Archimedes Principle

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1 Archimedes Principle applies in air the more air an object displaces, the greater the buoyant force on it if an object displaces its weight, it hovers at a constant altitude if an object displaces less air, it descends

2 Archimedes Principle CHECK YOUR NEIGHBOR As you sit in class, is there a buoyant force acting on you? A. no, as evidenced by an absence of lift B. yes, due to displacement of air

3 Archimedes Prinicple CHECK YOUR ANSWER As you sit in class, is there a buoyant force acting on you? A. no, as evidenced by an absence of lift B. yes, due to displacement of air Explanation: There is a buoyant force on you due to air displacement, but much less than your weight.

4 Buoyancy in Gas Gas-filled balloon will continue to rise until the weight of displaced air equals the total weight of the balloon the buoyant force on the balloon equals its weight (which says the same thing)

5 Floating Object A floating object displaces a volume of water equal to its own WEIGHT. Archimedes Principle: BF = W fluid

6 Submerged Object A submerged object displaces a volume of fluid equal to its own volume.

7 Question A piece of iron placed on a block of wood makes it float lower in the water. If the iron were instead suspended beneath the wood, would it float as low, lower or higher?

8 Question A piece of iron placed on a block of wood makes it float lower in the water. If the iron were instead suspended beneath the wood, would it float as low, lower or higher? Answer Higher. When the iron is on top, its whole weight pushes the wood into the water. But when the iron is submerged, buoyancy on it reduces its effective weight and less of the block is pulled beneath the water line.

9 Continuity of Fluid Flow If the area decreases, the speed increases. v 1 v 2 v < v 1 2

10 Bernoulli s Principle Where the speed of a fluid increases, internal pressure in the fluid decreases.

11 Bernoulli s Principle: LIFT

12 Bernoulli s Principle

13 Bernoulli s Ball Why does this happen?

14 Floating Volume A floating object displaces a weight of fluid equal to its own weight.

$What fraction is submerged?$

15 Archimedes Principle Fraction of Object Floating V submerged V object = ρ ρ object fluid What is the density of the object? What fraction is submerged? ~1/3 Density is 1/3 that of water.

16 Question The glass is full to the brim with ice water and ice cubes. When the ice melts, will the water level decrease? Overflow? Remain the same? WHY?

17 Question Here is a glass of ice water with an ice cube floating in it. When the ice cube melts, will the water level rise, drop or remain the same? Assume constant temperature. BF Answer W Since the cube floats, the BF equals its weight. BF = W ice Weight of the water displaced equals the weight of the ice cube. m water g= m ice g Mass of the water displaced equals the mass of the ice cube. When the ice melts, it is water and since it has the same mass and density as the displaced water, it has the same volume, filling up the space where of the displaced water. The level remains unchanged.

18 HW Chapter 8: Exercises: 4, 6, 16, 24, 28, 34, 36 Problems: 3, 5, 6, 7

19 Temperature Temperature a number that corresponds to the warmth or coldness of an object measured by a thermometer is a per-particle property no upper limit definite limit on lower end

20 Temperature Scale Temperature Celsius scale named after Anders Celsius ( ) zero C for freezing point of water to 100 C for boiling point of water Fahrenheit scale named after G. D. Fahrenheit ( ) 32 F for freezing point of water to 212 F for boiling point of water Kelvin scale named after Lord Kelvin ( ) 0 K for freezing point of water to 373 K for boiling point of water zero at absolute zero, same size degrees as Celsius scale Kelvins, rather than degrees are used

21 Temperature Temperature is proportional to the average translational kinetic energy per particle in a substance. gas how fast the gas particles are bouncing to and fro liquid how fast particles slide and jiggle past one another solid how fast particles move as they vibrate and jiggle in place

22 Gas Particles are in constant RANDOM motion Particles have different speeds Pressure is given by the momentum transferred by particles colliding Average KE of each particle is ~ T

23 The Internal Energy of a system is a measure of the total Energy due to ALL random molecular motions: (Translations KE, Rotational KE, Vibrational KE) and internal POTENTIAL energies due to interactive forces (electromagnetic, strong, weak, gravitational) Mechanical Energy is due to the kinetic and potential energies of the system itself in an external reference frame. Temperature is a measure of the AVERAGE Translational KE ONLY! Heat is a flow of thermal energy from hotter to colder because of a difference in temperature. (think water fall!)

24 Temperature CHECK YOUR NEIGHBOR There is twice as much molecular kinetic energy in 2 liters of boiling water as in 1 liter of boiling water. Which will be the same for both? A. temperature B. thermal energy C. both A and B D. neither A nor B

25 Temperature CHECK YOUR ANSWER There is twice as much molecular kinetic energy in 2 liters of boiling water as in 1 liter of boiling water. Which will be the same for both? A. temperature B. thermal energy C. both A and B D. neither A nor B Explanation: Average kinetic energy of molecules is the same, which means temperature is the same for both.

26 Temperature CHECK YOUR NEIGHBOR To say that body A has a higher temperature than body B is to say that body A has more A. thermal energy. B. mass. C. kinetic energy per particle. D. potential energy.

27 Temperature CHECK YOUR ANSWER To say that body A has a higher temperature than body B is to say that body A has more A. thermal energy. B. mass. C. kinetic energy per particle. D. potential energy.

28 Heat Heat internal energy transferred from one thing to another due to a temperature difference internal energy in transit Flow of Internal Energy from a high-temperature substance to a low-temperature substance until thermal equilibrium is reached internal energy never flows unassisted from a lowtemperature to a high-temperature substance

29 Heat CHECK YOUR NEIGHBOR If a red hot thumbtack is immersed in warm water, the direction of heat flow will be from the A. warm water to the red hot thumbtack. B. red hot thumbtack to the warm water. C. no heat flow D. not enough information

30 Heat CHECK YOUR ANSWER If a red hot thumbtack is immersed in warm water, the direction of heat flow will be from the A. warm water to the red hot thumbtack. B. red hot thumbtack to the warm water. C. no heat flow D. not enough information

Quantity of Heat Energy ratings of foods and fuels are determined from energy released when they are burned. Unit of energy, the Calorie, is common for foods. 4.18 joules = 1 calorie 4.

31 Quantity of Heat Energy ratings of foods and fuels are determined from energy released when they are burned. Unit of energy, the Calorie, is common for foods joules = 1 calorie 4.18 joules of heat are required to change the temperature of 1 gram of water by 1 Celsius degree kilocalorie or 1000 calories called a Calorie heat needed to change the temperature of 1 kg of water by 1 C

32 Quantity of Heat CHECK YOUR NEIGHBOR The same quantity of heat is added to different amounts of water in two equal-size containers. The temperature of the smaller amount of water A. decreases more. B. increases more. C. does not change. D. not enough information

33 Quantity of Heat CHECK YOUR ANSWER The same quantity of heat is added to different amounts of water in two equal-size containers. The temperature of the smaller amount of water A. decreases more. B. increases more. C. does not change. D. not enough information

34 Quantity of Heat CHECK YOUR NEIGHBOR You heat a half-cup of tea and its temperature rises by 4 C. How much will the temperature rise if you add the same amount of heat to a full cup of tea? A. 0 C B. 2 C C. 4 C D. 8 C

35 Quantity of Heat CHECK YOUR ANSWER You heat a half-cup of tea and its temperature rises by 4 C. How much will the temperature rise if you add the same amount of heat to a full cup of tea? A. 0 C B. 2 C C. 4 C D. 8 C

36 Specific Heat: Thermal Inertia The Specific Heat of a substance is the amount of Energy it requires to raise the temperature of 1 gram, 1 degree Celsius. Q Q J = mcδt c = = 0 mδt kg C The higher the specific heat, the more energy it takes and the longer it takes to heat up and to cool off. The lower the specific heat, the less energy it takes and the quicker it takes to heat up and cool off. Substances with HIGH specific heat STORE heat energy and make good thermal moderators. (Ex: Water, Oceans)

37 Specific Heat c c c water glycerin iron J = 4186 kg Why does water have such a high specific heat? Heat goes into other modes of energy so that temperature changes slowly. 0 0 J = 2410 kg J = 452 kg C C 0 C

38 Specific Heat Capacity CHECK YOUR NEIGHBOR Which has the higher specific heat capacity, water or land? A. Water. B. Land. C. both of the above are the same D. neither of the above

39 Specific Heat Capacity CHECK YOUR ANSWER Which has the higher specific heat capacity, water or land? A. Water. B. Land. C. both of the above are the same D. neither of the above Explanation: A substance with small temperature changes for large heat changes has a high specific heat capacity. Water takes much longer to heat up in the sunshine than does land. This difference is a major influence on climate.

40 The Laws of Thermodynamics Thermodynamics movement of heat First law of thermodynamics states that the heat added to a system transforms to an equal amount of some other form of energy more specifically, heat added = increase internal energy + external work done by the system Energy can neither be created nor destroyed.

41 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

42 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.

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.

43 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

44 3rd Law of Thermo It is not possible to lower the temperature of any system to absolute zero.

45 Absolute Zero As temperature of a gas changes, volume of a gas changes. at zero degrees with pressure constant, volume changes by 1/273 for each degree Celsius Absolute Zero lowest limit of temperature molecules have lost all available kinetic energy

46 Thermal Expansion: Linear

47 Thermal Expansion Thermal expansion due to rise in temperature of a substance, molecules jiggle faster and move farther apart most substances expand when heated and contract when cooled railroad tracks laid on winter days expand and buckle in hot summer warming metal lids on glass jars under hot water loosens the lid by more expansion of the lid than the jar

Thermal Expansion Thermal expansion (continued) plays a role in construction and devices example: use of reinforcing steel with the same rate of

48 Thermal Expansion Thermal expansion (continued) plays a role in construction and devices example: use of reinforcing steel with the same rate of expansion as concrete expansion joints on bridges gaps on concrete roadways and sidewalks allow for concrete expansion in the summer and contraction in the winter

49 Thermal Expansion Thermal expansion (continued) different substances expand at different rates example: when the temperature of a bimetallic strip of brass and iron is increased, greater expansion occurs for the brass strip that bends to turn a pointer, to regulate a valve, or to close a switch Bimetallic strips are used in heaters, oven thermometers, refrigerators, and electric toasters.

50 Thermal Expansion CHECK YOUR NEIGHBOR When stringing telephone lines between poles in the summer, it is advisable to allow the lines to A. sag. B. be taut. C. be close to the ground. D. allow ample space for birds.

51 Thermal Expansion CHECK YOUR ANSWER When stringing telephone lines between poles in the summer, it is advisable to allow the lines to A. sag. B. be taut. C. be close to the ground. D. allow ample space for birds. Explanation: Telephone lines are longer in a warmer summer and shorter in a cold winter. Hence, they sag more on hot summer days than in winter. If the lines are not strung with enough sag in summer, they might contract too much and snap during the winter especially when carrying ice.

52 Thermal Expansion Δ L = αl ΔT 0 0 Δ V = βv ΔT Coefficients determined experimentally! Liquids expand more than solids! β ~ 3α

53 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

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

56 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

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

58 Thermal Expansion CHECK YOUR NEIGHBOR When a sample of 0 C water is heated, it first A. expands. B. contracts. C. remains unchanged. D. not enough information

59 Thermal Expansion CHECK YOUR ANSWER When a sample of 0 C water is heated, it first A. expands. B. contracts. C. remains unchanged. D. not enough information Explanation: Water continues to contract until it reaches a temperature of 4 C. With further increase in temperature beyond 4 C, water then expands.

60 Thermal Expansion CHECK YOUR NEIGHBOR When a sample of 4 C water is cooled, it A. expands. B. contracts. C. remains unchanged. D. not enough information

61 Thermal Expansion CHECK YOUR ANSWER When a sample of 4 C water is cooled, it A. expands. B. contracts. C. remains unchanged. D. not enough information Explanation: Parts of the water will crystallize and occupy more space.

Volume above and below How does the volume of the billions of hexagonal open spaces in the structures of ice crystals in a piece of ice compare to the portion of ice that floats above the water line?

62 Volume above and below How does the volume of the billions of hexagonal open spaces in the structures of ice crystals in a piece of ice compare to the portion of ice that floats above the water line? ρ water =1000 kg/m 3 ρ ice = 917 kg/m 3 Answer: The volume is the same! When the ice melts, the open spaces are filled in by the amount of ice that extends above the water level. This is also why the water level doesn t rise when ice melts.

Conceptual Physics Fundamentals

Conceptual Physics Fundamentals Chapter 8: TEMPERATURE, HEAT, AND THERMODYNAMICS This lecture will help you understand: Temperature Absolute Zero Internal Energy Heat Quantity of Heat The Laws of Thermodynamics