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# Heat Engines

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1. Heat Engines • Coal fired steam engines. • Petrol engines • Diesel engines • Jet engines • Power station turbines

2. DECChttp://www.decc.gov.uk/assets/decc/statistics/publications/flow/193-energy-flow-chart-2009.pdfDECChttp://www.decc.gov.uk/assets/decc/statistics/publications/flow/193-energy-flow-chart-2009.pdf

3. Combined Cycle

4. THE LAWS OF THERMODYNAMICS 1. You cannot win you can only break even. 2. You can only break even at absolute zero. 3. You can never achieve absolute zero.

5. S = k log W

6. Atoms don’t care. • What happens most ways happens most often

7. Boyle’s Law p p  1/V 1/V

8. Charles’s Law V V  T T

9. Pressure Law p p  T T

10. Common sense Law p p  N Number of molecules, N

11. Isotherms (constant temperature) p p Isochors (constant volume) 1/V T Isobars (constant pressure) V T

12. pV = constant T For ideal gases only A gas that obeys Boyles law In summary… p  1/V p  T V  T

13. Ideal gas? Most gases approximate ideal behaviour Ideal gases assume:- • No intermolecular forces Not true - gases form liquids then solids as temperature decreases • Volume of molecules is negligible Not true - do have a size

14. pV = constant T p2V2 p1V1 T1 T2 Only useful if dealing with same gas before (1) and after (2) an event =

15. Ideal Gas Law pV = nRT p = pressure, Pa V = volume, m3 n = number of moles R = Molar Gas constant (8.31 J K-1 mol-1 ) T = temperature, K Macroscopic model of gases

16. Which can also be written as … pV = NkT N = number of molecules k = Boltzmann’s constant (1.38 x 10-23 J K-1)

17. z v y x Kinetic Theory First there was a box and one molecule… Molecule:- mass = m velocity = v

18. 2mv -2mv -v v mv - mu pmol Molecule Remember p = F so a force is felt by the box t Molecule hits side of box…(elastic collision) = -mv - mv = -2mv pbox = -pmol = 2mv Box

19. z y x s 2x = = v v Molecule collides with side of box, rebounds, hits other side and rebounds back again. Time between hitting same side, t

20. F = p = p v = 2mv v = mv2 t 2x 2x Force exerted on box x Time Actual force during collision Average force, exerted by 1 molecule on box Average Force

21. Consider more molecules -v6 z v2 v5 v1 -v8 vN v3 v4 -v7 y x All molecules travelling at slightly different velocities so v2 varies - take mean - v2

22. F = Nmv2 Mean square velocity x Nmv2 Nmv2 Pressure = Force = = Area xyz V Nmv2 1 p= V 3 Force created by N molecules hitting the box… But, molecules move in 3D Kinetic Theory equation

23. Brownian Motion Why does it support the Kinetic Theory? • confirms pressure of a gas is the result of randomly moving molecules bombarding container walls • rate of movement of molecules increases with temperature • confirms a range of speeds of molecules • continual motion - justifies elastic collision

24. 1 Nmv2 pV= 3 pV = NkT Nmv2 = NkT 1 3 Microscopic Macroscopic (In terms of molecules) (In terms of physical observations)

25. mv2 =3kT (1) Already commented that looks a bit like K.E. K.E. = ½mv2 3 K.E. = kT 2 Average K.E. of one molecule Rearrange (and remove N) Substitute into (1)

26. 3 K.E.Total = NkT 2 3 NkT U = 2 Total K.E. of gas (with N molecules) This is translational energy only - not rotational, or vibrational And generally referred to as internal energy, U

27. 3 NkT U = 2 Physically hit molecules Energy and gases Internal Energy of a gas Sum of the K.E. of all molecules How can the internal energy (K.E.) of a gas be increased? 1) Heat it - K.E.  T 2) Do work on the gas

28. Change in Internal Energy Work done on material Energy transferred thermally = + U = W + Q Basically conservation of energy Also known as the First Law of Thermodynamics

29. Heat, Q – energy transferred between two areas because of a temperature difference +ve when energy added -ve when energy removed Work, W – energy transferred by means that is independent of temperature i.e. change in volume +ve when work done on gas - compression -ve when work done by gas - expansion

30. Bonds between atoms Jiggling around (vibrational energy) Einstein’s Model of a solid Atom requires energy to break them U  kT

31. Mechanical properties change with temperature T = high can break and make bonds quickly – atoms slide easily over each other Liquid: less viscous Solid: more ductile T = low difficult to break bonds – atoms don’t slide over each other easily Solid: more brittle Liquid: more viscous

32. Activation energy,  Can think of bonds as potential wells in which atoms live Activation energy,  - energy required for an event to happen i.e. get out of a potential well

33. The magic /kT ratio  - energy needed to do something kT - average energy of a molecule /kT = 1 Already happened /kT = 10 - 30 Probably will happen /kT > 100 Won’t happen

34. Probability 1 Exponential 0 Energy Probability of molecule having a specific energy

35. e-/kT /kT Boltzmann Factor e-/kT Probability of molecules achieving an event characterised by activation energy,  1 0.37 10 - 30 4.5 x 10-6 - 9.36 x 10-14 3.7 x 10-44 > 100 Nb. 109 to 1013 opportunities per second to gain energy

36. Amongst particles Entropy Number of ways quanta of energy can be distributed in a system Lots of energy – lots of ways Not much energy – very few ways An “event” will only happen if entropy increases or remains constant

37. 2nd law of thermodynamics S = k ln W S = entropy k = Boltzmann’s constant W = number of ways

38. At a thermal boundary Energy will go from hot to cold Hot Number of ways decreases – a bit Cold Number of ways increases – significantly Result - entropy increase