Physics 101: Lecture 29 Ideal Gas Law & Kinetic Theory

1. Physics 101: Lecture 29Ideal Gas Law & Kinetic Theory • Today’s lecture will cover Textbook Chapter14

2. Fundamental building blocks of matter ? • Molecules are formed from atoms, held together by the electromagnetic force. • Atoms consist of a positively charged nucleus and electrons, held together by the electromagnetic force. • The nucleus is formed from protons and neutrons, held together by the strong force. • Protons and neutrons are formed from up and down quarks (p: uud, n: ddu), held together by the strong force. • State-of-the art: http://particleadventure.org/particleadventure http://www.aps.org/units/dpf/quarks_unbound 12 fundamental matter particles (+12 anti-matter particles): six quarks and six leptons (e.g., electron) 4 fundamental forces (interactions): electromagnetic (exchange of photon) weak (exchange of W and Z bosons) : b decay (sun) strong (exchange of gluon) and gravity (exchange of graviton ?)

3. The Periodic Table Mendelejew and Meyer (1869)

4. Look carefully The Periodic Table proton neutron electron • Atomic number 1 • Atom H • Atomic mass 1.00797 u • 1 u = 1 atomic mass unit • = (mass of 12C atom)/12 • approximately #neutrons + #protons

5. 4 x He = 16.01 u Mass difference = 0.01 u = binding energy E = mc2 Energy vs Mass He (m=4.0026 u) O (M=15.9995 u) energy is mass and vice versa:

6. Molecules, Atoms and Moles • Avogadro (1776-1856): All gases at same pressure, volume and temperature contain the same number of gas particles. One mole of a substance contains as many particles as they are atoms in 12 g of C12, i.e. 6.022 x 1023 atoms. NA = 6.022 x 1023 1/mol is Avogadro’s Number number of moles = number of particles/NA n = N/NA and number of moles = mass (in gram)/mass per mole (g/mol) • Mass of 1 mol of a substance in grams = molecular mass in u • e.g., 1 mol of N2 has mass of 2x14=28 grams • mparticle = mass per mole/NA

7. H2O correct O2 Concept Question Which contains the most molecules ? 1. 1 mol of water (H2O) 2. 1 mol of oxygen gas (O2) 3. Same

8. H2O (3 atoms) correct O2 (2 atoms) Concept Question Which contains the most atoms ? 1. A mol of water (H2O) 2. A mol of oxygen gas (O2) 3. Same

9. H2O (M = 16 + 1 + 1) correct O2 (M = 16 + 16) Concept Question Which weighs the most ? 1. 1 mol of water (H2O) 2. 1 mol of oxygen gas (O2) 3. Same

10. The Ideal Gas Law • Ideal gas: low density => the only interaction that occurs between gas particles (and surrounding walls) is elastic collision => An ideal gas is highly compressible, i.e. if P increases V decreases ! • Boyle and Mariotte (1662,1667) found experimentally that P V = constant if T=constant (and N=const.) Experiments also revealed that P is proportional to T (V and N constant) P is proportional to N (V and T is constant) => P V is proportional to N T !

11. 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 (K) • k B = Boltzmann’s constant • kB = 1.38 x 10-23 J/K • note: pV has units of N m or J (energy!)

12. The Ideal Gas Law • P V = N kB T kB is Boltzmann’s constant: kB= 1.38 x 10-23 J/K • Alternate way to write this • N = number of moles (n) x NA molecules/mole • P V = N kB T • n NA kB T • n (NAkB)T • n R T • P V = n R T • R = ideal gas constant = NAkB = 8.31 J/(mol K)

13. Kinetic Theory:The relationship between energy and temperature(for monatomic ideal gas) Per molecule

14. correct Concept Question 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? 1. 2 2. 3. 4 • If v doubles, v2 quadruples • Therefore, T quadruples