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2. Chapter 18 Heat Flow and the First Law of Thermodynamics

3. Main Points of Chapter 18 Changes in thermal systems – isothermal, adiabatic Reversible and irreversible processes Heat flow Phase changes Thermal resistance Mechanical equivalent of heat Work done by thermal systems Internal energy of ideal gases First law of thermodynamics

4. 18-1 Changes in Thermal Systems Change where system is always in thermal equilibrium: reversible process Change where system is not always in thermal equilibrium: irreversible process Examples of irreversible processes: Free expansion melting of ice in warmer liquid frictional heating

5. 18-1 Changes in Thermal Systems Example of a Reversible Process: Cylinder must be pulled or pushed slowly enough that the system remains in thermal equilibrium

6. 18-1 Changes in Thermal Systems Example of an Irreversible Process: The gas expands freely when the valve is opened.

7. 18-2 Heat Flow Temperature of a system is closely related to its internal (thermal) energy System can transfer energy by changing temperature or phase of another, by doing work, or both When temperature of system changes, there has been heat flow Q Heat capacity connects heat flow to temperature change: (18-1a)

8. 18-2 Heat Flow Heat capacity depends on material, and also on the quantity of material present. Eliminate quantity dependence by introducing specific heat c and molar heat capacity c ′: Here, m is the mass in grams, and n the number of moles. Units of heat flow: calories; 1 cal is heat needed to raise 1g of water from 14.5°C to 15.5°C.

9. 18-2 Heat Flow Specific Heats and Molar Heat Capacities

10. 18-2 Heat Flow A phase change occurs when a solid melts to a liquid, a liquid boils to a gas, a gas condenses to a liquid, and a liquid freezes to a solid. Each of these phase changes requires a certain amount of heat, although the temperature does not change.

11. 18-2 Heat Flow If a solid becomes liquid, or vice versa, the amount of heat per gram is the latent heat of fusion. If a liquid becomes gas, or vice versa, the amount of heat per gram is the latent heat of vaporization.

12. 18-2 Heat Flow This diagram shows how water (in the form of ice) behaves as heat is steadily added to it:

13. 18-2 Heat Flow: Some Latent Heats

14. 18-3 Heat Flow in Materials If one end of a solid of length L is maintained at a temperature T 1 and the other at a lower temperature T 2, the rate of heat flow depends on the temperature difference, the cross-sectional area of the solid, and its length: (18-7)

15. 18-3 Heat Flow in Materials As long as ΔT is small enough to keep the relationship linear, we can write: (18-8) where κ is the thermal conductivity.

16. 18-3 Heat Flow in Materials

17. Thermal resistance, also known as R value, is inversely proportional to conductivity and depends on the thickness of the material: (18-9) If the R value is high, the material is a good insulator; if it is low, the material is a poor insulator.

18. 18-3 Heat Flow in Materials Two different materials can be connected in series (so the heat flows first through one and then the other) or parallel (so they are next to each other and heat flows through both simultaneously. In series: (18-11)

19. 18-3 Heat Flow in Materials In parallel: (18-12)

20. 18-4 The Mechanical Equivalent of Heat Temperature of a system can also be raised by performing mechanical work on it. No experiment can detect whether a change in temperature was due to mechanical work or to heat flow: heat flow must be an energy transfer!

21. 18-4 The Mechanical Equivalent of Heat Therefore, can relate units of heat flow to units of work: (18-13) This is now the numerical definition of the calorie.

22. 18-5 Work Done by Thermal Systems Work can be done by, instead of on, thermal systems, as in the expansion of a gas. Using the definitions of work and pressure: (18-14) (18-15) Then: (18-16) The next slide shows that the work done by a cyclic transformation is the area enclosed by the p-V curve.

23. 18-5 Work Done by Thermal Systems

24. Types of transformations Isobaric (constant pressure): Isochoric (constant volume): no work is done, as there is no movement Adiabatic (no heat flow in or out of system): temperature can change only if work is done. (18-18)

25. 18-5 Work Done by Thermal Systems Types of transformations (cont) Internal (or thermal) energy U in adiabatic transformations: Infinitesimal: Finite: (18-21) (18-22)

26. 18-5 Work Done by Thermal Systems (18-23) A finite change in internal energy is independent of the path between A and B; therefore:

27. 18-6 The First Law of Thermodynamics (18-24) First law is a statement of conservation of energy: Change in internal energy of system equals is work done on system plus heat flow into system. In differential form, (18-25b)

28. 18-6 The First Law of Thermodynamics In a closed cycle: If the volume is constant: If pressure is constant: (18-26) (18-27) (18-28)

29. 18-7 Internal Energy of Ideal Gases Joule experiment: on left, have a container filled with a dilute (ideal) gas. Open stopcock; gas expands, doing no work – find that its temperature does not change (on right) The temperature of an ideal gas undergoing free expansion remains constant.

30. 18-7 Internal Energy of Ideal Gases (18-31) Therefore, for an ideal gas, U is a function only of temperature. Combining this with the energy changes in in constant-volume transformations: C V is independent of temperature over a large range; when it is: (18-32)

31. 18-7 Internal Energy of Ideal Gases Can also express C p in terms of C V : so that: (18-33)

32. 18-8 More Applications for Ideal Gases (18-35) Work done during isothermal transformation (18-34)

33. 18-8 More Applications for Ideal Gases In an adiabatic transformation, The p-V curve has the form: (18-36) where (18-37)

34. 18-8 More Applications for Ideal Gases (18-43) Earth’s atmosphere is cooler the higher one goes. When the air rises, it expands, and its temperature decreases. Assuming the air is an ideal gas, the temperature is found to decrease linearly with altitude:

35. Summary of Chapter 18 Reversible change of state: system always in thermal equilibrium When temperature changes, internal energy has changed – may happen through heat transfer or through mechanical work For constant volume: For constant pressure: In general: (18-4) (18-5) (18-6)

36. Summary of Chapter 18 Specific heat is heat capacity of 1 g of material; molar heat capacity is heat capacity of 1 mol Thermal conductivity: (18-8) R value: (18-9) Heat flow is energy transfer; can express calorie as energy unit: (18-13)

37. Summary of Chapter 18 For adiabatic transition (dQ = 0): (18-21) Change in internal energy can be caused by mechanical work and heat transfer: (18-24) For an ideal gas: (18-33)