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Short Version : 17. Thermal Behavior of Matter

Short Version : 17. Thermal Behavior of Matter. 17.1. Gases. The Ideal Gas Law :. k = 1.38 10 23 J / K = Boltzmann’s constant N = number of molecules. N A = 6.022 10 23 = Avaogadro’s number = number of atoms in 12 g of 12 C. n = number of moles (mol).

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Short Version : 17. Thermal Behavior of Matter

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  1. Short Version : 17. Thermal Behavior of Matter

  2. 17.1. Gases The Ideal Gas Law: k = 1.381023 J / K = Boltzmann’s constant N = number of molecules NA = 6.0221023 = Avaogadro’s number = number of atoms in 12 g of 12C. n = number of moles (mol) A piston-cylinder system. = 8.314 J / K mol = Universal gas constant All gases become ideal if sufficiently dilute.

  3. Example 17.1. STP What volume is occupied by 1.00 mol of an ideal gas at standard temperature & pressure (STP), where T = 0C, & p = 101.3 kPa = 1 atm? ( last figure subject to round-off error )

  4. Kinetic Theory of the Ideal Gas • Kinetic theory ( Newtonian mechanics ): • Gas consists of identical “point” molecules of mass m. • No interaction between molecules, except when they collide. • Random motion. • Collisions with wall are elastic.

  5. in Molecule i collides with right-hand wall (RHW). Momentum transfer to wall is No intermolecular collision  Next collision with RHW occurs at Average force of i on RHW: out Random motion   Ideal gas law is recovered if T~ K

  6. Example 17.2. Air Molecule Find K of a molecule in air at room temperature ( 20C = 293K), & determine the speed of a N2 molecule with this energy. Thermal speed:

  7. Distribution of Molecular Speeds Maxwell-Boltzmann Distribution: (elastic collisions between free particles) 80 K • High-E tail extends rapidly with T • chemical reaction easier at high T • cooling of liquid • ( by escape of high-E molecules) 300K vth vth

  8. Real Gases • Important corrections to the ideal gas model: • finite size of molecules  available V reduced. • Attractive interaction between molecules (van der Waals forces)  reduced P.  minimum volume van der Waals equation

  9. 17.2. Phase Changes Phase changes take place at fixed T = TCuntil whole system is in the new phase. ( breaking / building bonds raises U but keeps K unchanged ) Heat of transformation L = energy per unit mass needed to change phase. Lf= Heat of fusion ( solid  liquid ) Lv= Heat of vaporization ( liquid  gas ) Ls= Heat of sublimation ( solid  gas )

  10. Water: • Same E to melt 1 g ice • or heat water by 80 C

  11. Conceptual Example 17.1. Water Phases You put a block of ice initially at －20C in a pan on a hot stove with a constant power output, and heat it until it has melted, boiled, and evaporated. Make a sketch of temperature versus time for this experiment. steam warming boiling water warming melting ice warming T vs t for a block of ice, initially at －20 C, that is supplied with constant power under atmospheric P.

  12. Example 17.4. Enough Ice? When 200 g of ice at 10 C are added to 1.0 kg of water at 15 C, is there enough ice to cool the water to 0 C? If so, how much ice is left in the mixture? Heat released to bring water down to 0 C Heat required to bring ice up to 0 C Heat required to bring ice up to 0 C  more than enough ice Ice needed:  ice left =

  13. Phase Diagrams AB: low P, s  g Sublimation: solid  gas e.g., dry ice ( s-CO2 ) PC Solid Melting C.P. CD: medium P, s  l  g liquid 壓力 C.P. : Critical point Supercritical fluid : l-g indistinguishable Boiling Gas Sublimation GH: medium T, l  g T.P. TC EF: high P, s  l / f Phase diagram: P vs T Triple point: s-l-g coexist = 273.16K, 0.6 kPa for H2O Caution: Phase transition doesn’t occur instantaneously

  14. 17.3. Thermal Expansion Coefficient of volume expansion : Prob. 69 Coefficient of linear expansion : Prob. 72

  15. Example 17.5. Spilled Gasoline A steel gas can holds 20 L at 10C. It’s filled to the brim at 10C. If the temperature is now increased to 25C, by how much does the can’s volume increase? How much gas spills out? Table 17.2:   Spilled gas:

  16. Thermal Expansion of Water At 1C Reason: Ice crystal is open  ice  water  ice floats max water occurs at 4C > 0 < 0 At fixed T Tm , ice melts if P. Application: skating.

  17. Application: Aquatic Life & Lake Turnover Anomalous behavior of ice-water makes aquatic life in freezing weather possible. If deep enough, bottom water stays at 4C even when surface is iced over. In a lake where bottom water stays at 4C year round, surface & bottom water can mix (turnover) only in spring time when both are at 4 C.

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