Moving Observer and Source. Demo 4C - 02 Doppler. Molecular Picture of Gas PHYSICS 220. Lecture 22. Combine: f o = f s (1-v o /v) / (1-v s /v)

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1 PHYSICS 220 Lecture 22 Temperature and Ideal Gas Moving Observer and Source Combine: f o = f s (1-v o /v) / (1-v s /v) A: You are driving along the highway at 65 mph, and behind you a police car, also traveling at 65 mph, has its siren turned on. B: You and the police car have both pulled over to the side of the road, but the siren is still turned on. In which case does the frequency of the siren seem higher to you? A) Case A B) Case B C) same f v f v s v o Lecture 22 Purdue University, Physics Demo 4C - 02 Doppler Wave from rear of speaker reflects off wall and mixes with front emitted wave When front is moving toward you back is moving away from wall and vv Molecular Picture of Gas Gas is made up of many individual molecules Each molecule has same weight Can find number by dividing mass by weight of each molecule Pick mass = mol, wt, One wave is Doppler shifted up or down and other shifted in the opposite way so they have different frequencies You hear the beats between the two frequencies Number of moles n = N / N A N A = Avogadro s number = 6.022!10 23 mole -1 N A = number of particles (can be atoms or molecules) per mole 1 mole = amount of substance that contains as many elementary entities as there are atoms in exactly 12 grams of carbon-12 Lecture 22 Purdue University, Physics 220 4

2 Atoms, Molecules and Moles 1 mole = 6.022! molecules (N A = Avogadro s Number) N A = Number of atoms or molecules that make a mass equal to the substance's atomic or molecular weight in grams. 1 u = 1 atomic mass unit = (mass of 12 C atom)/12 Approximately # of neutrons + # of protons Atomic weight A Which weighs more? A) A mole of water (H 2 O) B) A mole of oxygen gas (O 2 ) C) Same H 2 O (M = ) 1 u = 1.66! kg = 1gram/N A Mass of 1 mole of stuff in grams = molecular mass in u E.g. 1 mole of N 2 has mass of 2! 14 = 28 grams O 2 (M = ) Lecture 22 Purdue University, Physics Lecture 22 Purdue University, Physics Internal Energy All objects have internal energy (measured in Joules) random motion of molecules +energy associated with intermolecular bonds kinetic energy potential energy collisions of molecules gives rise to pressure Amount of internal energy depends on temperature related to average kinetic energy per molecule how many molecules Mass Heat flowing into gas Q changes internal energy Q = C "T where C is the heat capacity of total gas C = nc n = number of moles c is specific heat or heat capacity per mole Specific heat specific heat related to how many different ways a molecule can move Translation (the only one for monatomic gas) Rotation vibration the more ways it can move, the higher the specific heat Each possible motion that can hold energy has energy in it If the system is in thermal equilibrium In thermal equilibrium every degree of freedom individually has the same temperature

3 Temperature Zeroth Law of Thermodynamics If two (or more) objects are in thermal equilibrium, they are at the same temperature. Feel Measure If two objects are in thermal equilibrium with a third, then the two are in equilibrium with each other. Temperature Scales Temperature Scales Celcius Farenheit Anders Celsius ( ) Kelvin Daniel G. Fahrenheit ( ) 9 C K = C F = Lord Kelvin ( ) Water boils Water freezes 5 F-32 9 C = K-273 C = ( ) NOTE: K=0 is absolute zero, meaning (almost) zero KE/molecule

4 Gay-Lussac s Law Other Empirical Laws If const V: P # T Charles s law If const P: "V # "T V # T Boyle s Law Avogadro s Law If const T: P # 1/V Inventor of the hydrogen balloon If const P and T: V # N Lecture 24 Purdue University, Physics Lecture 24 Purdue University, Physics P V = N k B T The Ideal Gas Law P = pressure in N/m 2 (or Pascals) V = volume in m 3 N = number of molecules T = absolute temperature in K k B = Boltzmann s constant = 1.38 x J/K Note: P V has units of N-m or J (energy!) PV = Nk B T The Ideal Gas Law Alternate way to write this N = number of moles (n) x N A molecules/mole PV= Nk B T nn A k B T n(n A k B )T nrt P V = n R T n = number of moles R = ideal gas constant = N A k B = 8.31 J/mol/K Lecture 24 Purdue University, Physics Lecture 24 Purdue University, Physics

5 Exercise You inflate the tires of your car so the pressure is 30 psi, when the air inside the tires is at 20 degrees C. After driving on the highway for a while, the air inside the tires heats up to 38 C. Which number is closest to the new air pressure? A) 16 psi B) 32 psi C) 57 psi What happens to the pressure of the air inside a hot-air balloon when the air is heated? (Assume V is constant) A) Increases B) Same C) Decreases Careful, you need to use the temperature in K P = P 0 (38+273)/(20+273) Balloon is still open to atmospheric pressure, so it stays at 1 atm Lecture 24 Purdue University, Physics Lecture 24 Purdue University, Physics What happens to the buoyant force on the balloon when the air is heated? (Assume V remains constant) A) Increases B) Same C) Decreases What happens to the number of air molecules inside the balloon when the air is heated? (Assume V remains constant) A) Increases B) Same C) Decreases F B = $ V g $ is density of outside air! PV = Nk B T P and V are constant. If T increases N decreases. Lecture 24 Purdue University, Physics Lecture 24 Purdue University, Physics

6 Balloon In terms of the ideal gas law, explain briefly how a hot air balloon works. Once the air in a balloon gets hot enough, the net weight of the balloon plus this hot air is less than the weight of an equivalent volume of cold air, and the balloon starts to rise. When temperature increases the volume of the gas increases, thus reducing the density of the gas making it lighter that then surrounding air, which causes the balloon to rise. Note! this is not a pressure effect, it is a density effect. As T increases, the density decreases the balloon then floats due to Archimedes principle. The pressure remains constant! Lecture 24 Purdue University, Physics

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