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## Heat Engines

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**Heat Engines**• Coal fired steam engines. • Petrol engines • Diesel engines • Jet engines • Power station turbines**DECChttp://www.decc.gov.uk/assets/decc/statistics/publications/flow/193-energy-flow-chart-2009.pdf**DECChttp://www.decc.gov.uk/assets/decc/statistics/publications/flow/193-energy-flow-chart-2009.pdf**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.**Atoms don’t care.**• What happens most ways happens most often**Boyle’s Law**p p 1/V 1/V**Charles’s Law**V V T T**Pressure Law**p p T T**Common sense Law**p p N Number of molecules, N**Isotherms**(constant temperature) p p Isochors (constant volume) 1/V T Isobars (constant pressure) V T**pV**= constant T For ideal gases only A gas that obeys Boyles law In summary… p 1/V p T V T**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**pV**= constant T p2V2 p1V1 T1 T2 Only useful if dealing with same gas before (1) and after (2) an event =**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**Which can also be written as …**pV = NkT N = number of molecules k = Boltzmann’s constant (1.38 x 10-23 J K-1)**z**v y x Kinetic Theory First there was a box and one molecule… Molecule:- mass = m velocity = v**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**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**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**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**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**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**1**Nmv2 pV= 3 pV = NkT Nmv2 = NkT 1 3 Microscopic Macroscopic (In terms of molecules) (In terms of physical observations)**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)**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**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**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**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**Bonds between atoms**Jiggling around (vibrational energy) Einstein’s Model of a solid Atom requires energy to break them U kT**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**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**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**Probability**1 Exponential 0 Energy Probability of molecule having a specific energy**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**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**2nd law of thermodynamics**S = k ln W S = entropy k = Boltzmann’s constant W = number of ways**ΔS = ΔQ**T**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