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

Molecular Picture of Gas Gas is made up of many individual molecules Number of moles n = N / NA NA = Avogadro’s number = 6.0221023 mole-1 NA= 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

Atoms, Molecules and Moles 1 mole = 6.022  1023 molecules (NA = Avogadro’s Number) NA = 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 12C atom)/12 Approximately # of neutrons + # of protons Atomic weight A 1 u = 1.66  10-27 kg = 1gram/NA Mass of 1 mole of “stuff” in grams = molecular mass in u E.g. 1 mole of N2 has mass of 2  14 = 28 grams Lecture 22 Purdue University, Physics 220

Purdue University, Physics 220 iClicker Which contains more molecules ? A) A mole of water (H2O) B) A mole of oxygen gas (O2) C) Same H2O O2 Lecture 22 Purdue University, Physics 220

Purdue University, Physics 220 Question Which contains more atoms ? B) A mole of water (H2O) C) A mole of oxygen gas (O2) A) Same H2O (3 atoms) O2 (2 atoms) Lecture 22 Purdue University, Physics 220

Purdue University, Physics 220 Question Which weighs more ? A) A mole of water (H2O) B) A mole of oxygen gas (O2) C) Same H2O (M = 16 + 1 + 1) O2 (M = 16 + 16) Lecture 22 Purdue University, Physics 220

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 “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

Temperature Feel Measure

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 with a third, then the two are in equilibrium with each other. Perhaps do hot water, and cold, comment on what happens after time.

Temperature Scales Anders Celsius (1701 - 1744) Daniel G. Fahrenheit (1686 - 1736) Lord Kelvin (1824 - 1907)

Temperature Scales Farenheit Celcius Kelvin 100 373.15 212 Water boils 32 Farenheit 100 Celcius 273.15 373.15 Kelvin Water boils Water freezes NOTE: K=0 is “absolute zero”, meaning (almost) zero KE/molecule

iClicker K = C + 273 A) One B) Two C) Same Two cups of coffee are heated to 100 degrees Fahrenheit. 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 + 273

Purdue University, Physics 220 Gay-Lussac’s Law If const V: P  T Inventor of the hydrogen balloon Lecture 24 Purdue University, Physics 220

Purdue University, Physics 220 Other Empirical Laws Charles’s law If const P: V  T V  T Boyle’s Law Avogadro’s Law If const T: P  1/V If const P and T: V  N Lecture 24 Purdue University, Physics 220

Purdue University, Physics 220 The Ideal Gas Law P V = N kB T P = pressure in N/m2 (or Pascals) V = volume in m3 N = number of molecules T = absolute temperature in K k B = Boltzmann’s constant = 1.38 x 10-23 J/K Note: P V has units of N*m or J (energy!) Lecture 24 Purdue University, Physics 220

Purdue University, Physics 220 The Ideal Gas Law PV = NkBT Alternate way to write this N = number of moles (n) x NA molecules/mole PV= NkBT nNAkB T n(NAkB)T nRT P V = n R T n = number of moles R = ideal gas constant = NAkB = 8.31 J/mol/K Lecture 24 Purdue University, Physics 220

Purdue University, Physics 220 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 = P0 (38+273)/(20+273) Lecture 24 Purdue University, Physics 220

Purdue University, Physics 220 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 24 Purdue University, Physics 220

Purdue University, Physics 220 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 FB = r V g r is density of outside air! Lecture 24 Purdue University, Physics 220

Purdue University, Physics 220 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 = NkBT P and V are constant. If T increases N decreases. Lecture 24 Purdue University, Physics 220

Purdue University, Physics 220 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 220