University College - Chemistry Chem 112A Lecture Notes - Lecture 20: Boltzmann Equation, Boltzmann Constant, Thermodynamics
13 Dec 2016
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Remember: for phase changes there is constant temperature. For the above example, s = kb * ln(2v/v) = kbln2. 6. (cid:2868)(cid:2870) (cid:2869)(cid:2868)(cid:3118)(cid:3119)=(cid:883). (cid:885)8 (cid:883)(cid:882) (cid:2870)(cid:2871)j/k: (cid:1845)=(cid:3003)ln(cid:4666) (cid:4667, where kb is the boltzmann constant, (cid:3003)= = 8. (cid:2871)(cid:2869)(cid:2872, where is the number of microstates, we know that (cid:2870)=(cid:884) (cid:2869, s = s2 s1 = (cid:3003)ln(cid:4666) (cid:2870)(cid:4667) (cid:3003)ln(cid:4666) (cid:2869)(cid:4667, s = (cid:3003)ln (cid:4666) (cid:3118) (cid:3117)(cid:4667) (cid:3118) (cid:3117) is the ratio of microstates for the end/beginning of the expansion: for two gas atoms, (cid:3118) (cid:3117) = 22 (the bottom two is because we doubled the volume, the top. S = (cid:3003)ln (cid:4666)(cid:884)(cid:2870)(cid:4667: for one mole of atoms, s = (cid:3003)ln(cid:4666)(cid:884)(cid:4667)=(cid:3002)(cid:3003)ln (cid:4666)(cid:884)(cid:4667) S = (cid:1844)ln(cid:4666)(cid:884)(cid:4667: really, (cid:2779)(cid:2778)=(cid:2188)=(cid:2870)=(cid:884, so for one gas atom: s = (cid:3003)ln (cid:4666)v(cid:3118)v(cid:3117)(cid:4667, for one mole of atoms: s = (cid:1844)ln (cid:4666)v(cid:3118)v(cid:3117)(cid:4667, for n moles of atoms: s = (cid:4666)(cid:2779)(cid:2778)(cid:4667, =(cid:1844)(cid:1846)(cid:4672)v(cid:3118)v(cid:3117)(cid:4673) = s, therefore s = (cid:2199)(cid:2200)(cid:2187)
