Announcements 9/9/11 • Prayer • Lab 1 due tomorrow • Lab 2 starts tomorrow
Worked problems: • How much mass does the air in this room have? (MM 0.029 kg/mol) • According to the ideal gas law, what is the density of air at 1 atm, for 300 K? For arbitrary T? • A hot air balloon is 520 kg (including passengers). It’s spherical, with radius = 8 m. The temperature is 300K outside (80.3F), pressure is 1 atm. How hot does the pilot have to get the air inside the balloon for it to lift off? Some answers: 1.175 kg/m3; 378K (221F)
Reading quiz (graded): • Who was the famous Austrian physicist whose name was on two equations in today’s reading assignment? • Niels Bohr • Ludwig Boltzmann • Johann Carl Friedrich Gauss • Hermann von Helmholtz • Erwin Schrödinger
Thought question (ungraded): • In air, the molecular mass of oxygen molecules is 32 g/mol; the molecular mass of nitrogen molecules is 28 g/mol. Which molecules are traveling faster on average? • Oxygen • Nitrogen • Same speed Demo: heavy vs light molecules
Equipartition Theorem • “The total kinetic energy of a system is shared equally among all of its independent parts, on the average, once the system has reached thermal equilibrium.” • “independent”: e.g. x, y, z (for translational KE) • “parts”: translational, rotational, vibrational • Specifically, each “degree of freedom”, of each molecule, has “thermal energy” of … ½kBT
Thought quiz • Compare a monatomic molecule such as Ne to a diatomic molecule such as O2. If they are at the same temperature(*), which has more kinetic energy? • Ne • O2 • Same • Not enough information to tell (*) let’s assume the temperature is “high”. Relative to what, we’ll discuss in a minute.
Disclaimer Thermal energy (measured by kBT) must be comparable to the quantum energy levels, or some degrees of freedom get “frozen out” From section 21.4: diatomic hydrogen Y-axis: heat added, divided by temperature change (per mole) Units: J/molK
Translational KE and vrms • Worked problem: what is average speed (vrms) of oxygen molecules at 300K?
Molecular View of Pressure • Related problem: What is average pressure by baseballs (m = 145 g) on a wall (A = 9 m2). Speed = 85 mph (38 m/s). Elastic collisions, each lasting for 0.05 seconds. (This is the time the ball is in contact with the wall.) A baseball hits the wall every 0.5 seconds. • Actual problem: a cube filled with gas • Pressure on right wall from one molecule? • Pressure on right wall from all molecules Answer: 2.45 Pa Answer: 2mvx/(L2 tbetween hits) = mvx2/L3 Answer: P = Nmvx2/V
Molecular View of Pressure, cont. • Result for v instead of vx: P = N m ⅓ v2 / V • What does PV equal? • Compare to: PV = N kB T • What does v equal? What does T equal? • What is temperature? (revisited)
Demo • Demo: kinetic theory machine • Thought question: Which “molecules” have the most kinetic energy? • The heavy ones • The light ones • Same • (Repeat) Which ones have the fastest average velocity?