Lect02 - William Thomson (1824 1907) a.k.a. Lord Kelvin q...

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Physics 213: Lecture 2, Pg 1 William Thomson (1824 – 1907) William Thomson (1824 – 1907) a.k.a. “Lord Kelvin” a.k.a. “Lord Kelvin” First wrote down Second Law of Thermodynamics (1852) Became Professor at University of Glasgow at age 22! (not age 1.1 x 10 21 )
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Physics 213: Lecture 2, Pg 2 Ideal Gases: Energy, Work and Heat Ideal Gases: Energy, Work and Heat Thermal reservoir Physics 213 … Lecture 2 Physics 213 … Lecture 2 http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm increasing T Volume Pressure Equipartition First Law of Thermodynamics - internal energy - work and heat References for Lecture 3 and 4: Elements Ch 3,4A-C and 5 Topics
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Physics 213: Lecture 2, Pg 3 Equipartition and Absolute Temperature One of the principal aims of this course is to gain a generally applicable definition of absolute temperature from statistical mechanics (counting) . For now: absolute temperature T is proportional to the average translational kinetic energy of a particle in a gas: <KE trans > = constant x T In fact*, the same constant is involved in the rotational and vibrational energies of a particle. In this classical model, each independent quadratic term in the energy of a particle in the gas (e.g., ½ mv x 2 , ½ κ u x 2 , ½ Ιϖ 1 2 ) is found to have the average energy: < energy > mode = ½ kT Equipartition Theorem* . * We will show later WHY and WHEN this theorem applies with k = Boltzmann constant = 1.38 x 10 -23 J/K Constant independent of m!
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Physics 213: Lecture 2, Pg 4 Classical Classical Equipartition of Energy --- examples Equipartition of Energy --- examples Vibrations in solids kinetic + potential energy -- in 3 dimensions < ½ κ u x 2 > + < ½ mv x 2 > + < ½ κ u y 2 > + < ½ mv y 2 > + < ½ κ u z 2 > + < ½ mv z 2 > = 3 kT = average thermal energy per atom If there are N atoms in the solid, the total thermal energy is 3NkT. Diatomic molecules translational + rotational kinetic energy < ½ mv x 2 > + < ½ mv y 2 > + < ½ mv z 2 > + < ½ I ϖ 1 2 > + < ½ I 2 2 > = 5( ½ kT) free point particles translational kinetic energy (x, y, z components) < ½ mv x 2 > + < ½ mv y 2 > + < ½ mv z 2 > = 3( ½ kT) v mass on a spring kinetic + potential energy < ½ κ u x 2 > + < ½ mv x 2 > = kT Average energy is independent of mass! (At normal temperatures, vibrational modes are not active for common molecules. We will see why later.) u x Equilibrium position (½ kT per quadratic degree of freedom)
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Physics 213: Lecture 2, Pg 5 Bowling Ball Puzzle Bowling Ball Puzzle Why does the Bowling ball slow down? Explain in terms of the Equipartition Theorem. (Hint: Treat the mass as one big particle.)
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Physics 213: Lecture 2, Pg 6 Bowling Ball Puzzle: Bowling Ball Puzzle: Why does the Bowling ball slow down? Explain in terms of the Equipartition Theorem. (Hint: Treat the mass as one big particle.) What’s the average speed of the bowling ball after it comes into equilibrium with the room? Assume that M =
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This note was uploaded on 12/11/2011 for the course PHYS 213 taught by Professor Kuwait during the Spring '09 term at University of Illinois at Urbana–Champaign.

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Lect02 - William Thomson (1824 1907) a.k.a. Lord Kelvin q...

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