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UB, Phy101: Chapter 14, Pg 1 Okay, so I was watching this video of some U.S. warplane breaking the sound barrier and there was this, sort of, vertical halo around the entire mid-section of the plane----a ring of smoke, so to speak. It looked really cool. What the hell was that?!

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UB, Phy101: Chapter 14, Pg 2 Physics 101: Chapter 14 Ideal Gas Law & Kinetic Theory l Today’s lecture will cover Textbook Chapter

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UB, Phy101: Chapter 14, Pg 3 Aside: The Periodic Table

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UB, Phy101: Chapter 14, Pg 4 The Periodic Table Explained ? proton neutron electron Look carefully

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UB, Phy101: Chapter 14, Pg 5 Energy vs Mass (more in Physics 102) He (m= u) O (M= u) 4 x He = u Mass difference= 0.01 u = binding energy So energy is the same as mass somehow ?? E = mc 2

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UB, Phy101: Chapter 14, Pg 6 Atoms, Molecules, and Moles l 1 mole = x molecule (N A = Avogadro’s Number) l 1 = 1 atomic mass unit = (mass of 12 C atom)/12 »approximately #neutrons + #protons » atomic weight W l Mass of 1 mole of “stuff” in grams = molecular mass in è e.g., 1 mole of N 2 has mass of 2x14=28 grams

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UB, Phy101: Chapter 14, Pg 7 Back to Physics 101: Chapter 14, Preflight Which contains the most molecules ? 1. A mole of water (H 2 O) 2. A mole of oxygen gas (O 2 ) 3. Same H2OH2O O2O2 correct

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UB, Phy101: Chapter 14, Pg 8 Chapter 14, Preflight Which contains the most atoms ? 1. A mole of water (H 2 O) 2. A mole of oxygen gas (O 2 ) 3. Same H 2 O (3 atoms) O 2 (2 atoms) correct

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UB, Phy101: Chapter 14, Pg 9 Chapter 14, Preflight Which weighs the most ? 1. A mole of water (H 2 O) 2. A mole of oxygen gas (O 2 ) 3. Same H 2 O (M = ) O 2 (M = ) correct

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UB, Phy101: Chapter 14, Pg 10 The Ideal Gas Law l pV = Nk B T è p = pressure in N/m 2 (or Pascals) è V = volume in m 3 è N = number of molecules è T = absolute temperature (K) è k B = Boltzmann’s constant »k B = 1.38 x J/K »note: pV has units of N-m or J (energy!)

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UB, Phy101: Chapter 14, Pg 11

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UB, Phy101: Chapter 14, Pg 12 The Ideal Gas Law l pV = Nk B T l Alternate way to write this è N = number of moles (n) x N A molecules/mole è pV= Nk B T »nN A k B T »n(N A k B )T »nRT l pV = nRT è R = ideal gas constant = N A k B = 8.31 J/(mol-K)

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UB, Phy101: Chapter 14, Pg 13 The Ideal Gas Law l pV = nRT è R = ideal gas constant = N A k B = 8.31 J/mol/K l Other units: è R =.0823 l-atm/mol/K è R = 1.99 cal/mol/K

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UB, Phy101: Chapter 14, Pg 14 Ideal Gas Law: Applications pV = nRT l When T is constant, pV is constant (Boyle’s Law) Isothermal process demo Isothermal process demo l When p is constant, V is proportional to T Isobaric process demo Isobaric process demo è Hot air balloon, helium and oxygen in LN 2 l When V is constant, p is proportional to T Isohoric process demoprocess demo è Open tube manometer

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UB, Phy101: Chapter 14, Pg 15 Chapter 14, Preflight In terms of the ideal gas law, explain briefly how a hot air balloon works. now we now that hot air rises. so therefore the bolloon collects all the hot air until it over comes the weight of the basket below and you have lift off Note! this is not a pressure effect, it is a volume effect. As T increases, volume increase, so that density decreases the balloon then floats due to Archimedes principle. The pressure remains constant! Charles Law. As a gas is heated, it expands. When the air in the balloon expands, its density goes down. Thus, it is less dense than surrounding air and "floats" Hot air, being less dense than cold air, can lift the balloon. For a gas with a constant molecular weight, the pressure is proportional to the product of the density and the temperature. Less molecules of hot air are needed compared to cold air to achieve the same pressure. The density of hot air is less than that of cold air, which allows the ballon to float.

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UB, Phy101: Chapter 14, Pg 16

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UB, Phy101: Chapter 14, Pg 17 Kinetic Theory: The relationship between energy and temperature (for monatomic ideal gas) Per molecule DEMO

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UB, Phy101: Chapter 14, Pg 18 Chapter 14, Preflight Suppose you want the rms (root-mean-square) speed of molecules in a sample of gas to double. By what factor should you increase the temperature of the gas? correct If v doubles, v 2 quadruples Therefore, T quadruples

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