PHYSICS 220. Lecture 22. Textbook Sections Lecture 22 Purdue University, Physics 220 1

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1 PHYSICS 220 Lecture 22 Temperature and Ideal Gas Textbook Sections Lecture 22 Purdue University, Physics 220 1

2 Overview Last Lecture Speed of sound v = sqrt(b/ρ) Intensity level β = (10 db) log 10 ( I / I 0 ) Standing Waves f n = n v/(2l) open at both ends n=1,2,3, f n = n v/(4l) open at one end n=1,3,5, Doppler Effect f o = f s (v-v o ) / (v-v s ) Beats Today ω L = 1 2 ω ω 1 2 Temperature Ideal Gas ( ) Lecture 22 Purdue University, Physics 220 2

3 Quiz 1) The intensity of a sound wave is directly proportional to A) the frequency B) the square of the speed of sound C) the amplitude D) the square of the amplitude 2) If the distance to a point source of sound is doubled, by what factor does the intensity decrease? A) 1x B) 4x C) 8x D) 2x Lecture 22 Purdue University, Physics 220 3

4 Thermodynamics Thermodynamics is about the transfer of energy between systems of particles Thermodynamics focuses on energy rather than forces Conservation of energy is a key pillar of thermodynamics It is also about the way changes in the energy of a system affects its properties Several new quantities, such as temperature and heat, are needed to describe the properties p of systems and their interactions Lecture 22 Purdue University, Physics 220 4

5 System A thermodynamic system contains multiple l particles, usually a very large number The particles in a system stem are able to exchange energy with one another via collisions Systems are able to exchange energy with other systems The balloon filled with oxygen molecules is an example of a system Lecture 22 Purdue University, Physics 220 5

6 Properties of a System Because of the extremely large numbers of molecules, it is not feasible (although it is possible) to describe the system in terms of Newton s Laws In comparing two systems, they may not be identical on the molecular l levell The positions and velocities of all the molecules won t be the same Various properties of the systems as a whole will be the same System wide properties p include temperature and pressure We are generally interested in the macroscopic properties of the system They describe the behavior of the system on a scale much larger than the individual particles Macroscopic properties contrast with microscopic properties such as position and velocity Lecture 22 Purdue University, Physics 220 6

7 Molecular Picture of Gas Gas is made up of many individual molecules Number density is number of molecules/volume N/V = ρ/m ρ is the mass density m is the mass for one molecule Number of moles n = N/N N A N A = Avogadro s number = mole -1 N A = number of 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 7

8 Atoms, Molecules and Moles 1 mole = molecules (N A = Avogadro s Number) N A = Number of atoms or molecules l that make a mass equal to the substance's atomic or molecular weight in grams. 1u=1atomic 1 mass unit = (mass of 12 Catom)/12 Approximately # of neutrons + # of protons Atomic weight A 1 u = 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 Lecture 22 Purdue University, Physics 220 8

9 Question Which contains more atoms? B) A mole of water (H 2 O) C) A mole of oxygen gas (O 2 ) A) Same H 2 O (3 atoms) O 2 (2 atoms) Lecture 22 Purdue University, Physics 220 9

10 Question 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 = ) O 2 (M = ) Lecture 22 Purdue University, Physics

11 Number Density ILQ Two gas cylinders are filled such that they have the same mass of gas (in the same volume). One cylinder is filled with Helium, the other with Oxygen. Which container has the larger number density? A) Helium B) Oxygen C) Same Helium molecule is lighter than Oxygen molecule. If you have the same mass, you must have many more Helium molecules than Oxygen. So the Helium number density is larger. Lecture 22 Purdue University, Physics

12 Internal Energy and Temperature All objects have internal energy (measured in Joules) random motion of molecules l kinetic 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 specific heat related to how many different ways a molecule can move translation rotation vibration the more ways it can move, the higher the specific heat Lecture 22 Purdue University, Physics

13 Temperature Temperature is not contained in or derivable from Newton s laws Temperature is a new quantity and requires a new unit of measure A macroscopic definition can be determined from looking at two systems Lecture 22 Purdue University, Physics

14 Temperature, cont. Assume each system has its own temperature and T 1 >T 2 System 1 is hotter than system 2 If the systems are brought into contact, energy is transferred spontaneously from system 1 to system 2 Eventually, the two systems will have the same energy They will reach thermal equilibrium Their final temperature will be somewhere between the two initial temperatures Lecture 22 Purdue University, Physics

15 Zeroth Law of Thermodynamics If two (or more) objects are in thermal equilibrium, they are at the same temperature. If two objects are in thermal equilibrium i with a third, then the two are in equilibrium i with each other. Lecture 22 Purdue University, Physics

16 Temperature Microscopic View If the temperature of the gas increases, the average speed of the gas atoms increases, and the pressure will also increase A measurement of the pressure gives a direct way to find the temperature Such a device is called a gas thermometer The temperature of a system of particles is related to the average particle speed Lecture 22 Purdue University, Physics

17 Temperature Scales Anders Celsius ( ) Daniel G. Fahrenheit ( ) Lord Kelvin ( ) Lecture 22 Purdue University, Physics

18 Temperature Scales Farenheit Celcius Kelvin Water boils Water freezes F = 9 5 C + 32 C = 5 ( 9 F-32 ) K = C C = K NOTE: K=0 is absolute zero, meaning (almost) zero KE/molecule l Lecture 22 Purdue University, Physics

19 Temperature Scales, cont. Two reference points are the temperatures at which water freezes and boils Celsius Water freezes at 0 C Water boils at 100 C Fahrenheit Water freezes at 32 F Water boils at 212 F Kelvin Water freezes at K Water boils at K No degree symbol is used with kelvins All three scales are linear The freezing and boiling points of water can be used to develop conversions among the scales Lecture 22 Purdue University, Physics

20 Temperature Limits Temperatures extend well above the boiling point of water They also extend below the freezing point of water The lower limit to temperature is absolute zero 0 K Lecture 22 Purdue University, Physics

21 Temp Scales ILQ Two cups of coffee are heated to 100 degrees Fahrenheit. h Cup 1 is then heated an additional 20 degrees Centigrade, cup 2 is heated an additional 20 Kelvin. Which cup of coffee is hotter? A) One B) Two C) Same K = C Lecture 22 Purdue University, Physics

22 Sick ILQ You measure your body temperature with a thermometer calibrated in Kelvin. What do you hope the reading is (assuming you are not trying to fake some sort of illness)? A) 307 K B) 310 K C) 313 K F = 98.6 D) 317 K C = 5 (F-32) = 37 9 K = C = 310 Lecture 22 Purdue University, Physics

23 Charles s Law In 0 C In K Inventor of the hydrogen balloon If const P: ΔV ΔT V T Lecture 22 Purdue University, Physics

24 Other Empirical Laws Gay-Lussac s Law Boyle s Law Avogadro s Law If const V: P T If const T: P 1/V If const P and T: V N Lecture 22 Purdue University, Physics

25 The Ideal Gas Law PV=Nk B T P = pressure in N/m 2 (or Pascals) V = volume in m 3 N = number of molecules T = absolute temperature t in K k B = Boltzmann s constant = 1.38 x J/K Note: P V has units of N-m or J (energy!) Lecture 22 Purdue University, Physics

26 The Ideal Gas Law PV = Nk B T 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 22 Purdue University, Physics

27 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 Careful, you need to use the temperature in K P = P 0 (38+273)/(20+273) Lecture 22 Purdue University, Physics

28 Question 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 Balloon is still open to atmospheric pressure, so it stays at 1 atm Lecture 22 Purdue University, Physics

29 Question What happens to the buoyant force on the balloon when the air is heated? (Assume V remains constant) A) Increases B) Same C) Decreases F B = ρ V g ρ is density of outside air! Lecture 22 Purdue University, Physics

30 Question 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 PV = Nk B T P and V are constant. If T increases N decreases. Lecture 22 Purdue University, Physics

31 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 22 Purdue University, Physics

32 Summary of Concepts Temperature measure of average Kinetic Energy of molecules Gas made up of molecules Ideal Gas Law PV = n R T P = pressure in N/m 2 (or Pascals) V = volume in m 3 n = # moles R = 8.31 J/ (K mole) T = Temperature (K) Lecture 22 Purdue University, Physics