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Gas Behavior

Gas Behavior. formulas from models. § 18.3–18.4. Ideal Gas Model. molecules: non-interacting point masses collide elastically with surfaces. Temperature T is related to kinetic energy K K tr = 1/2 kT per mode of motion k = 1.3806505  10 –23 J/K (Boltzmann constant). 3 kT / m.

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Gas Behavior

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  1. Gas Behavior formulas from models § 18.3–18.4

  2. Ideal Gas Model • molecules: non-interacting point masses • collide elastically with surfaces • Temperature T is related to kinetic energy K • Ktr = 1/2 kT per mode of motion • k = 1.3806505  10–23 J/K (Boltzmann constant)

  3. 3kT/m = 3RT/M v = RMS Speed 1/2 mv2 = 3/2 kT v2 = 3kT/m M = molar mass

  4. Ly Lz Lx Ideal Gas EOS • What is the pressure?

  5. Ideal Gas Model • shows expansion with increasing T at constant p • shows p increase with increasing T at constant V • shows p = 0 at T = 0 K

  6. Ideal Gas Model Does not address interaction behavior • condensation • mean-free path • sound transmission • slow diffusion

  7. nRT p = – an2 V– nb V2 van der Waals EOS • Molecules have volume • Molecules attract (dimerize)

  8. Heat Capacity • Energy to raise the temperature of a sample of gas

  9. Constant-Volume Heating Heat capacity of an ideal gas dU = dK + pdV Ktr = 3/2 NkT dKtr = 3/2 NkdT dV= 0 Cv = dU/dT = 3/2 Nk = 3/2 nR

  10. Constant-Volume Heating Heat capacity of a diatomic gas dU = dK + pdV Ktr = 3/2 NkT; Krot = 2/2 NkT dKt = 5/2 NkdT dV= 0 Cv = dU/dT = 5/2 Nk =5/2 nR

  11. Heat Capacities of Solids Law of Dulong and Petit Six modes of motion Kvib in x, y, z directions Uel in x, y, z directions U = 6N(1/2 kT) = 3NkT dU = 3NkdT dV  0 Cv = dU/dT = 3 Nk =3 nR

  12. Phases of Matter Behavior and diagrams § 18.6

  13. Variables and Diagrams • State Variables: p, V, n, T • Hard to visualize in 2-D • Useful plots: p-V, p-T

  14. p-V plots Ideal gas Real Substance Source: Y&F, Figure 18.6 Source: Y&F, Figure 18.7

  15. p-T plot Gas Source: Y&F, Figure 17.5b

  16. p-T plot Phase Diagram Source: Y&F, Figure 18.24

  17. p-V-T Surface Ideal Gas Source: Y&F, Figure 18.27

  18. p-V-T Surface Real Substance Source: Y&F, Figure 18.26

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