Consider the specific heat of copper, J/g C o. What this means is that it takes Joules of heat to raise 1 gram of copper 1 degree

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1 P eσat 4 Net radiation (s: surrounding T) P eσa( T 4 4 T net S )

2 c Q [ J /( kg K) J /( kg C )] m T Consider the speciic heat o copper, J/g C o. What this means is that it takes Joules o heat to raise 1 gram o copper 1 degree celcius. Thus, i we take 1 gram o copper at 25 o C and add Joule o heat to it, we will ind that the temperature o the copper will have risen to 26 0 C. We can then ask: How much heat wil it take to raise by 1 C 0 2g o copper?. Clearly the answer is J or each gram or 2x0.385 J J.

3 The Golden Gate Bridge in San Francisco is about 1350 meters long. (A) The seasonal temperature variation in San Francisco ranges rom about 0 C to 30 C. How much will the bridge expand between these two extremes? (B) What percent o the length o a subcompact automobile, 2.5 meters, does this gap represent? α steel 12 x 10-6 C -1 α asphalt x 10-5 /C L ( const.) T αl T 0 α : Coeicient o linear 5 1 L m 30K 2. 5m K 100%! -1 expansion [K ]

4 T Q ka t L k : thermal conductivity [ W mk ] or Power Q t T ka L

5 Phases and Phase Changes Phase a state o matter Properties describe matter. A block o wood, milk, and air all have properties. All the material on earth is in three states - solid, liquid, and gas. The "state" o the matter reers to the group o matter with the same properties. In other words, you group the objects together according to their properties. Nowadays we know two more states o matter (Bose-Einstein condensate and Plasma). 1. Bose-Einstein condensate 1924 predicted 1995 created Cornell and Wieman (Nobel Prize 2001) We all know that some things eel hot, and others cold, but is there more to temperature than that? When an object eels hot, the atoms inside it are moving ast in random directions, and when it eels cold, they are moving slowly. Our body interprets that random atomic motion into what we eel as hot and cold, and a thermometer interprets that atomic motion as a certain number o degrees or better Kelvin.

6 So when I'm heating something, I'm just making its atoms move aster? Exactly. I the object is a solid the atoms are vibrating back and orth, and i it is a gas like the air, the atoms are lying around much like little balls. What happens i you set the temperature o the atoms in the box as low as it can go? The atoms are stopped. So that is as cold as the atoms can be. We call that Absolute Zero and that is really cold. The coldest place in nature is the depths o outer space. There it is 3 degrees above Absolute Zero Why doesn't it get down all the way to Absolute Zero? A big step was when Cornell and Wieman cooled a small sample o atoms down to only a ew billionths (0.000,000,001) o a degree above Absolute Zero! That was what they needed to do to see Bose-Einstein condensation It is only at the special incredibly low temperatures needed or BEC that they lose their individual identities and coalesce into a single blob. Some people have called this a "super atom" or just that reason

7 2. Gas The volume o a quantity o gas is dependent on its temperature and the surrounding pressure. I aected by gravity, it will take the shape o its container, but much o it will also spread out into the surrounding area. A gas is matter that has no shape or size o its own. 3. Liquid A liquid has a size or volume. Volume means it takes up space. But a liquid doesn't have a deinite shape. It takes the shape o its container with the help o gravity Gas dierent than liquid? I you put a gas in a cylinder and apply pressure with a piston, such as you might do with a tire pump, the volume o the gas can change considerably. This is not the case with water or a solid. Their volumes may change only slightly with an increase o pressure. 4. Solid The solid state o matter is when the material has a deinite volume or size and distinct shape at a given temperature. A piece o iron at room temperature has a shape and size that does not change. Ice is another solid, but its temperature must be below 0 o C (32 o F).

8 5. Plasma The plasma state is not related to blood plasma, the most common usage o the word; rather, the term has been used in physics since the 1920s to represent an ionized gas. Lightning is commonly seen as a orm o plasma. When enough heat is applied, a gas may be ionized: an electron will gain enough energy to escape its atom. This atom is let one electron short and now has a net positive charge; now it is called an ion. In a suiciently heated gas, ionization happens many times, creating clouds o ree electrons and ions; however, not all the atoms are necessarily ionized, and some may remain completely intact with no net charge. This ionized gas mixture, consisting o ions, electrons, and neutral atoms, is called plasma. Although plasma includes electrons and ions and conducts electricity, it is macroscopically neutral: in measurable quantities, the number o electrons and ions are equal.

9 Ideal Gas (Basic properties) (We use the motion o microscopic gas particles to describe or explain the macroscopic quantities) Ideal gas means: no interaction between its molecules Equation o state or an ideal gas (State o a gas depends on P,T,N,V) P V N k T k: Boltzmann constant 1.38x10-23 J/K N: Number o molecules n N A N A : Advogados Number 6.022x10 23 molecules/mol One mole o a substance contains the same number o particles as there are atoms in 12 grams o 12 C. The number o atoms in 12 grams o 12 C is 23-1 Avogadro s number. N A mol

10 Experiments done on dilute gases (a gas where interactions between molecules can be ignored) show that: For constant pressure V T Charles Law For constant volume P T Gay-Lussac s Law For constant temperature P 1 V Boyle s Law For constant pressure and temperature V N Avogadro s Law

11 Charle s Law V/Tconstant Jacques Alexandre César Charles (November 12, 1746 April 7, 1823) was a French inventor, scientist, mathematician, and balloonist. Volume (ml) Temper Temper ature ature ( o C) (K) V / T (K) Graph lower pressure isobar Expansion o Hydrogen gas at constant pressure

12 A sample o gas at 101.3kPa had a volume o 1.2L at 100 o C. What would its volume be at 0 o C at the same pressure? V i 1.2L V? T i 100 o C K T 0 o C K 1.2/373 V / x 10-3 V /273 V 3.22 x 10-3 x L (880 ml) 0.88 dm 3

13 Robert Boyle (25 January December 1691) was a natural philosopher, chemist, physicist, inventor, and early gentleman scientist Compression o Hydrogen gas at 25 o C Pressure Volume P x V (mm Hg)* (ml) x 10 4 P 1 V isotherm x x x x x 10 PV const.

14 Joseph Louis Gay-Lussac (December 6, 1778 May 9, 1850) was a French chemist and physicist. P T P/Tconstant lower volume isochor pressure

15 Putting all o these statements together gives the ideal gas law (microscopic orm): PV NkT k J/K is Boltzmann s constant The ideal gas law can also be written as (macroscopic orm): PV nrt R N A k 8.31 J/K/mol is the universal gas constant and n is the number o moles. n: Number o moles

16 P NkT V

17 Example: What is the volume o 1 mol H 2 at S.T.P. Standard Temperature and Pressure, 0 o C (273K) and 101.3kPa (1 atm) V n R T / P 1 mol * 8.31 JK -1 mol -1 * 273 K / 101,300 Pa 22.4 dm liter What is the volume o 1mol O 2 at STP?

18 Example: A cylinder in a car engine takes V i m 3 o air into the chamber at 30 C and at atmospheric pressure. The piston then compresses the air to one-ninth o the original volume and to 20.0 times the original pressure. What is the new temperature o the air? Here, V V i /9, P 20.0P i, and T i 30 C 303 K. P V i i P V NkT i NkT The ideal gas law holds or each set o parameters (beore compression and ater compression).

19 Example continued: Take the ratio: i i i i T T NkT NkT PV P V The inal temperature is i T V P T The inal temperature is ( ) K K i i i i i i i V V P P T V P T The inal temperature is 673 K 400 C.

20 Kinetic Theorie Macroscopic quantities: T, P, V Microscopic quantities : Position and velocity (momentum) o molecules Each molecule has mass and behaves as a point particle Newton s Laws o motion are valid Collisions o molecules are elastic No interactions with other molecules We start with a simple model: Gas particles have random motions. Each time a particle collides with the walls o its container there is a orce exerted on the wall. The orce per unit area on the wall is equal to the pressure in the gas.

21 Ideal Gas Pressure, Temperature, and RMS Speed Consider the molecule o mass m moving inside a container o dimensions L L L as shown in the igure. We will ollow the motion o the molecule along the x-axis. The molecule bounces o the walls 2L with time interval t between collisions. vx 2 p mvx ( mv x x ) 2mvx mvx The ratio Fx. Here px is the momentum t t 2 L / v L transer to the wall. The orce exerted by one molecule F p exerted by all the molecules on the wall is given by ( ) ( vx 1 + vx vxn ) x ( 1 2 ) ( ) x p t Fx mvx 1 / L + mvx2 / L mvxn / L m p ( vx 1 + vx vxn ). L L L The root mean square (RMS) value or v is deined as vx v.... avg x + vx + + vxn N vx N avg x x. Thus the pressure

22 Nm ( 2 Thus the gas pressure p v ). 3 x L avg For each molecule the speed v vx + vy + vz. The average values o the squares or each v component are equal. Thus: vx. Thus p rms nmv 3V 2 rms. This equation tells us how the gas pressure depends on the speed 3Vp o the gas molecules. I we solve this equation or vrms we get vrms, nm v 3nRT 3RT. nm M v rms 3kT m

23 v rms PV T 3kT m NkT PV Nk

24 The distribution o speeds in a gas is given by the Maxwell- Boltzmann Distribution.

25 Escape speed v E 11.2 km/sec

26 Example (text problem 13.70): What are the rms speeds o helium atoms, and nitrogen, hydrogen, and oxygen molecules at 25 C? v rms 3kT m On the Kelvin scale T 25 C 298 K. Element Mass (kg) rms speed (m/s) He H N O

27 p nmv 3V 2 rms. 1 P N 3 therore m( v V P m( v 2 ) AV AV 1 N 3 V ~ K ( K : Kinetic Energy 2 ) 1 3 ) N 2K V AV 2 3 N K V AV p 2 3 K AV N V p N k T / V K T AV K AV 2 3 k 3 kt 2

28 Example (text problem 13.60): What is the temperature o an ideal gas whose molecules have an average translational kinetic energy o J? 3 K tr kt 2 2 Ktr T 3k 1550 K

29 Phase equilibrium and evaporation Vapor-Pressure- Curve

30 Phase diagrams Sublimation curve: rate at which solid sublimes to orm a gas rate at which gas deposites to orm a solid Vapor-Pressure-Curve: rate at which liquid boils to orm a gas rate at which gas condenses to orm a liquid Fusion Curve: rate at which solid melts to orm a liquid rate at which liquid reezes to orm a solid

31 Fusion curve or a typical substance Fusion curve or water

32 The critical point marks the end o the vapor pressure curve. A path around this point (i.e. the path does not cross the curve) does not result in a phase transition. Past the critical point it is not possible to distinguish between the liquid and gas phases. On a phase diagram, the triple point is the set o P and T where all three phases can coexist in equilibrium.

33 Sublimation is what happens to a comet as it approaches the sun. The term describes what happens when a rozen material changes to gaseous orm. ). The most common example o sublimation is that o dry ice, which is the common name o rozen CO 2. At room temperature the rozen gas would rather be a gas than rozen solid. When a comet approaches the sun, the comet comes to a region o space where it is warm enough that the rozen gases inside the nucleus would rather be gaseous than rozen solid, and that is when the tail and coma o the comet orm.

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35 Latent Heat The latent heat, L, is the heat that must be added to or removed rom one kilogram o a substance to convert it rom one phase in the other L latent heat o usion solid liquid L v latent heat o vaporization liquid gas Q ml [J/K] During a phase transormation (e.g. ice water) the temperature remains constant. Example: We heat an ice cube rom 253 K Speciic heat: Latent heat: Speciic heat: Q m c ice T (heat up ice to melting point) Q m L (Temperature is constant) Q m c water T (Ice is all melted. Now we heat up the water)

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37 Material Water Ammonia Copper Benzene Ethyl alcohol Gold Nitrogen Lead Oxygen Latent heat o usion, L (J/kg) 33.5 x x x x x x x x x 10 4 Latent heat o vaporization, L v (J/kg) 22.6 x x x x x x x x x 10 5

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39 Phase Changes and Energy Conservation System wants to get into thermal equilibrium. Heat lows rom hot to cold, but temperature o water cannot be below K!!!!!!!!! The system has to convert water into ice! Example:

40 Example I kj o heat are supplied to 500 g o water at 22 C, what is the inal temperature o the water? Q T mc T T i + Q mc mc ( T T ) i kj 22 C + 82 C ( 0.5 kg)( kj/kg C)

41 A kg aluminum teakettle contains 2.00 kg o water at 15.0 C. How much heat is required to raise the temperature o the water (and kettle) to 100 C? The heat needed to raise the temperature o the water to T is ( 2 kg )( kj/kg C )( 85 C ) 712 kj. Qw mw cw Tw The heat needed to raise the temperature o the aluminum to T is Q ( 0.4 kg)( kj/kg C)( 85 C) 30.6 kj. Al malcal TAl Then Q total Q w + Q Al 732 kj.

42 A 75 g cube o ice at C is placed in kg o water at 50.0 C in an insulating container so that no heat is lost to the environment. Will the ice melt completely? What will be the inal temperature o this system? The heat required to completely melt the ice is Q ice m ice c ice T ice + m L ice ( kg)( 2.1 kj/kg C)( 10 C) + ( kg)( kj/kg) 27 kj The heat required to cool the water to the reezing point is Q w m c T w w ( 0.5 kg)( kj/kg C)( 50 C) 105 kj w

43 Since Q ice < Q water the ice will completely melt. 0 Q + Q ice w 0 m c T + m ice ice 0 m ice c ice T + m 0 27 kj + m + T 32.4 C ice ice L L ( m ) ice w + m + c ice c w ( T T ) + m c ( T T ) ice,i ( m ) ice + m w c w T m w c w T i w T 105 kj w w w,i

44 Compute the heat o usion o a substance rom these data: kj will change kg o the solid at 21 C to liquid at 327 C, the melting point. The speciic heat o the solid is kj/kg K. Q mc T + ml Q mc T L 22.8 kj/kg m