gas – a gas obeying the ideal gas law: • R – gas constant • R = 8.31 J/mol ∙ K • kB – Boltzmann constant • kB = 1.38 x 1023 J/K

22. Ideal gases • The gas under consideration is a pure substance • All molecules are identical • Macroscopic properties of a gas: P, V, T • The number of molecules in the gas is large, and the average separation between the molecules is large compared with their dimensions – the molecules occupy a negligible volume within the container • The molecules obey Newton’s laws of motion, but as a whole they move randomly (any molecule can move in any direction with any speed)

23. Ideal gases • The molecules interact only by short-range forces during elastic collisions • The molecules make elastic collisions with the walls and these collisions lead to the macroscopic pressure on the walls of the container • At low pressures the behavior of molecular gases approximate that of ideal gases quite well

24. Ideal gases

25. Ideal gases • Root-mean-square (RMS) speed:

26. Translational kinetic energy • Average translational kinetic energy: • At a given temperature, ideal gas molecules have the same average translational kinetic energy • Temperature is proportional to the average translational kinetic energy of a gas

27. Internal energy • For the sample of n moles, the internal energy: • Internal energy of an ideal gas is a function of gas temperature only

28. James Clerk Maxwell (1831-1879) • Distribution of molecular speeds • Not all the molecules have the same speed • Maxwell’s speed distribution law: • Nvdv – fraction of molecules with speeds in the range from v to v + dv

29. Distribution of molecular speeds • Distribution function is normalized to 1: • Average speed: • RMS speed: • Most probable • speed:

30. Thermal expansion • Thermal expansion: increase in size with an increase of a temperature • Linear expansion: • Volume expansion:

31. Thermal expansion

32. Chapter 17 Problem 30 A copper wire is 20 m long on a winter day when the temperature is - 12°C. By how much does its length increase on a 26°C summer day?

33. Questions?

34. Answers to the even-numbered problems Chapter 16 Problem 22 2500 J/(kg K)

35. Answers to the even-numbered problems Chapter 16 Problem 40 2.0 × 102 Pa/K

36. Answers to the even-numbered problems Chapter 17 Problem 18 3.2 × 1023

37. Answers to the even-numbered problems Chapter 17 Problem 36 11 L