Thermodynamics

1. Thermodynamics Introduction: what is thermodynamics about? • Study heat, temperature, internal energy, gas, liquid, solid, melting, boiling, exploding, P-V-T. • Explain bulk properties of matter and the correlation with the mechanics of atoms and molecules. • Understand why/ how the refrigerator cools stuff • Understand why/ how automobile engines power cars • Understand why/ how power plants work • Understand where the work due to friction goes Note: presentation main figures are that of Halliday and Resnick 6th edition unless otherwise specified.

2. Chapter 18Temperature, Heat and the First Law of Thermodynamics 18.2 Thermodynamics 18.3 Zeroth law of thermodynamics 18.4 Measuring temperature and the constant volume gas thermometer 18.5 The Celsius and the Fahrenheit scales 18.6 Thermal expansion 18.7 Temperature and Heat 18.8 The Absorption of Heat by Solids and Liquids 18.9 Heat and Work 18.10 The FLTD 18.11 Special cases of FLTD 18.12 Heat Transfer

3. 18.2 Thermodynamics: is the study of thermal (internal) energy of systems. The zero kelvin (or absolute zero) temperature is the limiting low temperature. Room temperature ~ 300 K Frozen water: 273.15 K Boiling water: 373.15 K Outer space ~ 3 K Big Bang ~ 1039 Liquid helium ~ 4 K (limiting) lowest: 0 K

4. 18.3 The Zeroth Law of thermodynamics (ZLTD): “If bodies A and B are each in thermal equilibrium with a third body C, then they are in thermal equilibrium with each other.” What do we mean by thermal equilibrium? If two systems (confined within an insulating box) are put in contact, and there is no net transfer of thermal energy between them, we say that the two systems are in “thermal equilibrium”.

5. ZLTD: Every body has a property which we call temperature. When two bodies are in thermal equilibrium they have the same temperature; when two bodies have the same temperature they are in thermal equilibrium! Why did we call it the “zeroth” law? It is a logical afterthought; came to light only in the 1930s’!!

6. 18.4 Measuring Temperature: Triple Point of Water: Water may exist at different temperatures; however, there is only one temperature at which liquid water, water vapor and solid water (ice) can coexist. We call this temperature the “triple point of water” and is denoted T3. We define this temperature to be 273.16 K. T3 = 273.16 K Hence, a degree kelvin is 1/273.16 of the difference in temperature between triple point of water and absolute zero!

7. The constant-volume gas thermometer:

8. Gases behave according to the Universal gas law: p V = n R T Therefore, T = C p (1) also, T3 = C p3 (2) dividing (1) by (2): T = T3 (p/ p3) (3) T and p are absolute temperature and pressure As usual, for real gases, the Universal gas law works better for high T, low p and low n (low density of gas). Therefore, T = (273.16 K) limgas -> 0 (p/ p3)

9. 18.5 The Celsius and Fahrenheit Scales: If TC is the temperature on the Celsius scale, and TF is the temperature on the Fahrenheit scale, then: TC = T - 273.15 and TF = (9/5) TC + 32 Note that: DTC = DT and DTF = (9/5) DTC

10. It will help to remember that: 0 oC = 32 oF = 273.15 K and, 100 oC = 212 oF = 373.15 K Example: What is 104 degrees Fahrenheit on the Celsius and Kelvin scales?

11. 18.6 Thermal Expansion: Linear expansion: When a metal rod of length L heats up by a difference in temperature DT, it will increase in length by DL according to: DL = L aDT a is called the coefficient of linear expansion. a is usually positive. When the rod cools down, is DT positive or negative? Is DL positive or negative? Does the rod expand or shrink/ contract?

12. Is linear expansion good or bad? It is normally bad (teeth fillings, railroad tracks/ expansion slots, …etc. ), but can be good (thermostat bimetal strip, aircraft manufacturing !!) What would it mean for a to be negative? Does this make sense? Are there material with negative a ? Assuming a is positive (as is the case in almost all materials), what happens to a hole when a punctured metal bar heats up?

13. Note: In general, agas > aliquid > asolid Does this make sense to you? What effect does this have on the ‘familiar’ liquid-in-glass thermometers? Example: H&R (19-E10) An aluminum flagpole is 33 m high. By how much does its length increase as the temperature increases by 15 Co? Hint: aAl = 23 x 10(-6) /Co

14. 18.7 Temperature, Heat and Thermal Energy: Internal energy: all of the energy belonging to a system (while stationary) including nuclear energy, chemical energy, elastic energy as well as thermal energy. Thermal energy: is that portion of internal energy that consists of kinetic and potential energies associated with random motion of atoms and molecules. It changes when temperature changes. Thermal energy transfer (heat): is the transfer of thermal energy caused by temperature difference between the system and its surroundings.

15. Heat is usually denoted Q. Sign convention: Q > 0 when heat is absorbed by the system. Q < 0 when heat is released/ lost / expelled from the system. Q = 0 when there is no thermal energy transfer. Can energy be transferred between two systems even when there is no heat (i.e. no thermal energy transfer)? Must heat change the amount of thermal energy in the system! Heat and work are not intrinsic properties of a system. They describe a processnot a state.

16. Units of heat: The amount of heat necessary to raise the temperature of 1 g of water from 14.5 to 15.5 degrees Celsius is called a calorie, abbreviated cal 1 calorie = 1 cal = 4.186 J 1 Calorie = 1 kilocalorie = 4.186 kJ The amount of heat necessary to raise the temperature of 1 lb of water from 63 to 64 degrees Fahrenheit is called a Btu. 1 cal = 3.969 10-3 Btu = 4.186 J Interaction: How many joules is a Btu?

17. Heat Capacity (C): If an object absorbs energy Q when heating from temperature Ti to temperature Tf, then the heat capacity (C) is such that: Q = C (Tf - Ti) = C DT 18.8 The Absorption of Heat by Solids and Liquids: What are the units for C? J/K or cal/K or J/oC or kJ/K, …etc. Example: 1440 joules of heat is supplied to an aluminum nugget. It is found that its temperature increases by 8 degrees Celsius. What is the heat capacity of this nugget?

18. Specific Heat (c): Is the heat capacity per unit mass: c = C/m Q = m c DT What are the units of c? Example: What is the mass of the aluminum nugget in previous example? Hint: cAl = 900 J/(kg K)

19. Can the heat capacity of different objects made from the same material be different? Can the specific heat of different objects made from the same material be different? What is the specific heat of water? 1 cal/(g oC) = 1 Btu/(lb oF) = 4190 J/(kg K) What is great about cH2O ?

20. Molar Specific Heat (cm): Is the heat capacity per mole of substance: cm = C/n Q = n cmDT What are the units of cm? Example: What is the molar specific heat of aluminum nugget of the previous example? Hint: MAl = 27 gram/mole

21. Can C, c or cm be negative? We said that heat and work are processes; so, does the specific heat depend on the process or is it a ‘property’ of the substance? For solid and liquids, there is little dependence on the process. For gases, the specific heat depends considerably on the process. Must the temperature of an object increase when we add heat? It can “transform” from one state (solid, liquid or gas) to another while staying at the same temperature!!

22. The amount of heat per unit mass needed for the transformation is called the latent heat of transformation (L). Q = m L What are the units for L? For vaporization or condensation use Lv. For melting or freezing use Lf. Which is larger for a specific material: Lv or Lf ? Braintweezer: why does your hand feel cold when perfume evaporates of it?

23. Interaction: What happens to 1/5 kg of water, in a 340 liter closed container, originally at -2oC when supplied with: i- 12000 cal? ii- 19600 cal? iii- 100000 cal? iv- 150000 cal? cp = 35.4 J/(mol K) cv = 27 J/(mol K) Lv = 2256 kJ/kg Lf = 333 kJ/kg cice = 0.5 cal/ (g K)

24. Let’s calculate the infinitesimal the work done by the system: dW = F · ds = p dV 18.9 A Closer look at Heat and Work: A “thermodynamic process” can proceed from an initial “state” to a final state. The work done by the system during a process is: W = dW = p dV Sign convention for W: work done by the system: W is positive work done on the system: W is negative

25. Work (W) and heat (Q) depend on the process, not only on the initial and final states. W = p dV The ‘amount’ of work is the area under the curve of a p-V diagram!! In (e), the work is negative! The net work in a thermodynamic cycle is the area inside the closed curve. Clockwise: positive Counterclockwise: negative In which process (a, b, c, du, dd) is the work done by the system greatest? W & Q are path dependent!!

26. FLTD: DEint = Eint,f - Eint,i = Q - W 18.10 The First Law of Thermodynamics: Experimentally, Q-W is independent of the process!! It makes sense to think that Q-W represents a change in some intrinsic property of the system. We call this property internal energy (Eint). This does make sense!! The internal energy increases when heat is added or when there is negative work (when work is done on the system).

27. Check point (19-5): in which of the four processes is: (see figure) A- the change in internal energy of the system greatest? B- the work done by the system greatest? C- the heat absorbed by the system greatest?

28. 18.11 Some Special Cases of the First Law of Thermodynamics: Adiabatic process: No thermal energy transfer; when the system is very well insulated, or when the process is very rapid (e.g. internal combustion engine). Q = 0 DEint = -W What does this mean/ does this make sense?

29. Constant volume (Isovolumetric) process: constant volume, no work! W = 0 DEint = Q Q (i.e.heat goes into increasing the internal energy; e.g. during the explosion in an engine cylinder). Cyclical process: No change in system properties including internal energy! DEint = 0 Q =W

30. Free expansion: Q = W = 0 DEint = 0 Adiabatic Free Expansion in an ideal gas: T does not change (why?)

31. 18.12 Heat transfer Mechanisms: 1- Conduction: Heat transfers by the exchange of kinetic energy between molecules; cooler (less energetic) molecules increase in temperature through collisions with more energetic (hotter) molecules / atoms/ electrons. (e.g., holding a rod over a flame). Good conductors: Poor conductors:

32. Law of heat conduction: For an insulated rod of length L and cross section A with ends in thermal contact with heat reservoirs at TH and TC. The average power conducted (Pcond) is: L = |Dx| Pcond = Q/t = (-) k A DT/Dx k: thermal conductivity. Large k means good conductors Pcond: thermal energy transfer rate Dx = x-end – x-start DT = Tx-end – Tx-start` Negative sign indicates that heat flows from higher temperature to lower temperature. No temperature gradient no transfer!

33. Thermal resistance to conduction (R): R = L/k High R means good resistor (poor conductor). Conduction through a composite slab: Pcond = A DT/SRi

34. Example: H&R (19-E54) The average rate at which energy is conducted outward through the ground surface in North America is 54.0mW/m2, and the average conductivity of the near surface rocks is 2.5 W/(m K). Assuming a surface temperature of 10.0 oC, find the temperature at a depth of 35.0 km. 2- Convection: Transfer of heat through motion of fluid (e.g. candle, wind, oceans, inside the sun)

35. Have you ever thought why a car radiator is painted black? 3- Radiation: Prad = se A T4 s = 5.6703 10-8 W/(m2 K4) e is the “emissivity”. Good absorbers are good radiators and have e ~ 1. Bad absorbers are good reflectors and have e ~ 0. Pabs = se A Tenv4 Pnet, abs = se A (Tenv4- T4)

36. Example: H&R (19-P62) A sphere of radius 0.500 m, temperature 27.0 oC, and emissivity 0.850 is located in an environment of temperature 77.0 oC. At what rate does the sphere: (a) emit and (b) absorb thermal radiation. (c) what is the sphere’s net rate of energy exchange?