17. Thermal Behavior of Matter

1. 17. Thermal Behavior of Matter Gases Phase Changes Thermal Expansion

2. What unusual property of water is evident in this photo? Ice is less dense than water.

3. 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.

4. 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 )

5. 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.

6. 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

7. 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:

8. 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

9. 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

10. 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 )

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

12. 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.

13. Making the Connection If you start with 0.95 kg of ice at －20C and supply heat at the rate of 1.6 kW, how much time will it take until you’re left with only water vapor? Heat needed to warm ice to 0 C : Heat needed to melt ice at 0 C : Heat needed to warm water to 100 C : Heat needed to vaporize water at 100 C : Time needed :

14. GOT IT? 17.2. You bring a pot of water to boil & then forget about it. 10 min later you come back & find it still boiling. Is its temperature (a) less, (b) greater than, or (c) equal to 100 C ?

15. Example 17.3. Meltdown! A nuclear power plant’s reactor vessel cracks, draining all cooling water. Although nuclear fission stops, radioactive decay continues to heat the reactor’s 2.5105 kg uranium core at the rate of 120 MW. Once the melting point is reached, how much energy will it take to melt the core? How long will the melting take? Table 17.1: for U Time to melt the core:

16. 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 =

17. 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

19. 17.3. Thermal Expansion Coefficient of volume expansion : Prob. 69 Coefficient of linear expansion : Prob. 72

21. GOT IT? 17.3. If a donut-shaped object is heated, will the hole get (a) larger, or (b) smaller ?

22. 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:

23. 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.

24. 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.