Lec37 - Welcome Back! Lecture 37 Monday 11/30/09 Chapter...

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Unformatted text preview: Welcome Back! Lecture 37 Monday 11/30/09 Chapter 18: Thermal Properties of Matter, cont’d. • Heat capacities -- Molar heat capacity at constant volume CV • Equipartition theorem -- Define the translational, rotational, and vibrational degrees of freedom f of a molecule -- The molar internal energy is equally partitioned between the degrees of freedom in units of RT/2: U = n f R T / 2, C V = f R / 2 Molar Specific Heats of Gases at Constant Volume CV At Room Temperature Monatomic Diatomic He Ar H2 N2 O2 CO2 SO2 CV (J/mol·K) 12.47 12.47 20.42 why? 20.76 21.10 28.46 31.39 Polyatomic Kinetic Theory: CV = 3R/2 = 12.47 J/mol·K Note: 5R/2 = 20.79 J/mol·K 7R/2 = 29.10 J/mol·K Question Solution How many rotational degrees of freedom does the water molecule have? 1. 1 2. 2 3. 3 4. 4 The rotational kinetic energy of a molecule is 1 1 1 2 2 K rot = I x x + I y y + I z z2 . 2 2 2 There are three independent terms in this expression for the energy, so there are 3 rotational degrees of freedom for the H 2O molecule. Molar Specific Heat of a H2 gas versus Temperature Figure 18.19: The effective number of degrees of freedom of a diatomic molecule increases with increasing temperature from 3 to 5 to 7, due to quantum mechanical effects. ...
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This note was uploaded on 10/21/2010 for the course PHYS 221 taught by Professor Herrera-siklody during the Fall '08 term at Iowa State.

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Lec37 - Welcome Back! Lecture 37 Monday 11/30/09 Chapter...

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