Thermodynamics

1. Thermodynamics Temperature, Heat, Work Heat Engines

2. Introduction • In mechanics (dynamics) we deal with quantities such as mass, position, velocity, acceleration, energy, momentum, etc., which describe the condition of objects.

3. Thermodynamics • In thermodynamicswe deal with the energy and work of a system. • We describe the system in terms of observables which are the net result of the mechanics quantities of all the molecules which make up the system.

4. Thermodynamics • These observables are volume, temperature, pressure, heat energy, work. • Thermodynamics deals with those quantities and their relationships.

5. Thermodynamics deals with what kind of quantities? • Macroscopic • Microscopic

6. We all know about Volume. • Pressure:

7. Example • 120 lb woman putting all her weight on 2 in2 of heels. • Pressure = 120 lb/2 in2 = 60 lb/in2. • Is that a lot? • Comparison: 1 atm = 14.7 lb/in2. Thus of heals is approximately 4 atm. • This is the pressure you would feel at a depth of approximately 135 ft of water.

8. Temperature and Heat • Everyone has a qualitative understanding of temperature, but it is not very exact. • Question: Why can you put your hand in a 400 F oven and not get instantly burned, but if you touch the metal rack, you do? • Answer: Even though the air and the rack are at the same temperature, they have very different energy contents.

9. Construction of a Temperature Scale • Choose fixed point temperatures that are easy to reconstruct in any lab, e.g. freezing point of water, boiling point of water, or anything else you can think of. • Fahrenheit: Original idea: 0F Freezing point of Salt/ice 100F Body Temperature Using this ice melts at 32F and water boils at 212F (Not overly convenient) Note: 180F between boiling an freezing.

10. Celsius (Centigrade) Scale: 0C Ice Melts 100C Water Boils Note a change of 1C = a change of 1.8F.

11. Conversion between Fahrenheit and Celsius

12. Absolute or Kelvin Scale • The lowest temperature on the Celsius Scale is -273.15C.

13. Absolute or Kelvin Scale

14. Absolute or Kelvin Scale • The lowest possible temperature on the Celsius Scale is -273.15C. • The Kelvin Scale just takes this value and calls it 0 Kelvins, or absolute zero. • Note: the size of 1K is the same as 1C. • To convert from C to K just add 273.15 K = C + 273.15

15. When do you use which scale. • Fahrenheit: everyday use (the weather). • Use either Kelvin or Celsius when measuring differences in temperature. • Use Kelvin when doing absolute temperature measurements or calculating energies or pressures

16. Heat • Heat is the energy of random motion of the particles in the gas, i.e. the kinetic energy of the molecules. • Nice web simulation • gas simulation

17. Temperature is a measure of the average kinetic energy of the molecules in a body. • The higher the temperature, the faster the particles (atoms/molecules) are moving, i.e. more kinetic energy. • We will take heat to mean the thermal energy in a body OR the thermal energy transferred into/out of a body

18. Specific Heat • It is easy to change the temperature of some materials (e.g. air), hard to change the temperature of others (e.g. water) • Specific heat c describes how much energy Q is needed to change the temperature (T) of an body of mass m • c is the specific heat and is a property of the material, not a particular object. • Note: DT - changes in temperature, either Kelvin or Celsius will do.

19. Units of Heat • Heat is a form of energy so we can always use Joules. • More common in thermodynamics is the calorie: By definition 1 calorie is the amount of heat required to change the temperature of 1 gram of water 1C. • 1 Cal = 1 food calorie = 1000 cal.

20. The English unit of heat is the Btu (British Thermal Unit.) It is the amount of heat required to change the temperature of 1 lb of water 1F. • Conversions: 1 cal =4.186 J 1Btu = 252 cal

21. Units of Specific Heat Note that by definition, the specific heat of water is 1 cal/gC.

23. Water has a specific heat of 1 cal/gK and iron has a specific heat of 0.107 cal/gK. If we add equal amounts of heat to equal masses of iron and water, which will have the larger change in temperature? • The iron. • They will have equal changes since the same amount of heat is added to each. • The water. • None of the above.

24. Example Calculation • Compare the amount of heat energy required to raise the temperature of 1 kg of water and 1 kg of iron 20 C? • c = Q/mDT  Q = cmDT • Qw = (1000 g)(1 cal/gC)(20C) = 20000 cal • QFe = (1000 g)(0.107 cal/gC)(20C) = 2140 cal

25. What is the increase in the temperature of 0.5 kg of aluminum when 2000 J of heat is added (c = 900 J/kgC)? • 0.95C • 1.1C • 2.2C • 4.4C

26. Heat Transfer Mechanisms • Conduction: (mostly solids) Heat transfer without mass transfer. • Convection: (liquids/gas) Heat transfer with mass transfer. • Radiation: By EM radiation; takes place even in a vacuum.

27. Which heat transfer mechanisms require matter? • Conduction & convection • Conduction & radiation • Radiation & convection

28. Conduction

29. Conduction

31. Example

32. Convection • Typically very complicated. • Very efficient way to transfer energy. • Vortex formation is very common feature. • liquid convection • vortex formation • Sunspot • solar simulation

33. Convection Examples • Ocean Currents

34. Plate tectonics

35. Radiation • Everything that has a temperature radiates energy. • Method that energy from sun reaches the earth.

36. Note: if we double the temperature, the power radiated goes up by 24 =16. • If we triple the temperature, the radiated power goes up by 34=81. • A lot more about radiation when we get to light.

38. Work Done by a Gas • Work=(Force)x(distance) =Fy • Force=(Presssure)x(Area) • W=P(Ay) =PV

39. First Law of ThermodynamicsConservation of energy • When heat is added into a system it can either 1) change the internal energy of the system (i.e. make it hotter) or 2) go into doing work. Q = W + U. Note: For our purposes, Internal Energy is the part of the energy that depends on Temperature.

40. Heat Engines • Cycle refers to closed path on a PV diagram • Since the system is described by pressure and volume it is in the same state when P and V are the same

41. Heat Engines • If we can create an “engine” that operates in a cycle, we return to our starting point each time and therefore have the same internal energy. Thus, for a complete cycle Q = W

42. Heat Engines • https://www.youtube.com/watch?v=s3N_QJVucF8

43. Model Heat Engine • Qhot = W + Qcold or • Qhot – Qcold = W (what goes in must come out)

44. Efficiency • We want to write an expression that describes how well our heat engine works. • Qhot = energy that you pay for. • W = work done (what you want.) • Qcold = Waste energy. Efficiency = e = W/Qhot

45. If we had a perfect engine, all of the input heat would be converted into work and the efficiency would be 1. • The worst possible engine is one that does no work and the efficiency would be zero. • Real engines are between 0 and 1

46. Newcomen Engine(First real steam engine) e=0.005

47. Example Calculation • In every cycle, a heat engine absorbs 1000 J from a hot reservoir at 600K, does 400 J of work and expels 600 J into a cold reservoir at 300K. Calculate the efficiency of the engine. • e = 400 J/1000 J = 0.4 • This is actually a pretty good engine.

48. Example • In every cycle, a heat engine absorbs 1500 J from a hot reservoir at 500K, does 350 J of work and expels 1150 J into a cold reservoir at 300K. Calculate the efficiency of the engine.

49. The efficiency is • e = 0.23 • e = 0.3 • e = 0.6

50. Second Law of Thermodynamics(What can actually happen) • Heat does not voluntarily flow from cold to hot. OR • All heat engines have e < 1. (Not all heat can be converted into work.)