1. L39-s1,8 Physics 114 – Lecture 39 §13.6 The Gas Laws and Absolute Temperature Boyle’s Law: (~1650) − For a sample of gas, for which T = const, V 1/P or PV = const Effect of Temperature? Charles’ Law: (~1780) – For a sample of gas, for which P = constant, V T, if we redefine the origin of T → T(K) = T( 0 C) + 273.15 – absolute or Kelvin scale

2. L39-s2,8 Physics 114 – Lecture 39 Gay-Lussac’s Law: (~1820) − For a sample of gas, for which V = const, P T, where T is in kelvins (K) Study Example 13.9 §13.7 The Ideal Gas Law PV T Amount of gas? Expt.: if P and T are const, V m PV mT Constant? → PV = α RT, where α depends on m It turns out that α is conveniently expressed in moles

3. L39-s3,8 Physics 114 – Lecture 39 E.g., the number of moles in 96.0 g of O 2 for which the molecular mass is 2 X 16.0 = 32.0 The Ideal Gas Law then becomes, PV = nRTwhere R = 8.314 J/(mol. K) where R is the universal gas const and is the same for all gases

4. L39-s4,8 Physics 114 – Lecture 39 Reminder: P is the absolute pressure and T, the temperature, is measured in kelvins Of course real gases, as opposed to ideal gases, follow this law only when they are neither at very high pressures nor near their liquefaction point §13.8 Problem Solving with the Ideal Gas Law Study Problems 13.10, 13.11, 13.12 and 13.13

5. L39-s5,8 Physics 114 – Lecture 39 §13.9 Ideal Gas Law in Terms of Molecules: Avogadro’s Number Avogadro’s Hypothesis: Equal volumes of gas at the same temperature and pressure contain equal numbers of molecules This is consistent with R being the same for all gases Thus: PV = nRT states that, if P, V and T are the same for samples of two different gases, then n must be the same for these gases since R has the same value for all gases and the number of molecules in 1 mole is the same for all gases

6. L39-s6,8 Physics 114 – Lecture 39 The number of molecules in one mole of any pure substance is given by Avogadro’s number, N A The accepted value is: N A = 6.02 X 10 23 molecules/mole We have PV = nRT = which may be written, PV = N k T where and where k is known as the Boltzmann constant

7. L39-s7,8 Physics 114 – Lecture 39 §13.10 Kinetic Theory and the Molecular Interpretation of Temperature Assumptions: 1.Large number of mols each of of mass, m, moving randomly 2.Mols on average far apart wrt their diameter – force between mols = 0, unless they are colliding 3.Mols interact only when they collide and follow laws of classical mechanics 4.Collisions with the container walls are elastic and of short duration, compared with time between collisions

8. L39-s8,8 Physics 114 – Lecture 39 Consider one molecule colliding with the wall Δp 1 = -mv 1x – (mv 1x ) = -2 mv 1x for mol Δt = 2l/v 1x F 1 = Δp 1 /Δt = -2mv 1x / (2l/v 1x ) = -mv 1x 2 /l For N molecules, total force on wall F = (m/l) (v 1x 2 + v 2x 2 + v 3x 2 + … + v Nx 2 ) Since v 1x 2 + v 2x 2 + v 3x 2 + … + v Nx 2 = N (v x 2 ) ave F = (m/l) N (v x 2 ) ave With (v x 2 ) ave = v 2 ave /3 → P = F/A = ⅓ Nm v 2 ave /(Al) With V = Al → PV = ⅓ Nm v 2 ave = ⅔ N(½ mv 2 ave ) = ⅔ N KE ave Comparing with PV = NkT → KE ave = ½ mv 2 ave = ( 3 / 2 ) kT Thus T is a measure of KE ave of the molecules in the sample vxvx -v x x l