Physics 101: Lecture 29, Pg 1 Physics 101: Lecture 29 Ideal Gas Law & Kinetic Theory l Today’s lecture will cover Textbook Chapter 14

Physics 101: Lecture 29, Pg 2 Fundamental building blocks of matter ? l Molecules are formed from atoms, held together by the electromagnetic force. l Atoms consist of a positively charged nucleus and electrons, held together by the electromagnetic force. l The nucleus is formed from protons and neutrons, held together by the strong force. l Protons and neutrons are formed from up and down quarks (p: uud, n: ddu), held together by the strong force. l State-of-the art: 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) :  decay (sun) strong (exchange of gluon) and gravity (exchange of graviton ?)

Physics 101: Lecture 29, Pg 3 The Periodic Table Mendelejew and Meyer (1869)

Physics 101: Lecture 29, Pg 4 The Periodic Table proton neutron electron Look carefully Atomic number 1 Atom H Atomic mass u 1 u = 1 atomic mass unit = (mass of 12C atom)/12 approximately #neutrons + #protons

Physics 101: Lecture 29, Pg 5 Energy vs Mass He (m= u) O (M= u) 4 x He = u Mass difference= 0.01 u = binding energy energy is mass and vice versa: E = mc 2

Physics 101: Lecture 29, Pg 6 Molecules, Atoms and Moles l Avogadro ( ): 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 C 12, i.e x atoms. N A = x /mol is Avogadro’s Number number of moles = number of particles/N A n = N/N A and number of moles = mass (in gram)/mass per mole (g/mol) l Mass of 1 mol of a substance in grams = molecular mass in u è e.g., 1 mol of N 2 has mass of 2x14=28 grams è m particle = mass per mole/N è conversion factor: 1u = x kg

Physics 101: Lecture 29, Pg 7 Concept Question Which contains the most molecules ? 1. 1 mol of water (H 2 O) 2. 1 mol of oxygen gas (O 2 ) 3. Same H2OH2O O2O2 correct

Physics 101: Lecture 29, Pg 8 Concept Question Which contains the most atoms ? 1. A mol of water (H 2 O) 2. A mol of oxygen gas (O 2 ) 3. Same H 2 O (3 atoms) O 2 (2 atoms) correct

Physics 101: Lecture 29, Pg 9 Concept Question Which weighs the most ? 1. 1 mol of water (H 2 O) 2. 1 mol of oxygen gas (O 2 ) 3. Same H 2 O (M = ) O 2 (M = ) correct

Physics 101: Lecture 29, Pg 10 The Ideal Gas Law l Ideal gas: low density => the only interaction that occurs between gas particles (and surrounding walls) is elastic collision => An ideal gas is highly compressible. If V decreases P increases ! l 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 !

Physics 101: Lecture 29, Pg 11 The Ideal Gas Law l P V = N k B T è P = pressure in N/m 2 (or Pascals) è V = volume in m 3 è N = number of molecules è T = absolute temperature (K) è k B = Boltzmann’s constant »k B = 1.38 x J/K »note: pV has units of N m or J (energy!)

Physics 101: Lecture 29, Pg 12 The Ideal Gas Law l P V = N k B T k B is Boltzmann’s constant: k B = 1.38 x J/K l Alternate way to write this è N = number of moles (n) x N A molecules/mole è P V = N k B T »n N A k B T »n (N A k B )T »n R T l P V = n R T è R = ideal gas constant = N A k B = 8.31 J/(mol K)

Physics 101: Lecture 29, Pg 13 Kinetic Theory: The relationship between energy and temperature (for monatomic ideal gas) Per molecule

Physics 101: Lecture 29, Pg 14 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? correct If v doubles, v 2 quadruples Therefore, T quadruples