Prof. Werner J. Blau

Transcription

1 Prof. Werner J. Blau

2 Overview 1. General Concepts - Temperature, Heat, Phase Changes 2. Gases: Background Theory 3. Gases: Comparison with Experiments 4. Solids: Background Theory 5. Solids: Comparison with Experiments 6. Liquids: Background Theory 7. Liquids: Comparison with Experiments 8. Changes of Phase

3 3. Gases: Comparison with Experiment 3.1. Density 3.2. Expansivity 3.3. Heat Capacity 3.4. Thermal Conductivity

4 3.1 Density of Gases - Data Standard Temperature and Pressure (STP): T= K = 0 o C P= Pa = 1 atm

5 Density of Gases - Understanding Standard Temperature and Pressure (STP): T= K = 0 o C P= Pa = 1 atm Ideal Gas Equation: V = zrt / P with z = 1 mole: V = m 3

6 3.2 Expansivity of Gases Heating at Constant Pressure: V = V o β V T V = V o ( 1 + β V T ) Heating at Constant Volume: P = P o β p T P = P o ( 1 + β p T )

7 Expansivity of Gases - Data About times larger than liquids and solids

8 Expansivity of Gases - Understanding V = V o ( 1 + β V T ) T = T - T o V = zrt / P o V o = zrt o / P o β V = 1 / T o = K -1

9 3.3 Heat Capacity

10 Heat Capacity at Constant Pressure C p - Data

11 Heat Capacity at Constant Pressure C p - Data

12 Heat Capacity at Constant Pressure C p - Questions

13 Ratio of Heat Capacities γ = C p / C v - Data

14 Ratio of Heat Capacities γ = C p / C v - Data

15 Ratio of Heat Capacities γ = C p / C v - Questions

16 Heat Capacity of Gases - Understanding 1 First Law of Thermodynamics: Q = U - W Work Done by Gas: W = P V = z R T

17 Heat Capacity of Gases - Understanding 2 Heat Capacity at Constant Volume: W = P V = 0 Q = U U = z N A x p ½ k B T = ½ z p R T U = = ½ z p R T = Q C V = Q / T = ½ z p R per mole: z = 1 => C V = p J K -1 mol -1 p = 3 => C V = J K -1 mol -1 for Monatomic Gases

18 Heat Capacity of Gases - Understanding 3 Heat Capacity at Constant Pressure: W = P V = z R T - watch sign! U = = ½ z p R T Q = U - W = ½ z p R T - (- z R T) C P = Q / T = z R ( 1 + p/2) per mole: z = 1 => C P = ( 1 + p/2 ) J K -1 mol -1 p = 3 => C P = J K -1 mol -1 for Monatomic Gases

19 Ratio of Heat Capacities γ = C p / C v - Understanding 4 C V = Q / T = ½ z p R C P = Q / T = z R ( 1 + p/2) γ = C p / C v = 1 + 2/p p = 3 => γ = for Monatomic Gases

20 Heat Capacity of Gases - Comparison with Experiment 1

21 Heat Capacity of Gases - Comparison with Experiment 2 Degrees of Freedom: p = 2 ( C P / R - 1 ) and p = 2 / ( γ - 1 )

22 Heat Capacity of Gases - Comparison with Experiment 3

23 Heat Capacity of Gases - Comparison with Experiment 4 E ~ k B T ~ x 2000 J = J = ev With E = hf this corresponds to f = Hz (infrared)

24 Heat Capacity of Gases - Comparison with Experiment 5

25 3.4 Thermal Conductivity of Gases

26 Thermal Conductivity of Gases - Data

27 Thermal Conductivity of Gases - Questions Why does the thermal conductivity of gases increase at high temperature? Why is the thermal conductivity of gases independent of pressure across a wide range of pressures around atmospheric pressure? Why are the thermal conductivities of gases as low as they are? (c.f. 400 W m -1 K -1 for Cu, 10 W m -1 K -1 for Quartz)

28 Thermal Conductivity of Gases - Understanding 1

29 Thermal Conductivity of Gases - Understanding 2

30 Thermal Conductivity of Gases - Understanding 3

31 Thermal Conductivity of Gases - Understanding 4

32 Thermal Conductivity of Gases - Comparison with Experiment 1

33 Thermal Conductivity of Gases - Comparison with Experiment 2 Independent of pressure! Product of n and λ MFP ( ~ 1/n) Compensating each other exactly