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thermal_7_02_23_2011

thermal_7_02_23_2011 - Specific Heat of Diatomic Gases and...

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Specific Heat of Diatomic Gases and Solids The Adiabatic Process Lecture 7
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Specific Heat for Solids and Diatomic Gasses In this lecture, you will learn what determines the specific heat of diatomic gasses and elemental solids. The physics behind an adiabatic gas process will also be analyzed.
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From last lecture, you learned how to evaluate the heat capacity for an ideal monatomic gas The internal energy of N atoms in an ideal monatomic gas is an intrinsic, distributed property of the system ( 29 2 1 1 ( ) 2 2 av av av KE K m v kT for one molecule = = = 3 For ideal gas E int KE = 3 (½ NkT) = 3 (½ nRT) What makes diatomic molecules different? dE int dT C V = 3/2 nR C P = C V + nR = 5/2 nR equipartition theorem of N atoms: monatomic gas
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Velocity v Mass m r Rotational motion - another way to distribute energy? ϖ (rad/s) For now, no linear translation KE = ½ mv 2 ϖ = 2 π f v = r ϖ KE = ½ mr 2 ϖ 2 = ½ I ϖ 2 Typical value: CO, I 1.45 x 10 -46 kg•m 2
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Linear Motion Rotational Motion Inertia Newton’s 2 nd Law m F = m a I τ = I α By way of review, . . . Displacement Velocity d = v o t+½ at 2 θ = ϖ o t + ½ α t 2 v = v o + at ϖ = ϖ o + α t Momentum Conservation of momentum Kinetic Energy p = mv If F=0, then p = constant ½ mv 2 L = I ϖ If τ =0, then L = constant ½ I ϖ 2
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For diatomic molecules, additional energy can be disbursed in rotational motion KE = ½mv x 2 + ½mv y 2 + ½mv z 2 + ½I x’ ϖ x’ 2 + ½I y’ ϖ y’ 2 E int = 5 (½ nRT) C v = 5/2 nR C P = 7/2 nR translation + rotation 5 degrees of freedom
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