Temperature Thermal Expansion Ideal Gas Law Kinetic Theory Heat Heat Transfer Phase Changes Specific Heat Calorimetry

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2 Temperature Thermal Expansion Ideal Gas Law Kinetic Theory Heat Heat Transfer Phase Changes Specific Heat Calorimetry

3 Zeroeth Law Two systems individually in thermal equilibrium with a third system (such as a thermometer) are in thermal equilibrium with each other. That is, there is no flow of heat within a system in thermal equilibrium

4 1st Law of Thermo The change of internal energy of a system due to a temperature or phase change is given by (next chapter): Temperature Change: Q = mcδt Phase Change: Q = ml Q is positive when the system GAINS heat and negative when it LOSES heat.

5 2nd Law of Thermo Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction. Heat flows from hot to cold. Alternative: Irreversible processes must have an increase in Entropy; Reversible processes have no change in Entropy. Entropy is a measure of disorder in a system

6 3rd Law of Thermo It is not possible to lower the temperature of any system to absolute zero.

7 Absolute Zero In a constant volume thermometer, readings are virtually independent of the gas used If the lines for various gases are extended, the pressure is always zero when the temperature is o C This temperature is called absolute zero

8 Absolute Temperature Scale Absolute zero is used as the basis of the absolute temperature scale The size of the degree on the absolute scale is the same as the size of the degree on the Celsius scale To convert: T C = T

9 Absolute Temperature Scale, K The absolute temperature scale is based on two fixed points Adopted by in 1954 by the International Committee on Weights and Measures One point is absolute zero The other point is the triple point of water This is the combination of temperature and pressure where ice, water, and steam can all coexist

10 Phase Change: Triple Point A temperature and pressure at which all three phases exist in equilibrium. Lines of equilibrium Freezing-Melting Evaporation -Condensation Sublimation

11 Temperature is measured by a thermometer. Kelvin is the Absolute Scale. o 9 o T( F) = T( C) o 5 o T( C) = T( F) 32 9 o T( K) = T( C)

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14 What is "room temperature" (68 degrees F) in Celsius and Kelvin? o 5 o T( C) = T( F) 32 9 = o o T( K) = T( C) = K o = 20 C Do book quiz 2!

15 30 is HOT. 20 is NICE. 10 is CHILLY. Zero is ICE!

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17 Thermal Expansion: Linear Δ L = αl ΔT Coefficients determined experimentally! 0

18 Thermal Expansion: Volume Δ V = βv ΔT β ~ 3α 0

19 Thermal Expansion: Linear

20 Thermal Expansion: Linear The coefficient of linear expansion of steel is 12 x 10-6 / C. A railroad track is made of individual rails of steel 1.0 km in length. By what length would these rails change between a cold day when the temperature is -10 C and a hot day at 30 C? Δ L= αl ΔT 6 o 3 o o Δ L= (12 x10 / C)(10 m)(30 C ( 10 C)) 0 Δ L =.48m

21 Thermal Expansion: Linear Δ L= αl ΔT What change in temperature is needed to fill the gap, 1.3 x 10-3 m? 0 α brass = 19x10 C α = 23x10 C AL Δ +Δ = 3 Lbrass LAl 1.3x10 m 3 1.3x10 m o Δ T = = C α L + α L brass brass Al Al

22 Thermal Expansion When the temperature of a metal ring increases, does the hole become larger? Smaller? Or stay same?

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24 Circle Expansion The coefficient of linear expansion of aluminum is 23 x 10-6 /C. A circular hole in an aluminum plate is cm in diameter at 0 C. What is the diameter of the hole if the temperature of the plate is raised to 100 C? Δ L= αl ΔT = 0 6 o (23x10 / C)(2.725 cm)100 C o = 6.3x10 3 cm d = 2.731cm

25 Fluids: Liquids & Gases Fluids are substances that are free to flow. Atoms and molecules are free to move. They take the shape of their containers. Cannot withstand or exert shearing forces. Liquids: Incompressible (density constant) Gases: Compressible (density depends on pressure) Parameters to describe Fluids: Density: ρ = mass/volume Pressure: P = Force/Area [P] = N/m 2 = 1 Pascal (Pa)

26 Liquid Units There are 1000 liters in 1 cubic meter! 1 liter = 10-3 m 3 = 10 3 cm 3 1 liter of water has a mass of 1 kg and a weight of 9.8N. 1kg 1000kg ρ = = H2 0 liter m 3

27 Density ρ = Density of C: ρ water = 1g/cm 3 = 1000 kg/m 3 = 1kg/liter Density of 0 C: m V ρ Air = 1.29x10-3 g/cm 3 = 1.29 kg/m 3 Density depends on temperature! Most substances EXPAND upon heating. How does that change their densities? ρ = m V m = ρv REDUCES DENSITY!

28 Water: The Exception C: ρ water =1000 kg/m 3 0 C: ρ ice = 917 kg/m 3 Note: The graph is for ice water only. Ice is not on the graph!

29 Thermal Expansion: Water Water Expands when it cools below 4 C! Thus, the solid state is less dense than the liquid state:

30 Thermometer, Liquid in Glass A common type of thermometer is a liquid-in-glass The material in the capillary tube expands as it is heated The liquid is usually mercury or alcohol

31 Pressure in a fluid is due to the weight P = Force Area of a fluid. P mg ( ρv ) g = = A A ( ρ Ah) g = A = ρgh Pressure depends on Depth!

32 Pressure Acts ONLY Perpendicularly to the Surface Pressure depends on depth.

33 Pressure IN a Fluid Is due to the weight of the fluid above you Depends on Depth and Density Only Does NOT depend on how much water is present Acts perpendicular to surfaces (no shearing) Pressure s add At a particular depth, pressure is exerted equally in ALL directions including sideways (empirical fact)

34 The Atmosphere At sea level, the atmosphere has a density of about 1.29 kg/m 3. The average density up to 120 km is about 8.59 x10-2 kg/m 3.

35 The Atmosphere A square meter extending up through the atmosphere has a mass of about 10,000 kg and a weight of about 100,000 N. 1 N/m 2 is a Pascal. 5 1 = = 14.7 atm x Pa psi

36 Measuring Pressure 5 1atm = 1.013x10 Pa Why is the pressure at X equal to atmospheric pressure? P = ρgh Because if it didn t, the mercury would be pushed out of the dish! P = ρ mercury gh h h = ρ P mercury g 2 101,300 N / m = 13,600 kg / m x9.8 m / s 3 2 ρ mercury = 13.6ρ water ρ = 1000 kg / m water 3 h = 760mm

37 Measuring Pressure Can a barometer be made with Water instead of Mercury? P h = = ρ water P ρ water gh g h = 2 101,300 N / m 1000 kg / m x9.8 m / s 3 2 ρ mercury = 13.6ρ water ρ = 1000 kg / m water 3 h = 10.3m (Notice: 10.3m is just 13.6 x 760mm!)

38 Barometers Measuring Air Pressure Fluid in the tube adjusts until the weight of the fluid column balances the atmospheric force exerted on the reservoir. 10.3m Not to Scale!!! Mercury Barometer Water Barometer 5 1atm = 1.013x10 Pa = 760mm

39 Absolute vs. Gauge Pressure Absolute Pressure: P = P + ρ gh 0 Guage Pressure: P0 = ρgh Guage pressure is what you measure in your tires Absoulte pressure is the pressure at B and is what is used in PV = nrt

40 Why does the water stop when the top is closed? Pressure is greater in the fluid at the spout due to weight of water so water flows. Hand covers top and water keeps flowing until the pressure is reduced to 1 atm by increasing volume of air above the fluid just like with a closed barometer!

41 The absolute Pressure P of an ideal gas is directly proportional to the absolute (Kelvin) temperature T and the number of moles n of the gas and inversely proportional to the volume V of the gas: P V = nrt n = # moles R = 8.31 J/(mol-K) Universal Gas Constant

42 P V = nrt n = # moles R = 8.31 J/(mol-K) Universal Gas Constant Note: PV is units of Energy!

43 Atomic Units The Basics Atomic Number: # protons Atomic Mass: # atomic mass units (u) Atomic Mass Unit: 1/12 mass of C-12 atom amu = u = 1.66 x kg Atomic Mass of C = u (1% is C-13) Mass of 1 C = (12.011u) (1.66 x kg/u)

44 Moles and Avogadro s Number N A = x mol -1 Mole (mol) = # atoms or molecules (particles) as are in 12 grams of Carbon-12: 1 mole = x particles Avogadro s Number: the number of particles in one mole: N A = x mol -1 # moles n contained in a sample of N particles: n = N/ N A # particles in a sample is: N = n N A

45 More on Moles The mass / mol for any substance has the same numerical value as its atomic mass: mass/mol C-12 = 12 g / mol mass/mol Li = g / mol n = mass / (mass/mole) = mass / atomic mass n = mass / atomic mass

46 Q: How many moles are in 1 kg of Sodium? mass/mole = atomic mass Na: g / mol n = mass / (mass/mole) = 1000 g / ( g/mol) = 43.5 moles Q: How many atoms in 1 kg of Sodium? # particles in a sample is: N = n N A N = (43.5mol) x mol -1 = 2.62 x atoms

47 P V = nrt n = # moles R = 8.31 J/(mol-K) Universal Gas Constant PV = Nkt N= # particles k =1.38 x J/K Boltzmann s Constant Note: PV is units of Energy!

48 The only interaction between particles are elastic collisions (no sticky - no loss of KE) This requires LOW DENSITY Excellent Approximation for O, N, Ar, room temperature and pressures State is described by the Ideal Gas Law Non Ideal are Van der Waals gases

49 Ideal Gas Problem An ideal gas with a fixed number of molecules is maintained at a constant pressure. At 30.0 C, the volume of the gas is 1.50 m 3. What is the volume of the gas when the temperature is increased to 75.0 C? PV = nrt 1 1 PV = nrt 2 2 V = = V T 1 1 T 2 2 V T = V T = 348K 1.5m 1.72m 303K = 3 3

50 Hot Question Suppose you apply a flame to 1 liter of water for a certain time and its temperature rises by 10 degrees C. If you apply the same flame for the same time to 2 liters of water, by how much will its temperature rise? a) 1 degree b) 5 degrees c) 10 degrees d) zero degrees