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

As you sit in class, is there a buoyant force acting on you?

A. no, as evidenced by an absence of liftB. yes, due to displacement of air

Archimedes’ PrincipleCHECK YOUR NEIGHBOR

As you sit in class, is there a buoyant force acting on you?

A. no, as evidenced by an absence of liftB. yes, due to displacement of air

Explanation:There is a buoyant force on you due to air displacement, but much less than your weight.

Archimedes’ PrinicpleCHECK YOUR ANSWER

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)

fluidBF W=

A floating object displaces a volume of water equal to its own WEIGHT.

Floating Object

Archimedes Principle:

Submerged ObjectA submerged object displaces a volume of fluid

equal to its own volume.

QuestionA 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?

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?

AnswerHigher. 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.

Continuity of Fluid Flow

1 2v v<

1v

2v

If the area decreases, the speed increases.

Bernoulli’s PrincipleWhere the speed of a fluid increases,

internal pressure in the fluid decreases.

Bernoulli’s Principle: LIFT

Bernoulli’s Principle

Bernoulli’s BallWhy does this happen?

Floating VolumeA floating object displaces a weight of fluid equal to its own weight.

Archimedes PrincipleFraction of Object Floating

submerged

object

VV

What is the density of the object?

object

fluid

ρρ

=

What fraction is submerged? ~1/3

Density is 1/3 that of water.

QuestionThe 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?

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.

Since the cube floats, the BF equals its weight. BF = WiceWeight of the water displaced equals the weight of the ice cube.

mwaterg = micegMass 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.

W

BF

Answer

HW Chapter 8: Exercises: 4, 6, 16, 24, 28, 34, 36

Problems: 3, 5, 6, 7

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

TemperatureTemperature Scale• Celsius scale named after Anders Celsius (1701

–1744)– zero °C for freezing point of water to 100°C for boiling

point of water

• Fahrenheit scale named after G. D. Fahrenheit(1686–1736)– 32°F for freezing point of water to 212°F for boiling point

of water

• Kelvin scale named after Lord Kelvin (1824–1907) 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

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

• 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

•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!)

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. temperatureB. thermal energyC. both A and BD. neither A nor B

TemperatureCHECK 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. temperatureB. thermal energyC. both A and BD. neither A nor B

Explanation:Average kinetic energy of molecules is the same, which means temperature is the same for both.

TemperatureCHECK 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.

TemperatureCHECK 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.

TemperatureCHECK YOUR ANSWER

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 low-

temperature to a high-temperature substance

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 flowD. not enough information

HeatCHECK 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 flowD. not enough information

HeatCHECK YOUR ANSWER

Quantity of HeatEnergy 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

• 4.18 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

The same quantity of heat is added to different amounts of waterin 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

Quantity of HeatCHECK YOUR NEIGHBOR

The same quantity of heat is added to different amounts of waterin 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

Quantity of HeatCHECK 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°CB. 2°CC. 4°CD. 8°C

Quantity of HeatCHECK 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°CB. 2°CC. 4°CD. 8°C

Quantity of HeatCHECK YOUR ANSWER

Specific Heat: Thermal InertiaThe Specific Heat of a substance is the amount of Energy it requires to raise the temperature of 1 gram, 1 degree Celsius.

Q mc T= Δ 0

Q Jcm T kg C

= =Δ ⋅

•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)

Specific Heat

Why does water have such a highspecific heat?

Heat goes into other modes of energy so that temperature changes slowly.

0

0

0

4186

2410

452

water

glycerin

iron

Jckg C

Jckg C

Jckg C

=⋅

=⋅

=⋅

Which has the higher specific heat capacity, water or land?

A. Water.B. Land.C. both of the above are the sameD. neither of the above

Specific Heat CapacityCHECK YOUR NEIGHBOR

Which has the higher specific heat capacity, water or land?

A. Water.B. Land.C. both of the above are the sameD. 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.

Specific Heat CapacityCHECK YOUR ANSWER

The Laws of Thermodynamics

Thermodynamics• movement of heatFirst 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.

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

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 = mcΔTPhase 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.

• 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

3rd Law of Thermo

It is not possible to lower the

temperature of any system to absolute

zero.

Absolute ZeroAs 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

Thermal Expansion: Linear

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 ExpansionThermal 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

Thermal ExpansionThermal expansion (continued)

• different substances expand at different ratesexample:

• 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 aswitch

Bimetallic strips are used in heaters, oven thermometers, refrigerators, and electric toasters.

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.

Thermal ExpansionCHECK 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.

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.

Thermal ExpansionCHECK YOUR ANSWER

Thermal Expansion

0L L TαΔ = Δ 0V V TβΔ = Δ•Coefficients determined experimentally!•Liquids expand more than solids!• β ~ 3α

Thermal Expansion: LinearThe 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?

6 3(12 10 / )(10 )(30 ( 10 ))L x C m C C−Δ = − −o o o

.48L mΔ =

0L L TαΔ = Δ

Thermal Expansion

When the temperature of a metal ring increases, does the hole become larger?

Smaller? Or stay same?

Circle ExpansionThe coefficient of linear expansion of aluminum is 23 x 10-6/C°. A circular hole in an aluminum plate is 2.725 cm in diameter at 0°C. What is the diameter of the hole if the temperature of the plate is raised to 100°C?

0L L TαΔ = Δ6(23 10 / )(2.725 )100x C cm C−= o o

2.731d cm=36.3 10x cm−=

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

When a sample of 0°C water is heated, it first

A. expands.B. contracts.C. remains unchanged.D. not enough information

Thermal ExpansionCHECK YOUR NEIGHBOR

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.

Thermal ExpansionCHECK YOUR ANSWER

When a sample of 4°C water is cooled, it

A. expands.B. contracts.C. remains unchanged.D. not enough information

Thermal ExpansionCHECK YOUR NEIGHBOR

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.

Thermal ExpansionCHECK YOUR ANSWER

Volume above and belowHow 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?

ρwater =1000 kg/m3

ρice = 917 kg/m3

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.